## How to Write Hypothesis Test Conclusions (With Examples)

A   hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

• Whether we reject or fail to reject the null hypothesis.
• The significance level.
• A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level.   There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

## Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

• H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
• H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

## Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

• H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
• H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level.   There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

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## How to Write Hypothesis Test Conclusions (With Examples)

A   hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

• Whether we reject or fail to reject the null hypothesis.
• The significance level.
• A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level.   There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

## Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

• H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
• H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

## Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

• H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
• H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level.   There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

## 10 Examples of Using Probability in Real Life

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Statistics By Jim

Making statistics intuitive

## What is Hypothesis Testing?

Hypothesis testing in statistics uses sample data to infer the properties of a whole population . These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance can create in samples. These methods are also known as significance testing.

For example, researchers are testing a new medication to see if it lowers blood pressure. They compare a group taking the drug to a control group taking a placebo. If their hypothesis test results are statistically significant, the medication’s effect of lowering blood pressure likely exists in the broader population, not just the sample studied.

## Using Hypothesis Tests

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement the sample data best supports. These two statements are called the null hypothesis and the alternative hypothesis . The following are typical examples:

• Null Hypothesis : The effect does not exist in the population.
• Alternative Hypothesis : The effect does exist in the population.

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it. If you can reject the null, your data favor the alternative statement that an effect exists in the population.

Statistical significance in hypothesis testing indicates that an effect you see in sample data also likely exists in the population after accounting for random sampling error , variability, and sample size. Your results are statistically significant when the p-value is less than your significance level or, equivalently, when your confidence interval excludes the null hypothesis value.

Conversely, non-significant results indicate that despite an apparent sample effect, you can’t be sure it exists in the population. It could be chance variation in the sample and not a genuine effect.

## 5 Steps of Significance Testing

Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods:

• Formulate the Hypotheses : Write your research hypotheses as a null hypothesis (H 0 ) and an alternative hypothesis (H A ).
• Data Collection : Gather data specifically aimed at testing the hypothesis.
• Conduct A Test : Use a suitable statistical test to analyze your data.
• Make a Decision : Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
• Report the Results : Summarize and present the outcomes in your report’s results and discussion sections.

While the specifics of these steps can vary depending on the research context and the data type, the fundamental process of hypothesis testing remains consistent across different studies.

Let’s work through these steps in an example!

## Hypothesis Testing Example

Researchers want to determine if a new educational program improves student performance on standardized tests. They randomly assign 30 students to a control group , which follows the standard curriculum, and another 30 students to a treatment group, which participates in the new educational program. After a semester, they compare the test scores of both groups.

Download the CSV data file to perform the hypothesis testing yourself: Hypothesis_Testing .

The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter .

• Null Hypothesis (H 0 ) : The population means of the test scores for the two groups are equal (μ 1 = μ 2 ).
• Alternative Hypothesis (H A ) : The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2 ).

Choosing the correct hypothesis test depends on attributes such as data type and number of groups. Because they’re using continuous data and comparing two means, the researchers use a 2-sample t-test .

Here are the results.

The treatment group’s mean is 58.70, compared to the control group’s mean of 48.12. The mean difference is 10.67 points. Use the test’s p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.

Because the p-value (0.000) is less than the standard significance level of 0.05, the results are statistically significant, and we can reject the null hypothesis. The sample data provides sufficient evidence to conclude that the new program’s effect exists in the population.

## Limitations

Hypothesis testing improves your effectiveness in making data-driven decisions. However, it is not 100% accurate because random samples occasionally produce fluky results. Hypothesis tests have two types of errors, both relating to drawing incorrect conclusions.

• Type I error: The test rejects a true null hypothesis—a false positive.
• Type II error: The test fails to reject a false null hypothesis—a false negative.

Our exploration of hypothesis testing using a practical example of an educational program reveals its powerful ability to guide decisions based on statistical evidence. Whether you’re a student, researcher, or professional, understanding and applying these procedures can open new doors to discovering insights and making informed decisions. Let this tool empower your analytical endeavors as you navigate through the vast seas of data.

June 10, 2024 at 10:51 am

Thank you, Jim, for another helpful article; timely too since I have started reading your new book on hypothesis testing and, now that we are at the end of the school year, my district is asking me to perform a number of evaluations on instructional programs. This is where my question/concern comes in. You mention that hypothesis testing is all about testing samples. However, I use all the students in my district when I make these comparisons. Since I am using the entire “population” in my evaluations (I don’t select a sample of third grade students, for example, but I use all 700 third graders), am I somehow misusing the tests? Or can I rest assured that my district’s student population is only a sample of the universal population of students?

June 10, 2024 at 1:50 pm

I hope you are finding the book helpful!

Yes, the purpose of hypothesis testing is to infer the properties of a population while accounting for random sampling error.

In your case, it comes down to how you want to use the results. Who do you want the results to apply to?

If you’re summarizing the sample, looking for trends and patterns, or evaluating those students and don’t plan to apply those results to other students, you don’t need hypothesis testing because there is no sampling error. They are the population and you can just use descriptive statistics. In this case, you’d only need to focus on the practical significance of the effect sizes.

On the other hand, if you want to apply the results from this group to other students, you’ll need hypothesis testing. However, there is the complicating issue of what population your sample of students represent. I’m sure your district has its own unique characteristics, demographics, etc. Your district’s students probably don’t adequately represent a universal population. At the very least, you’d need to recognize any special attributes of your district and how they could bias the results when trying to apply them outside the district. Or they might apply to similar districts in your region.

However, I’d imagine your 3rd graders probably adequately represent future classes of 3rd graders in your district. You need to be alert to changing demographics. At least in the short run I’d imagine they’d be representative of future classes.

Think about how these results will be used. Do they just apply to the students you measured? Then you don’t need hypothesis tests. However, if the results are being used to infer things about other students outside of the sample, you’ll need hypothesis testing along with considering how well your students represent the other students and how they differ.

I hope that helps!

June 10, 2024 at 3:21 pm

Thank you so much, Jim, for the suggestions in terms of what I need to think about and consider! You are always so clear in your explanations!!!!

June 10, 2024 at 3:22 pm

You’re very welcome! Best of luck with your evaluations!

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## Keyboard Shortcuts

6.6 - confidence intervals & hypothesis testing.

Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests use data from a sample to test a specified hypothesis. Hypothesis testing requires that we have a hypothesized parameter.

The simulation methods used to construct bootstrap distributions and randomization distributions are similar. One primary difference is a bootstrap distribution is centered on the observed sample statistic while a randomization distribution is centered on the value in the null hypothesis.

In Lesson 4, we learned confidence intervals contain a range of reasonable estimates of the population parameter. All of the confidence intervals we constructed in this course were two-tailed. These two-tailed confidence intervals go hand-in-hand with the two-tailed hypothesis tests we learned in Lesson 5. The conclusion drawn from a two-tailed confidence interval is usually the same as the conclusion drawn from a two-tailed hypothesis test. In other words, if the the 95% confidence interval contains the hypothesized parameter, then a hypothesis test at the 0.05 $$\alpha$$ level will almost always fail to reject the null hypothesis. If the 95% confidence interval does not contain the hypothesize parameter, then a hypothesis test at the 0.05 $$\alpha$$ level will almost always reject the null hypothesis.

## Example: Mean Section

This example uses the Body Temperature dataset built in to StatKey for constructing a  bootstrap confidence interval and conducting a randomization test .

Let's start by constructing a 95% confidence interval using the percentile method in StatKey:

The 95% confidence interval for the mean body temperature in the population is [98.044, 98.474].

Now, what if we want to know if there is enough evidence that the mean body temperature is different from 98.6 degrees? We can conduct a hypothesis test. Because 98.6 is not contained within the 95% confidence interval, it is not a reasonable estimate of the population mean. We should expect to have a p value less than 0.05 and to reject the null hypothesis.

$$H_0: \mu=98.6$$

$$H_a: \mu \ne 98.6$$

$$p = 2*0.00080=0.00160$$

$$p \leq 0.05$$, reject the null hypothesis

There is evidence that the population mean is different from 98.6 degrees.

## Selecting the Appropriate Procedure Section

The decision of whether to use a confidence interval or a hypothesis test depends on the research question. If we want to estimate a population parameter, we use a confidence interval. If we are given a specific population parameter (i.e., hypothesized value), and want to determine the likelihood that a population with that parameter would produce a sample as different as our sample, we use a hypothesis test. Below are a few examples of selecting the appropriate procedure.

## Example: Cheese Consumption Section

Research question: How much cheese (in pounds) does an average American adult consume annually?

What is the appropriate inferential procedure?

Cheese consumption, in pounds, is a quantitative variable. We have one group: American adults. We are not given a specific value to test, so the appropriate procedure here is a  confidence interval for a single mean .

## Example: Age Section

Research question:  Is the average age in the population of all STAT 200 students greater than 30 years?

There is one group: STAT 200 students. The variable of interest is age in years, which is quantitative. The research question includes a specific population parameter to test: 30 years. The appropriate procedure is a  hypothesis test for a single mean .

## Try it! Section

For each research question, identify the variables, the parameter of interest and decide on the the appropriate inferential procedure.

Research question:  How strong is the correlation between height (in inches) and weight (in pounds) in American teenagers?

There are two variables of interest: (1) height in inches and (2) weight in pounds. Both are quantitative variables. The parameter of interest is the correlation between these two variables.

We are not given a specific correlation to test. We are being asked to estimate the strength of the correlation. The appropriate procedure here is a  confidence interval for a correlation .

Research question:  Are the majority of registered voters planning to vote in the next presidential election?

The parameter that is being tested here is a single proportion. We have one group: registered voters. "The majority" would be more than 50%, or p>0.50. This is a specific parameter that we are testing. The appropriate procedure here is a  hypothesis test for a single proportion .

Research question:  On average, are STAT 200 students younger than STAT 500 students?

We have two independent groups: STAT 200 students and STAT 500 students. We are comparing them in terms of average (i.e., mean) age.

If STAT 200 students are younger than STAT 500 students, that translates to $$\mu_{200}<\mu_{500}$$ which is an alternative hypothesis. This could also be written as $$\mu_{200}-\mu_{500}<0$$, where 0 is a specific population parameter that we are testing.

The appropriate procedure here is a  hypothesis test for the difference in two means .

Research question:  On average, how much taller are adult male giraffes compared to adult female giraffes?

There are two groups: males and females. The response variable is height, which is quantitative. We are not given a specific parameter to test, instead we are asked to estimate "how much" taller males are than females. The appropriate procedure is a  confidence interval for the difference in two means .

Research question:  Are STAT 500 students more likely than STAT 200 students to be employed full-time?

There are two independent groups: STAT 500 students and STAT 200 students. The response variable is full-time employment status which is categorical with two levels: yes/no.

If STAT 500 students are more likely than STAT 200 students to be employed full-time, that translates to $$p_{500}>p_{200}$$ which is an alternative hypothesis. This could also be written as $$p_{500}-p_{200}>0$$, where 0 is a specific parameter that we are testing. The appropriate procedure is a  hypothesis test for the difference in two proportions.

Research question:  Is there is a relationship between outdoor temperature (in Fahrenheit) and coffee sales (in cups per day)?

There are two variables here: (1) temperature in Fahrenheit and (2) cups of coffee sold in a day. Both variables are quantitative. The parameter of interest is the correlation between these two variables.

If there is a relationship between the variables, that means that the correlation is different from zero. This is a specific parameter that we are testing. The appropriate procedure is a  hypothesis test for a correlation .

## Module 9: Hypothesis Testing With One Sample

Drawing conclusions, learning outcomes.

• State a conclusion to a hypothesis test in statistical terms and in context

Establishing the type of distribution, sample size, and known or unknown standard deviation can help you figure out how to go about a hypothesis test. However, there are several other factors you should consider when working out a hypothesis test.

## Rare Events

Suppose you make an assumption about a property of the population (this assumption is the null hypothesis ). Then you gather sample data randomly. If the sample has properties that would be very unlikely to occur if the assumption is true, then you would conclude that your assumption about the population is probably incorrect. (Remember that your assumption is just an assumption —it is not a fact and it may or may not be true. But your sample data are real and the data are showing you a fact that seems to contradict your assumption.)

For example, Didi and Ali are at a birthday party of a very wealthy friend. They hurry to be first in line to grab a prize from a tall basket that they cannot see inside because they will be blindfolded. There are 200 plastic bubbles in the basket and Didi and Ali have been told that there is only one with a $100 bill. Didi is the first person to reach into the basket and pull out a bubble. Her bubble contains a$100 bill. The probability of this happening is $\displaystyle\frac{{1}}{{200}}={0.005}$. Because this is so unlikely, Ali is hoping that what the two of them were told is wrong and there are more $100 bills in the basket. A “rare event” has occurred (Didi getting the$100 bill) so Ali doubts the assumption about only one $100 bill being in the basket. ## Using the Sample to Test the Null Hypothesis Use the sample data to calculate the actual probability of getting the test result, called the p -value . The p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample . A large p -value calculated from the data indicates that we should not reject the null hypothesis . The smaller the p -value, the more unlikely the outcome, and the stronger the evidence is against the null hypothesis. We would reject the null hypothesis if the evidence is strongly against it. Draw a graph that shows the p -value. The hypothesis test is easier to perform if you use a graph because you see the problem more clearly. ## Recall: RECALL EVALUATING EXPRESSIONS We use letters to represent unknown numerical values, these are called variables. Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value then simplify the resulting expression using the order of operations. Suppose a baker claims that his bread height is more than 15 cm, on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm and the distribution of heights is normal. The null hypothesis could be H 0 : μ ≤ 15 The alternate hypothesis is H a : μ > 15 The words “is more than” translates as a “>” so “ μ > 15″ goes into the alternate hypothesis. The null hypothesis must contradict the alternate hypothesis. Since σ is known ( σ = 0.5 cm.), the distribution for the population is known to be normal with mean μ = 15 and standard deviation $\displaystyle\frac{\sigma}{\sqrt{n}}=\frac{0.5}{\sqrt{10}}=0.16$ Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm). Then is the mean height (17 cm) calculated from the sample unexpectedly large? The hypothesis test works by asking the question how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm. The p -value, then, is the probability that a sample mean is the same or greater than 17 cm when the population mean is, in fact, 15 cm. We can calculate this probability using the normal distribution for means. p -value = P ($\overline{x}$ > 17) which is approximately zero. A p -value of approximately zero tells us that it is highly unlikely that a loaf of bread rises no more than 15 cm, on average. That is, almost 0% of all loaves of bread would be at least as high as 17 cm purely by CHANCE had the population mean height really been 15 cm. Because the outcome of 17 cm is so unlikely (meaning it is happening NOT by chance alone) , we conclude that the evidence is strongly against the null hypothesis (the mean height is at most 15 cm). There is sufficient evidence that the true mean height for the population of the baker’s loaves of bread is greater than 15 cm. A normal distribution has a standard deviation of 1. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5. H 0 : μ ≤ 12 H a : μ > 12 The p -value is 0.0013 Draw a graph that shows the p -value. p- value = 0.0013 • Rare Events, the Sample, Decision and Conclusion. Provided by : OpenStax. Located at : https://openstax.org/books/statistics/pages/9-4-rare-events-the-sample-and-the-decision-and-conclusion . License : CC BY: Attribution . License Terms : Access for free at https://openstax.org/books/statistics/pages/1-introduction • Introductory Statistics. Authored by : Barbara Illowsky, Susan Dean. Provided by : OpenStax. Located at : https://openstax.org/books/introductory-statistics/pages/1-introduction . License : CC BY: Attribution . License Terms : Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction • Prealgebra. Provided by : OpenStax. Located at : https://openstax.org/books/prealgebra/pages/1-introduction . License : CC BY: Attribution . License Terms : Access for free at https://openstax.org/books/prealgebra/pages/1-introduction Privacy Policy • school Campus Bookshelves • menu_book Bookshelves • perm_media Learning Objects • login Login • how_to_reg Request Instructor Account • hub Instructor Commons ## Margin Size • Download Page (PDF) • Download Full Book (PDF) • Periodic Table • Physics Constants • Scientific Calculator • Reference & Cite • Tools expand_more • Readability selected template will load here This action is not available. ## 9.1: Introduction to Hypothesis Testing • Last updated • Save as PDF • Page ID 10211 • Kyle Siegrist • University of Alabama in Huntsville via Random Services $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ ( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ $$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$ $$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$ $$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vectorC}[1]{\textbf{#1}}$$ $$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$ $$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$ $$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$ ## Basic Theory Preliminaries. As usual, our starting point is a random experiment with an underlying sample space and a probability measure $$\P$$. In the basic statistical model, we have an observable random variable $$\bs{X}$$ taking values in a set $$S$$. In general, $$\bs{X}$$ can have quite a complicated structure. For example, if the experiment is to sample $$n$$ objects from a population and record various measurements of interest, then $\bs{X} = (X_1, X_2, \ldots, X_n)$ where $$X_i$$ is the vector of measurements for the $$i$$th object. The most important special case occurs when $$(X_1, X_2, \ldots, X_n)$$ are independent and identically distributed. In this case, we have a random sample of size $$n$$ from the common distribution. The purpose of this section is to define and discuss the basic concepts of statistical hypothesis testing . Collectively, these concepts are sometimes referred to as the Neyman-Pearson framework, in honor of Jerzy Neyman and Egon Pearson, who first formalized them. A statistical hypothesis is a statement about the distribution of $$\bs{X}$$. Equivalently, a statistical hypothesis specifies a set of possible distributions of $$\bs{X}$$: the set of distributions for which the statement is true. A hypothesis that specifies a single distribution for $$\bs{X}$$ is called simple ; a hypothesis that specifies more than one distribution for $$\bs{X}$$ is called composite . In hypothesis testing , the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis . The null hypothesis is usually denoted $$H_0$$ while the alternative hypothesis is usually denoted $$H_1$$. An hypothesis test is a statistical decision ; the conclusion will either be to reject the null hypothesis in favor of the alternative, or to fail to reject the null hypothesis. The decision that we make must, of course, be based on the observed value $$\bs{x}$$ of the data vector $$\bs{X}$$. Thus, we will find an appropriate subset $$R$$ of the sample space $$S$$ and reject $$H_0$$ if and only if $$\bs{x} \in R$$. The set $$R$$ is known as the rejection region or the critical region . Note the asymmetry between the null and alternative hypotheses. This asymmetry is due to the fact that we assume the null hypothesis, in a sense, and then see if there is sufficient evidence in $$\bs{x}$$ to overturn this assumption in favor of the alternative. An hypothesis test is a statistical analogy to proof by contradiction, in a sense. Suppose for a moment that $$H_1$$ is a statement in a mathematical theory and that $$H_0$$ is its negation. One way that we can prove $$H_1$$ is to assume $$H_0$$ and work our way logically to a contradiction. In an hypothesis test, we don't prove anything of course, but there are similarities. We assume $$H_0$$ and then see if the data $$\bs{x}$$ are sufficiently at odds with that assumption that we feel justified in rejecting $$H_0$$ in favor of $$H_1$$. Often, the critical region is defined in terms of a statistic $$w(\bs{X})$$, known as a test statistic , where $$w$$ is a function from $$S$$ into another set $$T$$. We find an appropriate rejection region $$R_T \subseteq T$$ and reject $$H_0$$ when the observed value $$w(\bs{x}) \in R_T$$. Thus, the rejection region in $$S$$ is then $$R = w^{-1}(R_T) = \left\{\bs{x} \in S: w(\bs{x}) \in R_T\right\}$$. As usual, the use of a statistic often allows significant data reduction when the dimension of the test statistic is much smaller than the dimension of the data vector. The ultimate decision may be correct or may be in error. There are two types of errors, depending on which of the hypotheses is actually true. Types of errors: • A type 1 error is rejecting the null hypothesis $$H_0$$ when $$H_0$$ is true. • A type 2 error is failing to reject the null hypothesis $$H_0$$ when the alternative hypothesis $$H_1$$ is true. Similarly, there are two ways to make a correct decision: we could reject $$H_0$$ when $$H_1$$ is true or we could fail to reject $$H_0$$ when $$H_0$$ is true. The possibilities are summarized in the following table: Hypothesis Test State | Decision Fail to reject $$H_0$$ Reject $$H_0$$ $$H_0$$ True Correct Type 1 error $$H_1$$ True Type 2 error Correct Of course, when we observe $$\bs{X} = \bs{x}$$ and make our decision, either we will have made the correct decision or we will have committed an error, and usually we will never know which of these events has occurred. Prior to gathering the data, however, we can consider the probabilities of the various errors. If $$H_0$$ is true (that is, the distribution of $$\bs{X}$$ is specified by $$H_0$$), then $$\P(\bs{X} \in R)$$ is the probability of a type 1 error for this distribution. If $$H_0$$ is composite, then $$H_0$$ specifies a variety of different distributions for $$\bs{X}$$ and thus there is a set of type 1 error probabilities. The maximum probability of a type 1 error, over the set of distributions specified by $$H_0$$, is the significance level of the test or the size of the critical region. The significance level is often denoted by $$\alpha$$. Usually, the rejection region is constructed so that the significance level is a prescribed, small value (typically 0.1, 0.05, 0.01). If $$H_1$$ is true (that is, the distribution of $$\bs{X}$$ is specified by $$H_1$$), then $$\P(\bs{X} \notin R)$$ is the probability of a type 2 error for this distribution. Again, if $$H_1$$ is composite then $$H_1$$ specifies a variety of different distributions for $$\bs{X}$$, and thus there will be a set of type 2 error probabilities. Generally, there is a tradeoff between the type 1 and type 2 error probabilities. If we reduce the probability of a type 1 error, by making the rejection region $$R$$ smaller, we necessarily increase the probability of a type 2 error because the complementary region $$S \setminus R$$ is larger. The extreme cases can give us some insight. First consider the decision rule in which we never reject $$H_0$$, regardless of the evidence $$\bs{x}$$. This corresponds to the rejection region $$R = \emptyset$$. A type 1 error is impossible, so the significance level is 0. On the other hand, the probability of a type 2 error is 1 for any distribution defined by $$H_1$$. At the other extreme, consider the decision rule in which we always rejects $$H_0$$ regardless of the evidence $$\bs{x}$$. This corresponds to the rejection region $$R = S$$. A type 2 error is impossible, but now the probability of a type 1 error is 1 for any distribution defined by $$H_0$$. In between these two worthless tests are meaningful tests that take the evidence $$\bs{x}$$ into account. If $$H_1$$ is true, so that the distribution of $$\bs{X}$$ is specified by $$H_1$$, then $$\P(\bs{X} \in R)$$, the probability of rejecting $$H_0$$ is the power of the test for that distribution. Thus the power of the test for a distribution specified by $$H_1$$ is the probability of making the correct decision. Suppose that we have two tests, corresponding to rejection regions $$R_1$$ and $$R_2$$, respectively, each having significance level $$\alpha$$. The test with region $$R_1$$ is uniformly more powerful than the test with region $$R_2$$ if $\P(\bs{X} \in R_1) \ge \P(\bs{X} \in R_2) \text{ for every distribution of } \bs{X} \text{ specified by } H_1$ Naturally, in this case, we would prefer the first test. Often, however, two tests will not be uniformly ordered; one test will be more powerful for some distributions specified by $$H_1$$ while the other test will be more powerful for other distributions specified by $$H_1$$. If a test has significance level $$\alpha$$ and is uniformly more powerful than any other test with significance level $$\alpha$$, then the test is said to be a uniformly most powerful test at level $$\alpha$$. Clearly a uniformly most powerful test is the best we can do. ## $$P$$-value In most cases, we have a general procedure that allows us to construct a test (that is, a rejection region $$R_\alpha$$) for any given significance level $$\alpha \in (0, 1)$$. Typically, $$R_\alpha$$ decreases (in the subset sense) as $$\alpha$$ decreases. The $$P$$-value of the observed value $$\bs{x}$$ of $$\bs{X}$$, denoted $$P(\bs{x})$$, is defined to be the smallest $$\alpha$$ for which $$\bs{x} \in R_\alpha$$; that is, the smallest significance level for which $$H_0$$ is rejected, given $$\bs{X} = \bs{x}$$. Knowing $$P(\bs{x})$$ allows us to test $$H_0$$ at any significance level for the given data $$\bs{x}$$: If $$P(\bs{x}) \le \alpha$$ then we would reject $$H_0$$ at significance level $$\alpha$$; if $$P(\bs{x}) \gt \alpha$$ then we fail to reject $$H_0$$ at significance level $$\alpha$$. Note that $$P(\bs{X})$$ is a statistic . Informally, $$P(\bs{x})$$ can often be thought of as the probability of an outcome as or more extreme than the observed value $$\bs{x}$$, where extreme is interpreted relative to the null hypothesis $$H_0$$. ## Analogy with Justice Systems There is a helpful analogy between statistical hypothesis testing and the criminal justice system in the US and various other countries. Consider a person charged with a crime. The presumed null hypothesis is that the person is innocent of the crime; the conjectured alternative hypothesis is that the person is guilty of the crime. The test of the hypotheses is a trial with evidence presented by both sides playing the role of the data. After considering the evidence, the jury delivers the decision as either not guilty or guilty . Note that innocent is not a possible verdict of the jury, because it is not the point of the trial to prove the person innocent. Rather, the point of the trial is to see whether there is sufficient evidence to overturn the null hypothesis that the person is innocent in favor of the alternative hypothesis of that the person is guilty. A type 1 error is convicting a person who is innocent; a type 2 error is acquitting a person who is guilty. Generally, a type 1 error is considered the more serious of the two possible errors, so in an attempt to hold the chance of a type 1 error to a very low level, the standard for conviction in serious criminal cases is beyond a reasonable doubt . ## Tests of an Unknown Parameter Hypothesis testing is a very general concept, but an important special class occurs when the distribution of the data variable $$\bs{X}$$ depends on a parameter $$\theta$$ taking values in a parameter space $$\Theta$$. The parameter may be vector-valued, so that $$\bs{\theta} = (\theta_1, \theta_2, \ldots, \theta_n)$$ and $$\Theta \subseteq \R^k$$ for some $$k \in \N_+$$. The hypotheses generally take the form $H_0: \theta \in \Theta_0 \text{ versus } H_1: \theta \notin \Theta_0$ where $$\Theta_0$$ is a prescribed subset of the parameter space $$\Theta$$. In this setting, the probabilities of making an error or a correct decision depend on the true value of $$\theta$$. If $$R$$ is the rejection region, then the power function $$Q$$ is given by $Q(\theta) = \P_\theta(\bs{X} \in R), \quad \theta \in \Theta$ The power function gives a lot of information about the test. The power function satisfies the following properties: • $$Q(\theta)$$ is the probability of a type 1 error when $$\theta \in \Theta_0$$. • $$\max\left\{Q(\theta): \theta \in \Theta_0\right\}$$ is the significance level of the test. • $$1 - Q(\theta)$$ is the probability of a type 2 error when $$\theta \notin \Theta_0$$. • $$Q(\theta)$$ is the power of the test when $$\theta \notin \Theta_0$$. If we have two tests, we can compare them by means of their power functions. Suppose that we have two tests, corresponding to rejection regions $$R_1$$ and $$R_2$$, respectively, each having significance level $$\alpha$$. The test with rejection region $$R_1$$ is uniformly more powerful than the test with rejection region $$R_2$$ if $$Q_1(\theta) \ge Q_2(\theta)$$ for all $$\theta \notin \Theta_0$$. Most hypothesis tests of an unknown real parameter $$\theta$$ fall into three special cases: Suppose that $$\theta$$ is a real parameter and $$\theta_0 \in \Theta$$ a specified value. The tests below are respectively the two-sided test , the left-tailed test , and the right-tailed test . • $$H_0: \theta = \theta_0$$ versus $$H_1: \theta \ne \theta_0$$ • $$H_0: \theta \ge \theta_0$$ versus $$H_1: \theta \lt \theta_0$$ • $$H_0: \theta \le \theta_0$$ versus $$H_1: \theta \gt \theta_0$$ Thus the tests are named after the conjectured alternative. Of course, there may be other unknown parameters besides $$\theta$$ (known as nuisance parameters ). ## Equivalence Between Hypothesis Test and Confidence Sets There is an equivalence between hypothesis tests and confidence sets for a parameter $$\theta$$. Suppose that $$C(\bs{x})$$ is a $$1 - \alpha$$ level confidence set for $$\theta$$. The following test has significance level $$\alpha$$ for the hypothesis $$H_0: \theta = \theta_0$$ versus $$H_1: \theta \ne \theta_0$$: Reject $$H_0$$ if and only if $$\theta_0 \notin C(\bs{x})$$ By definition, $$\P[\theta \in C(\bs{X})] = 1 - \alpha$$. Hence if $$H_0$$ is true so that $$\theta = \theta_0$$, then the probability of a type 1 error is $$P[\theta \notin C(\bs{X})] = \alpha$$. Equivalently, we fail to reject $$H_0$$ at significance level $$\alpha$$ if and only if $$\theta_0$$ is in the corresponding $$1 - \alpha$$ level confidence set. In particular, this equivalence applies to interval estimates of a real parameter $$\theta$$ and the common tests for $$\theta$$ given above . In each case below, the confidence interval has confidence level $$1 - \alpha$$ and the test has significance level $$\alpha$$. • Suppose that $$\left[L(\bs{X}, U(\bs{X})\right]$$ is a two-sided confidence interval for $$\theta$$. Reject $$H_0: \theta = \theta_0$$ versus $$H_1: \theta \ne \theta_0$$ if and only if $$\theta_0 \lt L(\bs{X})$$ or $$\theta_0 \gt U(\bs{X})$$. • Suppose that $$L(\bs{X})$$ is a confidence lower bound for $$\theta$$. Reject $$H_0: \theta \le \theta_0$$ versus $$H_1: \theta \gt \theta_0$$ if and only if $$\theta_0 \lt L(\bs{X})$$. • Suppose that $$U(\bs{X})$$ is a confidence upper bound for $$\theta$$. Reject $$H_0: \theta \ge \theta_0$$ versus $$H_1: \theta \lt \theta_0$$ if and only if $$\theta_0 \gt U(\bs{X})$$. ## Pivot Variables and Test Statistics Recall that confidence sets of an unknown parameter $$\theta$$ are often constructed through a pivot variable , that is, a random variable $$W(\bs{X}, \theta)$$ that depends on the data vector $$\bs{X}$$ and the parameter $$\theta$$, but whose distribution does not depend on $$\theta$$ and is known. In this case, a natural test statistic for the basic tests given above is $$W(\bs{X}, \theta_0)$$. • Privacy Policy Home » What is a Hypothesis – Types, Examples and Writing Guide ## What is a Hypothesis – Types, Examples and Writing Guide Table of Contents Definition: Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation. Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy. ## Types of Hypothesis Types of Hypothesis are as follows: ## Research Hypothesis A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments. ## Null Hypothesis The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables. ## Alternative Hypothesis An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate. ## Directional Hypothesis A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight. ## Non-directional Hypothesis A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight. ## Statistical Hypothesis A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result. ## Composite Hypothesis A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome. ## Empirical Hypothesis An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena. ## Simple Hypothesis A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor. ## Complex Hypothesis A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome. ## Applications of Hypothesis Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields: • Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem. • Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease. • Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior. • Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates. • Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior. • Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design. ## How to write a Hypothesis Here are the steps to follow when writing a hypothesis: ## Identify the Research Question The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field. ## Conduct a Literature Review Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge. ## Determine the Variables The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable. ## Formulate the Hypothesis Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence. ## Write the Null Hypothesis The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance. ## Refine the Hypothesis After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable. ## Examples of Hypothesis Here are a few examples of hypotheses in different fields: • Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.” • Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.” • Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.” • Education : “Implementing a new teaching method will result in higher student achievement scores.” • Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.” • Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.” • Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.” ## Purpose of Hypothesis The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction. The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect. In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon. ## When to use Hypothesis Here are some common situations in which hypotheses are used: • In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments. • In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena. • I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research. ## Characteristics of Hypothesis Here are some common characteristics of a hypothesis: • Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis. • Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis. • Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested. • Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions. • Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed. • Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion. • Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue. ## Advantages of Hypothesis Hypotheses have several advantages in scientific research and experimentation: • Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results. • Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries. • Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration. • Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results. • Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries. • Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings. ## Limitations of Hypothesis Some Limitations of the Hypothesis are as follows: • Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing. • May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions. • May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research. • Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis. • Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing. • May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables. ## About the author ## Muhammad Hassan Researcher, Academic Writer, Web developer ## You may also like ## Data Collection – Methods Types and Examples ## Delimitations in Research – Types, Examples and... ## APA Table of Contents – Format and Example ## Significance of the Study – Examples and Writing... ## Theoretical Framework – Types, Examples and... ## Survey Instruments – List and Their Uses • school Campus Bookshelves • menu_book Bookshelves • perm_media Learning Objects • login Login • how_to_reg Request Instructor Account • hub Instructor Commons ## Margin Size • Download Page (PDF) • Download Full Book (PDF) • Periodic Table • Physics Constants • Scientific Calculator • Reference & Cite • Tools expand_more • Readability selected template will load here This action is not available. ## 8.6: Hypothesis Test of a Single Population Mean with Examples • Last updated • Save as PDF • Page ID 130297 $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ ( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ $$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$ $$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$ $$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vectorC}[1]{\textbf{#1}}$$ $$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$ $$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$ $$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$ ## Steps for performing Hypothesis Test of a Single Population Mean Step 1: State your hypotheses about the population mean. Step 2: Summarize the data. State a significance level. State and check conditions required for the procedure • Find or identify the sample size, n, the sample mean, $$\bar{x}$$ and the sample standard deviation, s . The sampling distribution for the one-mean test statistic is, approximately, T- distribution if the following conditions are met • Sample is random with independent observations . • Sample is large. The population must be Normal or the sample size must be at least 30. Step 3: Perform the procedure based on the assumption that $$H_{0}$$ is true • Find the Estimated Standard Error: $$SE=\frac{s}{\sqrt{n}}$$. • Compute the observed value of the test statistic: $$T_{obs}=\frac{\bar{x}-\mu_{0}}{SE}$$. • Check the type of the test (right-, left-, or two-tailed) • Find the p-value in order to measure your level of surprise. Step 4: Make a decision about $$H_{0}$$ and $$H_{a}$$ • Do you reject or not reject your null hypothesis? Step 5: Make a conclusion • What does this mean in the context of the data? ## The following examples illustrate a left-, right-, and two-tailed test. Example $$\pageindex{1}$$. $$H_{0}: \mu = 5, H_{a}: \mu < 5$$ Test of a single population mean. $$H_{a}$$ tells you the test is left-tailed. The picture of the $$p$$-value is as follows: ## Exercise $$\PageIndex{1}$$ $$H_{0}: \mu = 10, H_{a}: \mu < 10$$ Assume the $$p$$-value is 0.0935. What type of test is this? Draw the picture of the $$p$$-value. left-tailed test ## Example $$\PageIndex{2}$$ $$H_{0}: \mu \leq 0.2, H_{a}: \mu > 0.2$$ This is a test of a single population proportion. $$H_{a}$$ tells you the test is right-tailed . The picture of the p -value is as follows: ## Exercise $$\PageIndex{2}$$ $$H_{0}: \mu \leq 1, H_{a}: \mu > 1$$ Assume the $$p$$-value is 0.1243. What type of test is this? Draw the picture of the $$p$$-value. right-tailed test ## Example $$\PageIndex{3}$$ $$H_{0}: \mu = 50, H_{a}: \mu \neq 50$$ This is a test of a single population mean. $$H_{a}$$ tells you the test is two-tailed . The picture of the $$p$$-value is as follows. ## Exercise $$\PageIndex{3}$$ $$H_{0}: \mu = 0.5, H_{a}: \mu \neq 0.5$$ Assume the p -value is 0.2564. What type of test is this? Draw the picture of the $$p$$-value. two-tailed test ## Full Hypothesis Test Examples Example $$\pageindex{4}$$. Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65 65 70 67 66 63 63 68 72 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution. Set up the hypothesis test: A 5% level of significance means that $$\alpha = 0.05$$. This is a test of a single population mean . $$H_{0}: \mu = 65 H_{a}: \mu > 65$$ Since the instructor thinks the average score is higher, use a "$$>$$". The "$$>$$" means the test is right-tailed. Determine the distribution needed: Random variable: $$\bar{X} =$$ average score on the first statistics test. Distribution for the test: If you read the problem carefully, you will notice that there is no population standard deviation given . You are only given $$n = 10$$ sample data values. Notice also that the data come from a normal distribution. This means that the distribution for the test is a student's $$t$$. Use $$t_{df}$$. Therefore, the distribution for the test is $$t_{9}$$ where $$n = 10$$ and $$df = 10 - 1 = 9$$. The sample mean and sample standard deviation are calculated as 67 and 3.1972 from the data. Calculate the $$p$$-value using the Student's $$t$$-distribution: $t_{obs} = \dfrac{\bar{x}-\mu_{\bar{x}}}{\left(\dfrac{s}{\sqrt{n}}\right)}=\dfrac{67-65}{\left(\dfrac{3.1972}{\sqrt{10}}\right)}$ Use the T-table or Excel's t_dist() function to find p-value: $$p\text{-value} = P(\bar{x} > 67) =P(T >1.9782 )= 1-0.9604=0.0396$$ Interpretation of the p -value: If the null hypothesis is true, then there is a 0.0396 probability (3.96%) that the sample mean is 65 or more. Compare $$\alpha$$ and the $$p-\text{value}$$: Since $$α = 0.05$$ and $$p\text{-value} = 0.0396$$. $$\alpha > p\text{-value}$$. Make a decision: Since $$\alpha > p\text{-value}$$, reject $$H_{0}$$. This means you reject $$\mu = 65$$. In other words, you believe the average test score is more than 65. Conclusion: At a 5% level of significance, the sample data show sufficient evidence that the mean (average) test score is more than 65, just as the math instructor thinks. The $$p\text{-value}$$ can easily be calculated. Put the data into a list. Press STAT and arrow over to TESTS . Press 2:T-Test . Arrow over to Data and press ENTER . Arrow down and enter 65 for $$\mu_{0}$$, the name of the list where you put the data, and 1 for Freq: . Arrow down to $$\mu$$: and arrow over to $$> \mu_{0}$$. Press ENTER . Arrow down to Calculate and press ENTER . The calculator not only calculates the $$p\text{-value}$$ (p = 0.0396) but it also calculates the test statistic ( t -score) for the sample mean, the sample mean, and the sample standard deviation. $$\mu > 65$$ is the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with $$t = 1.9781$$ (test statistic) and $$p = 0.0396$$ ($$p\text{-value}$$). Make sure when you use Draw that no other equations are highlighted in $$Y =$$ and the plots are turned off. ## Exercise $$\PageIndex{4}$$ It is believed that a stock price for a particular company will grow at a rate of$5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows:$4, $3,$2, $3,$1, $7,$2, $1,$1, $2. Perform a hypothesis test using a 5% level of significance. State the null and alternative hypotheses, find the p -value, state your conclusion, and identify the Type I and Type II errors. • $$H_{0}: \mu = 5$$ • $$H_{a}: \mu < 5$$ • $$p = 0.0082$$ Because $$p < \alpha$$, we reject the null hypothesis. There is sufficient evidence to suggest that the stock price of the company grows at a rate less than$5 a week.

• Type I Error: To conclude that the stock price is growing slower than $5 a week when, in fact, the stock price is growing at$5 a week (reject the null hypothesis when the null hypothesis is true).
• Type II Error: To conclude that the stock price is growing at a rate of $5 a week when, in fact, the stock price is growing slower than$5 a week (do not reject the null hypothesis when the null hypothesis is false).

## Example $$\PageIndex{5}$$

The National Institute of Standards and Technology provides exact data on conductivity properties of materials. Following are conductivity measurements for 11 randomly selected pieces of a particular type of glass.

1.11; 1.07; 1.11; 1.07; 1.12; 1.08; .98; .98 1.02; .95; .95

Is there convincing evidence that the average conductivity of this type of glass is greater than one? Use a significance level of 0.05. Assume the population is normal.

• $$H_{0}: \mu \leq 1$$
• $$H_{a}: \mu > 1$$
• Plan : We are testing a sample mean without a known population standard deviation. Therefore, we need to use a Student's-t distribution. Assume the underlying population is normal.
• Do the calculations : $$p\text{-value} ( = 0.036)$$

4. State the Conclusions : Since the $$p\text{-value} (= 0.036)$$ is less than our alpha value, we will reject the null hypothesis. It is reasonable to state that the data supports the claim that the average conductivity level is greater than one.

The hypothesis test itself has an established process. This can be summarized as follows:

• Determine $$H_{0}$$ and $$H_{a}$$. Remember, they are contradictory.
• Determine the random variable.
• Determine the distribution for the test.
• Draw a graph, calculate the test statistic, and use the test statistic to calculate the $$p\text{-value}$$. (A t -score is an example of test statistics.)
• Compare the preconceived α with the p -value, make a decision (reject or do not reject H 0 ), and write a clear conclusion using English sentences.

Notice that in performing the hypothesis test, you use $$\alpha$$ and not $$\beta$$. $$\beta$$ is needed to help determine the sample size of the data that is used in calculating the $$p\text{-value}$$. Remember that the quantity $$1 – \beta$$ is called the Power of the Test . A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same.If the power is low, the null hypothesis might not be rejected when it should be.

• Data from Amit Schitai. Director of Instructional Technology and Distance Learning. LBCC.
• Data from energy.gov. Available online at http://energy.gov (accessed June 27. 2013).
• Data from Gallup®. Available online at www.gallup.com (accessed June 27, 2013).
• Data from Growing by Degrees by Allen and Seaman.
• Data from La Leche League International. Available online at www.lalecheleague.org/Law/BAFeb01.html.
• Data from the American Automobile Association. Available online at www.aaa.com (accessed June 27, 2013).
• Data from the American Library Association. Available online at www.ala.org (accessed June 27, 2013).
• Data from the Bureau of Labor Statistics. Available online at http://www.bls.gov/oes/current/oes291111.htm .
• Data from the Centers for Disease Control and Prevention. Available online at www.cdc.gov (accessed June 27, 2013)
• Data from the U.S. Census Bureau, available online at quickfacts.census.gov/qfd/states/00000.html (accessed June 27, 2013).
• Data from the United States Census Bureau. Available online at www.census.gov/hhes/socdemo/language/.
• Data from Toastmasters International. Available online at http://toastmasters.org/artisan/deta...eID=429&Page=1 .
• Data from Weather Underground. Available online at www.wunderground.com (accessed June 27, 2013).
• Federal Bureau of Investigations. “Uniform Crime Reports and Index of Crime in Daviess in the State of Kentucky enforced by Daviess County from 1985 to 2005.” Available online at http://www.disastercenter.com/kentucky/crime/3868.htm (accessed June 27, 2013).
• “Foothill-De Anza Community College District.” De Anza College, Winter 2006. Available online at research.fhda.edu/factbook/DA...t_da_2006w.pdf.
• Johansen, C., J. Boice, Jr., J. McLaughlin, J. Olsen. “Cellular Telephones and Cancer—a Nationwide Cohort Study in Denmark.” Institute of Cancer Epidemiology and the Danish Cancer Society, 93(3):203-7. Available online at http://www.ncbi.nlm.nih.gov/pubmed/11158188 (accessed June 27, 2013).
• Rape, Abuse & Incest National Network. “How often does sexual assault occur?” RAINN, 2009. Available online at www.rainn.org/get-information...sexual-assault (accessed June 27, 2013).
• Bipolar Disorder
• Therapy Center
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## How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

## Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

## Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

## At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

## The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

## Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

## How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

## The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

## Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

## Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

## A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

## Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

## Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

## Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not."

## Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

## Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

## Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

## Learn How To Write A Hypothesis For Your Next Research Project!

Undoubtedly, research plays a crucial role in substantiating or refuting our assumptions. These assumptions act as potential answers to our questions. Such assumptions, also known as hypotheses, are considered key aspects of research. In this blog, we delve into the significance of hypotheses. And provide insights on how to write them effectively. So, let’s dive in and explore the art of writing hypotheses together.

## What is a Hypothesis?

A hypothesis is a crucial starting point in scientific research. It is an educated guess about the relationship between two or more variables. In other words, a hypothesis acts as a foundation for a researcher to build their study.

Here are some examples of well-crafted hypotheses:

• Increased exposure to natural sunlight improves sleep quality in adults.

A positive relationship between natural sunlight exposure and sleep quality in adult individuals.

• Playing puzzle games on a regular basis enhances problem-solving abilities in children.

Engaging in frequent puzzle gameplay leads to improved problem-solving skills in children.

• Students and improved learning hecks.

S tudents using online  paper writing service  platforms (as a learning tool for receiving personalized feedback and guidance) will demonstrate improved writing skills. (compared to those who do not utilize such platforms).

• The use of APA format in research papers.

Using the  APA format  helps students stay organized when writing research papers. Organized students can focus better on their topics and, as a result, produce better quality work.

## The Building Blocks of a Hypothesis

To better understand the concept of a hypothesis, let’s break it down into its basic components:

• Variables . A hypothesis involves at least two variables. An independent variable and a dependent variable. The independent variable is the one being changed or manipulated, while the dependent variable is the one being measured or observed.
• Relationship : A hypothesis proposes a relationship or connection between the variables. This could be a cause-and-effect relationship or a correlation between them.
• Testability : A hypothesis should be testable and falsifiable, meaning it can be proven right or wrong through experimentation or observation.

## Types of Hypotheses

When learning how to write a hypothesis, it’s essential to understand its main types. These include; alternative hypotheses and null hypotheses. In the following section, we explore both types of hypotheses with examples.

## Alternative Hypothesis (H1)

This kind of hypothesis suggests a relationship or effect between the variables. It is the main focus of the study. The researcher wants to either prove or disprove it. Many research divides this hypothesis into two subsections:

• Directional

This type of H1 predicts a specific outcome. Many researchers use this hypothesis to explore the relationship between variables rather than the groups.

• Non-directional

You can take a guess from the name. This type of H1 does not provide a specific prediction for the research outcome.

Here are some examples for your better understanding of how to write a hypothesis.

• Consuming caffeine improves cognitive performance.  (This hypothesis predicts that there is a positive relationship between caffeine consumption and cognitive performance.)
• Aerobic exercise leads to reduced blood pressure.  (This hypothesis suggests that engaging in aerobic exercise results in lower blood pressure readings.)
• Exposure to nature reduces stress levels among employees.  (Here, the hypothesis proposes that employees exposed to natural environments will experience decreased stress levels.)
• Listening to classical music while studying increases memory retention.  (This hypothesis speculates that studying with classical music playing in the background boosts students’ ability to retain information.)
• Early literacy intervention improves reading skills in children.  (This hypothesis claims that providing early literacy assistance to children results in enhanced reading abilities.)
• Time management in nursing students. ( Students who use a  nursing research paper writing service  have more time to focus on their studies and can achieve better grades in other subjects. )

## Null Hypothesis (H0)

A null hypothesis assumes no relationship or effect between the variables. If the alternative hypothesis is proven to be false, the null hypothesis is considered to be true. Usually a null hypothesis shows no direct correlation between the defined variables.

Here are some of the examples

• The consumption of herbal tea has no effect on sleep quality.  (This hypothesis assumes that herbal tea consumption does not impact the quality of sleep.)
• The number of hours spent playing video games is unrelated to academic performance.  (Here, the null hypothesis suggests that no relationship exists between video gameplay duration and academic achievement.)
• Implementing flexible work schedules has no influence on employee job satisfaction.  (This hypothesis contends that providing flexible schedules does not affect how satisfied employees are with their jobs.)
• Writing ability of a 7th grader is not affected by reading editorial example. ( There is no relationship between reading an  editorial example  and improving a 7th grader’s writing abilities.)
• The type of lighting in a room does not affect people’s mood.  (In this null hypothesis, there is no connection between the kind of lighting in a room and the mood of those present.)
• The use of social media during break time does not impact productivity at work.  (This hypothesis proposes that social media usage during breaks has no effect on work productivity.)

As you learn how to write a hypothesis, remember that aiming for clarity, testability, and relevance to your research question is vital. By mastering this skill, you’re well on your way to conducting impactful scientific research. Good luck!

## Importance of a Hypothesis in Research

A well-structured hypothesis is a vital part of any research project for several reasons:

• It provides clear direction for the study by setting its focus and purpose.
• It outlines expectations of the research, making it easier to measure results.
• It helps identify any potential limitations in the study, allowing researchers to refine their approach.

In conclusion, a hypothesis plays a fundamental role in the research process. By understanding its concept and constructing a well-thought-out hypothesis, researchers lay the groundwork for a successful, scientifically sound investigation.

## How to Write a Hypothesis?

Here are five steps that you can follow to write an effective hypothesis.

## Step 1: Identify Your Research Question

The first step in learning how to compose a hypothesis is to clearly define your research question. This question is the central focus of your study and will help you determine the direction of your hypothesis.

## Step 2: Determine the Variables

When exploring how to write a hypothesis, it’s crucial to identify the variables involved in your study. You’ll need at least two variables:

• Independent variable : The factor you manipulate or change in your experiment.
• Dependent variable : The outcome or result you observe or measure, which is influenced by the independent variable.

## Step 3: Build the Hypothetical Relationship

In understanding how to compose a hypothesis, constructing the relationship between the variables is key. Based on your research question and variables, predict the expected outcome or connection. This prediction should be specific, testable, and, if possible, expressed in the “If…then” format.

## Step 4: Write the Null Hypothesis

When mastering how to write a hypothesis, it’s important to create a null hypothesis as well. The null hypothesis assumes no relationship or effect between the variables, acting as a counterpoint to your primary hypothesis.

## Step 5: Review Your Hypothesis

Finally, when learning how to compose a hypothesis, it’s essential to review your hypothesis for clarity, testability, and relevance to your research question. Make any necessary adjustments to ensure it provides a solid basis for your study.

In conclusion, understanding how to write a hypothesis is crucial for conducting successful scientific research. By focusing on your research question and carefully building relationships between variables, you will lay a strong foundation for advancing research and knowledge in your field.

## Hypothesis vs. Prediction: What’s the Difference?

Understanding the differences between a hypothesis and a prediction is crucial in scientific research. Often, these terms are used interchangeably, but they have distinct meanings and functions. This segment aims to clarify these differences and explain how to compose a hypothesis correctly, helping you improve the quality of your research projects.

## Hypothesis: The Foundation of Your Research

A hypothesis is an educated guess about the relationship between two or more variables. It provides the basis for your research question and is a starting point for an experiment or observational study.

The critical elements for a hypothesis include:

• Specificity: A clear and concise statement that describes the relationship between variables.
• Testability: The ability to test the hypothesis through experimentation or observation.

To learn how to write a hypothesis, it’s essential to identify your research question first and then predict the relationship between the variables.

## Prediction: The Expected Outcome

A prediction is a statement about a specific outcome you expect to see in your experiment or observational study. It’s derived from the hypothesis and provides a measurable way to test the relationship between variables.

Here’s an example of how to write a hypothesis and a related prediction:

• Hypothesis: Consuming a high-sugar diet leads to weight gain.
• Prediction: People who consume a high-sugar diet for six weeks will gain more weight than those who maintain a low-sugar diet during the same period.

## Key Differences Between a Hypothesis and a Prediction

While a hypothesis and prediction are both essential components of scientific research, there are some key differences to keep in mind:

• A hypothesis is an educated guess that suggests a relationship between variables, while a prediction is a specific and measurable outcome based on that hypothesis.
• A hypothesis can give rise to multiple experiment or observational study predictions.

To conclude, understanding the differences between a hypothesis and a prediction, and learning how to write a hypothesis, are essential steps to form a robust foundation for your research. By creating clear, testable hypotheses along with specific, measurable predictions, you lay the groundwork for scientifically sound investigations.

Here’s a wrap-up for this guide on how to write a hypothesis. We’re confident this article was helpful for many of you. We understand that many students struggle with writing their school research . However, we hope to continue assisting you through our blog tutorial on writing different aspects of academic assignments.

For further information, you can check out our reverent blog or contact our professionals to avail amazing writing services. Paper perk experts tailor assignments to reflect your unique voice and perspectives. Our professionals make sure to stick around till your satisfaction. So what are you waiting for? Pick your required service and order away!

## How to write a good hypothesis?

How to write a hypothesis in science, how to write a research hypothesis, how to write a null hypothesis, what is the format for a scientific hypothesis, how do you structure a proper hypothesis, can you provide an example of a hypothesis, what is the ideal hypothesis structure.

The ideal hypothesis structure includes the following;

• A clear statement of the relationship between variables.
• testable prediction.
• falsifiability.

If your hypothesis has all of these, it is both scientifically sound and effective.

## How to write a hypothesis for product management?

Writing a hypothesis for product management involves a simple process:

• First, identify the problem or question you want to address.
• State your assumption or belief about the solution to that problem. .
• Make a hypothesis by predicting a specific outcome based on your assumption.
• Make sure your hypothesis is specific, measurable, and testable.
• Use experiments, data analysis, or user feedback to validate your hypothesis.
• Make informed decisions for product improvement.

Following these steps will help you in effectively formulating hypotheses for product management.

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## AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 10.

• Idea behind hypothesis testing
• Examples of null and alternative hypotheses
• Writing null and alternative hypotheses
• P-values and significance tests
• Comparing P-values to different significance levels
• Estimating a P-value from a simulation
• Estimating P-values from simulations

## Using P-values to make conclusions

• (Choice A)   Fail to reject H 0 ‍   A Fail to reject H 0 ‍
• (Choice B)   Reject H 0 ‍   and accept H a ‍   B Reject H 0 ‍   and accept H a ‍
• (Choice C)   Accept H 0 ‍   C Accept H 0 ‍
• (Choice A)   The evidence suggests that these subjects can do better than guessing when identifying the bottled water. A The evidence suggests that these subjects can do better than guessing when identifying the bottled water.
• (Choice B)   We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water. B We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water.
• (Choice C)   The evidence suggests that these subjects were simply guessing when identifying the bottled water. C The evidence suggests that these subjects were simply guessing when identifying the bottled water.
• (Choice A)   She would have rejected H a ‍   . A She would have rejected H a ‍   .
• (Choice B)   She would have accepted H 0 ‍   . B She would have accepted H 0 ‍   .
• (Choice C)   She would have rejected H 0 ‍   and accepted H a ‍   . C She would have rejected H 0 ‍   and accepted H a ‍   .
• (Choice D)   She would have reached the same conclusion using either α = 0.05 ‍   or α = 0.10 ‍   . D She would have reached the same conclusion using either α = 0.05 ‍   or α = 0.10 ‍   .
• (Choice A)   The evidence suggests that these bags are being filled with a mean amount that is different than 7.4  kg ‍   . A The evidence suggests that these bags are being filled with a mean amount that is different than 7.4  kg ‍   .
• (Choice B)   We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4  kg ‍   . B We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4  kg ‍   .
• (Choice C)   The evidence suggests that these bags are being filled with a mean amount of 7.4  kg ‍   . C The evidence suggests that these bags are being filled with a mean amount of 7.4  kg ‍   .
• (Choice A)   They would have rejected H a ‍   . A They would have rejected H a ‍   .
• (Choice B)   They would have accepted H 0 ‍   . B They would have accepted H 0 ‍   .
• (Choice C)   They would have failed to reject H 0 ‍   . C They would have failed to reject H 0 ‍   .
• (Choice D)   They would have reached the same conclusion using either α = 0.05 ‍   or α = 0.01 ‍   . D They would have reached the same conclusion using either α = 0.05 ‍   or α = 0.01 ‍   .

## Ethics and the significance level α ‍

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• How to Write Discussions and Conclusions

The discussion section contains the results and outcomes of a study. An effective discussion informs readers what can be learned from your experiment and provides context for the results.

## What makes an effective discussion?

When you’re ready to write your discussion, you’ve already introduced the purpose of your study and provided an in-depth description of the methodology. The discussion informs readers about the larger implications of your study based on the results. Highlighting these implications while not overstating the findings can be challenging, especially when you’re submitting to a journal that selects articles based on novelty or potential impact. Regardless of what journal you are submitting to, the discussion section always serves the same purpose: concluding what your study results actually mean.

A successful discussion section puts your findings in context. It should include:

• the results of your research,
• a discussion of related research, and
• a comparison between your results and initial hypothesis.

Tip: Not all journals share the same naming conventions.

Our Early Career Researcher community tells us that the conclusion is often considered the most difficult aspect of a manuscript to write. To help, this guide provides questions to ask yourself, a basic structure to model your discussion off of and examples from published manuscripts.

• Was my hypothesis correct?
• If my hypothesis is partially correct or entirely different, what can be learned from the results?
• How do the conclusions reshape or add onto the existing knowledge in the field? What does previous research say about the topic?
• Why are the results important or relevant to your audience? Do they add further evidence to a scientific consensus or disprove prior studies?
• How can future research build on these observations? What are the key experiments that must be done?
• What is the “take-home” message you want your reader to leave with?

## How to structure a discussion

Trying to fit a complete discussion into a single paragraph can add unnecessary stress to the writing process. If possible, you’ll want to give yourself two or three paragraphs to give the reader a comprehensive understanding of your study as a whole. Here’s one way to structure an effective discussion:

## Writing Tips

While the above sections can help you brainstorm and structure your discussion, there are many common mistakes that writers revert to when having difficulties with their paper. Writing a discussion can be a delicate balance between summarizing your results, providing proper context for your research and avoiding introducing new information. Remember that your paper should be both confident and honest about the results!

• Read the journal’s guidelines on the discussion and conclusion sections. If possible, learn about the guidelines before writing the discussion to ensure you’re writing to meet their expectations.
• Begin with a clear statement of the principal findings. This will reinforce the main take-away for the reader and set up the rest of the discussion.
• Explain why the outcomes of your study are important to the reader. Discuss the implications of your findings realistically based on previous literature, highlighting both the strengths and limitations of the research.
• State whether the results prove or disprove your hypothesis. If your hypothesis was disproved, what might be the reasons?
• Introduce new or expanded ways to think about the research question. Indicate what next steps can be taken to further pursue any unresolved questions.
• If dealing with a contemporary or ongoing problem, such as climate change, discuss possible consequences if the problem is avoided.
• Be concise. Adding unnecessary detail can distract from the main findings.

## Don’t

• Rewrite your abstract. Statements with “we investigated” or “we studied” generally do not belong in the discussion.
• Include new arguments or evidence not previously discussed. Necessary information and evidence should be introduced in the main body of the paper.
• Apologize. Even if your research contains significant limitations, don’t undermine your authority by including statements that doubt your methodology or execution.
• Shy away from speaking on limitations or negative results. Including limitations and negative results will give readers a complete understanding of the presented research. Potential limitations include sources of potential bias, threats to internal or external validity, barriers to implementing an intervention and other issues inherent to the study design.
• Overstate the importance of your findings. Making grand statements about how a study will fully resolve large questions can lead readers to doubt the success of the research.

Snippets of Effective Discussions:

Consumer-based actions to reduce plastic pollution in rivers: A multi-criteria decision analysis approach

Identifying reliable indicators of fitness in polar bears

• How to Write a Great Title
• How to Write an Abstract
• How to Write Your Methods
• How to Report Statistics
• How to Edit Your Work

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• Science Writing

## How to Write a Good Lab Conclusion in Science

Last Updated: June 18, 2024 Fact Checked

This article was co-authored by Bess Ruff, MA . Bess Ruff is a Geography PhD student at Florida State University. She received her MA in Environmental Science and Management from the University of California, Santa Barbara in 2016. She has conducted survey work for marine spatial planning projects in the Caribbean and provided research support as a graduate fellow for the Sustainable Fisheries Group. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,766,585 times.

A lab report describes an entire experiment from start to finish, outlining the procedures, reporting results, and analyzing data. The report is used to demonstrate what has been learned, and it will provide a way for other people to see your process for the experiment and understand how you arrived at your conclusions. The conclusion is an integral part of the report; this is the section that reiterates the experiment’s main findings and gives the reader an overview of the lab trial. Writing a solid conclusion to your lab report will demonstrate that you’ve effectively learned the objectives of your assignment.

• Restate : Restate the lab experiment by describing the assignment.
• Explain : Explain the purpose of the lab experiment. What were you trying to figure out or discover? Talk briefly about the procedure you followed to complete the lab.
• Results : Explain your results. Confirm whether or not your hypothesis was supported by the results.
• Uncertainties : Account for uncertainties and errors. Explain, for example, if there were other circumstances beyond your control that might have impacted the experiment’s results.
• New : Discuss new questions or discoveries that emerged from the experiment.

• Your assignment may also have specific questions that need to be answered. Make sure you answer these fully and coherently in your conclusion.

## Discussing the Experiment and Hypothesis

• If you tried the experiment more than once, describe the reasons for doing so. Discuss changes that you made in your procedures.
• Brainstorm ways to explain your results in more depth. Go back through your lab notes, paying particular attention to the results you observed. [3] X Trustworthy Source University of North Carolina Writing Center UNC's on-campus and online instructional service that provides assistance to students, faculty, and others during the writing process Go to source

• Start this section with wording such as, “The results showed that…”
• You don’t need to give the raw data here. Just summarize the main points, calculate averages, or give a range of data to give an overall picture to the reader.
• Make sure to explain whether or not any statistical analyses were significant, and to what degree, such as 1%, 5%, or 10%.

• Use simple language such as, “The results supported the hypothesis,” or “The results did not support the hypothesis.”

## Demonstrating What You Have Learned

• If it’s not clear in your conclusion what you learned from the lab, start off by writing, “In this lab, I learned…” This will give the reader a heads up that you will be describing exactly what you learned.
• Add details about what you learned and how you learned it. Adding dimension to your learning outcomes will convince your reader that you did, in fact, learn from the lab. Give specifics about how you learned that molecules will act in a particular environment, for example.
• Describe how what you learned in the lab could be applied to a future experiment.

• On a new line, write the question in italics. On the next line, write the answer to the question in regular text.

• If your experiment did not achieve the objectives, explain or speculate why not.

• This can often set you apart from your classmates, many of whom will just write up the barest of discussion and conclusion.

## Community Q&A

• Ensure the language used is straightforward with specific details. Try not to drift off topic. Thanks Helpful 1 Not Helpful 0
• Once again, avoid using personal pronouns (I, myself, we, our group) in a lab report. The first-person point-of-view is often seen as subjective, whereas science is based on objectivity. Thanks Helpful 1 Not Helpful 0
• If you include figures or tables in your conclusion, be sure to include a brief caption or label so that the reader knows what the figures refer to. Also, discuss the figures briefly in the text of your report. Thanks Helpful 1 Not Helpful 0

• Take care with writing your lab report when working in a team setting. While the lab experiment may be a collaborative effort, your lab report is your own work. If you copy sections from someone else’s report, this will be considered plagiarism. Thanks Helpful 4 Not Helpful 0

## You Might Also Like

• ↑ https://phoenixcollege.libguides.com/LabReportWriting/introduction
• ↑ https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/english/literacy/Pages/puttingittogether.aspx
• ↑ https://writingcenter.unc.edu/tips-and-tools/brainstorming/
• ↑ http://www.socialresearchmethods.net/kb/hypothes.php
• ↑ https://libguides.usc.edu/writingguide/conclusion
• ↑ https://libguides.usc.edu/writingguide/introduction/researchproblem
• ↑ http://writingcenter.unc.edu/handouts/scientific-reports/
• ↑ https://phoenixcollege.libguides.com/LabReportWriting/labreportstyle

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Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including:

• Defining the term “hypothesis”
• Providing hypothesis examples
• Giving you tips for how to write your own hypothesis

So let’s get started!

## What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid.

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Forming a hypothesis
• Analyze the data

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

## Independent and Dependent Variables

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable.

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets.

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

## Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement!

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.

## The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

## #1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life:

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party.
• If I study every night this week, I’ll get a better grade on my exam.

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades).

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

## #2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say:

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.”

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis!

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship.

## 4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

## #1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think.

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example:

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.”

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

## #2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible.

Good hypotheses ensure that you can observe the results.

## #3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable.

In writing your hypothesis, always keep in mind how you'll execute the experiment.

## #4: Generalizability

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

## Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

## Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour.

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

## Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like:

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

## Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment.

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this:

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

## Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while:

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again!

## Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

## What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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## What Is a Hypothesis? (Science)

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A hypothesis (plural hypotheses) is a proposed explanation for an observation. The definition depends on the subject.

In science, a hypothesis is part of the scientific method. It is a prediction or explanation that is tested by an experiment. Observations and experiments may disprove a scientific hypothesis, but can never entirely prove one.

In the study of logic, a hypothesis is an if-then proposition, typically written in the form, "If X , then Y ."

In common usage, a hypothesis is simply a proposed explanation or prediction, which may or may not be tested.

## Writing a Hypothesis

Most scientific hypotheses are proposed in the if-then format because it's easy to design an experiment to see whether or not a cause and effect relationship exists between the independent variable and the dependent variable . The hypothesis is written as a prediction of the outcome of the experiment.

## Null Hypothesis and Alternative Hypothesis

Statistically, it's easier to show there is no relationship between two variables than to support their connection. So, scientists often propose the null hypothesis . The null hypothesis assumes changing the independent variable will have no effect on the dependent variable.

In contrast, the alternative hypothesis suggests changing the independent variable will have an effect on the dependent variable. Designing an experiment to test this hypothesis can be trickier because there are many ways to state an alternative hypothesis.

For example, consider a possible relationship between getting a good night's sleep and getting good grades. The null hypothesis might be stated: "The number of hours of sleep students get is unrelated to their grades" or "There is no correlation between hours of sleep and grades."

An experiment to test this hypothesis might involve collecting data, recording average hours of sleep for each student and grades. If a student who gets eight hours of sleep generally does better than students who get four hours of sleep or 10 hours of sleep, the hypothesis might be rejected.

But the alternative hypothesis is harder to propose and test. The most general statement would be: "The amount of sleep students get affects their grades." The hypothesis might also be stated as "If you get more sleep, your grades will improve" or "Students who get nine hours of sleep have better grades than those who get more or less sleep."

In an experiment, you can collect the same data, but the statistical analysis is less likely to give you a high confidence limit.

Usually, a scientist starts out with the null hypothesis. From there, it may be possible to propose and test an alternative hypothesis, to narrow down the relationship between the variables.

## Example of a Hypothesis

Examples of a hypothesis include:

• If you drop a rock and a feather, (then) they will fall at the same rate.
• Plants need sunlight in order to live. (if sunlight, then life)
• Eating sugar gives you energy. (if sugar, then energy)
• White, Jay D.  Research in Public Administration . Conn., 1998.
• Schick, Theodore, and Lewis Vaughn.  How to Think about Weird Things: Critical Thinking for a New Age . McGraw-Hill Higher Education, 2002.
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• How to conclude an essay | Interactive example

## How to Conclude an Essay | Interactive Example

Published on January 24, 2019 by Shona McCombes . Revised on July 23, 2023.

The conclusion is the final paragraph of your essay . A strong conclusion aims to:

• Tie together the essay’s main points
• Show why your argument matters
• Leave the reader with a strong impression

Your conclusion should give a sense of closure and completion to your argument, but also show what new questions or possibilities it has opened up.

This conclusion is taken from our annotated essay example , which discusses the history of the Braille system. Hover over each part to see why it’s effective.

Braille paved the way for dramatic cultural changes in the way blind people were treated and the opportunities available to them. Louis Braille’s innovation was to reimagine existing reading systems from a blind perspective, and the success of this invention required sighted teachers to adapt to their students’ reality instead of the other way around. In this sense, Braille helped drive broader social changes in the status of blindness. New accessibility tools provide practical advantages to those who need them, but they can also change the perspectives and attitudes of those who do not.

## Instantly correct all language mistakes in your text

Step 1: return to your thesis, step 2: review your main points, step 3: show why it matters, what shouldn’t go in the conclusion, more examples of essay conclusions, other interesting articles, frequently asked questions about writing an essay conclusion.

To begin your conclusion, signal that the essay is coming to an end by returning to your overall argument.

Don’t just repeat your thesis statement —instead, try to rephrase your argument in a way that shows how it has been developed since the introduction.

## Prevent plagiarism. Run a free check.

Next, remind the reader of the main points that you used to support your argument.

Avoid simply summarizing each paragraph or repeating each point in order; try to bring your points together in a way that makes the connections between them clear. The conclusion is your final chance to show how all the paragraphs of your essay add up to a coherent whole.

To wrap up your conclusion, zoom out to a broader view of the topic and consider the implications of your argument. For example:

• Does it contribute a new understanding of your topic?
• Does it raise new questions for future study?
• Does it lead to practical suggestions or predictions?
• Can it be applied to different contexts?
• Can it be connected to a broader debate or theme?

Try to end with a strong, decisive sentence, leaving the reader with a lingering sense of interest in your topic.

The easiest way to improve your conclusion is to eliminate these common mistakes.

## Don’t include new evidence

Any evidence or analysis that is essential to supporting your thesis statement should appear in the main body of the essay.

The conclusion might include minor pieces of new information—for example, a sentence or two discussing broader implications, or a quotation that nicely summarizes your central point. But it shouldn’t introduce any major new sources or ideas that need further explanation to understand.

## Don’t use “concluding phrases”

Avoid using obvious stock phrases to tell the reader what you’re doing:

• “In conclusion…”
• “To sum up…”

These phrases aren’t forbidden, but they can make your writing sound weak. By returning to your main argument, it will quickly become clear that you are concluding the essay—you shouldn’t have to spell it out.

Avoid using apologetic phrases that sound uncertain or confused:

• “This is just one approach among many.”
• “There are good arguments on both sides of this issue.”
• “There is no clear answer to this problem.”

Even if your essay has explored different points of view, your own position should be clear. There may be many possible approaches to the topic, but you want to leave the reader convinced that yours is the best one!

## Here's why students love Scribbr's proofreading services

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This conclusion is taken from an argumentative essay about the internet’s impact on education. It acknowledges the opposing arguments while taking a clear, decisive position.

The internet has had a major positive impact on the world of education; occasional pitfalls aside, its value is evident in numerous applications. The future of teaching lies in the possibilities the internet opens up for communication, research, and interactivity. As the popularity of distance learning shows, students value the flexibility and accessibility offered by digital education, and educators should fully embrace these advantages. The internet’s dangers, real and imaginary, have been documented exhaustively by skeptics, but the internet is here to stay; it is time to focus seriously on its potential for good.

This conclusion is taken from a short expository essay that explains the invention of the printing press and its effects on European society. It focuses on giving a clear, concise overview of what was covered in the essay.

The invention of the printing press was important not only in terms of its immediate cultural and economic effects, but also in terms of its major impact on politics and religion across Europe. In the century following the invention of the printing press, the relatively stationary intellectual atmosphere of the Middle Ages gave way to the social upheavals of the Reformation and the Renaissance. A single technological innovation had contributed to the total reshaping of the continent.

This conclusion is taken from a literary analysis essay about Mary Shelley’s Frankenstein . It summarizes what the essay’s analysis achieved and emphasizes its originality.

By tracing the depiction of Frankenstein through the novel’s three volumes, I have demonstrated how the narrative structure shifts our perception of the character. While the Frankenstein of the first volume is depicted as having innocent intentions, the second and third volumes—first in the creature’s accusatory voice, and then in his own voice—increasingly undermine him, causing him to appear alternately ridiculous and vindictive. Far from the one-dimensional villain he is often taken to be, the character of Frankenstein is compelling because of the dynamic narrative frame in which he is placed. In this frame, Frankenstein’s narrative self-presentation responds to the images of him we see from others’ perspectives. This conclusion sheds new light on the novel, foregrounding Shelley’s unique layering of narrative perspectives and its importance for the depiction of character.

If you want to know more about AI tools , college essays , or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!

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• A rephrased version of your overall thesis
• A brief review of the key points you made in the main body
• An indication of why your argument matters

The conclusion may also reflect on the broader implications of your argument, showing how your ideas could applied to other contexts or debates.

For a stronger conclusion paragraph, avoid including:

• Important evidence or analysis that wasn’t mentioned in the main body
• Generic concluding phrases (e.g. “In conclusion…”)
• Weak statements that undermine your argument (e.g. “There are good points on both sides of this issue.”)

The conclusion paragraph of an essay is usually shorter than the introduction . As a rule, it shouldn’t take up more than 10–15% of the text.

## Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, July 23). How to Conclude an Essay | Interactive Example. Scribbr. Retrieved June 18, 2024, from https://www.scribbr.com/academic-essay/conclusion/

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• http://orcid.org/0000-0001-8246-1684 Tanja Bedke 1 , 2 ,
• Friederike Stumme 1 , 2 ,
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• 1 I. Department of Medicine, Section of Molecular Immunology and Gastroenterology , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
• 2 Hamburg Center for Translational Immunology (HCTI) , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
• 3 Center of Diagnostics, Institute of Pathology , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
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• 5 I.Department of Medicine , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
• 6 Center for Experimental Medicine, Institute of Experimental Immunology and Hepatology , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
• 7 Martin Zeitz Center for Rare Diseases , University Medical Center Hamburg-Eppendorf , Hamburg , Germany
• Correspondence to Professor Samuel Huber, I. Department of Medicine, University Medical Center Hamburg-Eppendorf, Hamburg 20246, Germany; shuber{at}uke.de

Objective There is a strong clinical association between IBD and primary sclerosing cholangitis (PSC), a chronic disease of the liver characterised by biliary inflammation that leads to strictures and fibrosis. Approximately 60%–80% of people with PSC will also develop IBD (PSC-IBD). One hypothesis explaining this association would be that PSC drives IBD. Therefore, our aim was to test this hypothesis and to decipher the underlying mechanism.

Design Colitis severity was analysed in experimental mouse models of colitis and sclerosing cholangitis, and people with IBD and PSC-IBD. Foxp3 + Treg-cell infiltration was assessed by qPCR and flow cytometry. Microbiota profiling was carried out from faecal samples of people with IBD, PSC-IBD and mouse models recapitulating these diseases. Faecal microbiota samples collected from people with IBD and PSC-IBD were transplanted into germ-free mice followed by colitis induction.

Results We show that sclerosing cholangitis attenuated IBD in mouse models. Mechanistically, sclerosing cholangitis causes an altered intestinal microbiota composition, which promotes Foxp3 + Treg-cell expansion, and thereby protects against IBD. Accordingly, sclerosing cholangitis promotes IBD in the absence of Foxp3 + Treg cells. Furthermore, people with PSC-IBD have an increased Foxp3 + expression in the colon and an overall milder IBD severity. Finally, by transplanting faecal microbiota into gnotobiotic mice, we showed that the intestinal microbiota of people with PSC protects against colitis.

Conclusion This study shows that PSC attenuates IBD and provides a comprehensive insight into the mechanisms involved in this effect.

• INFLAMMATORY BOWEL DISEASE
• Cholangitis
• PRIMARY SCLEROSING CHOLANGITIS
• COLONIC MICROFLORA

## Data availability statement

Data are available upon reasonable request. All data relevant to the study are included in the article or uploaded as supplementary information.

This is an open access article distributed in accordance with the Creative Commons Attribution 4.0 Unported (CC BY 4.0) license, which permits others to copy, redistribute, remix, transform and build upon this work for any purpose, provided the original work is properly cited, a link to the licence is given, and indication of whether changes were made. See: https://creativecommons.org/licenses/by/4.0/ .

https://doi.org/10.1136/gutjnl-2023-330856

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## WHAT IS ALREADY KNOWN ON THIS TOPIC

There is a strong clinical association between IBD and primary sclerosing cholangitis (PSC). However, currently it is unknown, if this association is due to common genetic polymorphisms or if PSC may drive IBD.

Unexpectedly, we found that PSC attenuates IBD. Mechanistically, PSC causes an altered intestinal microbiota composition, which promotes Foxp3 + Treg-cell expansion, and thereby protects against IBD.

## HOW THIS STUDY MIGHT AFFECT RESEARCH, PRACTICE OR POLICY

We believe that our data build a basis for the development of new therapeutical strategies targeting the microbiota-Foxp3 + Treg-cell axis in IBD.

## Introduction

IBD is characterised by chronic relapsing intestinal inflammation. The exact aetiology of IBD is not completely understood, but it is known that IBD is characterised by chronic inflammation, intestinal dysbiosis and mucosal barrier defects. Thus, one hypothesis is that IBD is a result of an aberrant immune response against intestinal bacteria in genetically susceptible individuals. 1–3 There is a strong clinical association between IBD and primary sclerosing cholangitis (PSC), a chronic, cholestatic liver disease characterised by inflammation and fibrosis of the bile ducts inside and outside the liver. Approximately 60%–80% of people with PSC have concomitant IBD (from here on referred to as PSC-IBD). 1 4 Conversely, only about 5% of people with IBD will develop PSC during their disease course. 2 Notably, people suffering from PSC-IBD have a phenotype distinct from Crohn’s disease (CD) and Ulcerative colitis (UC), characterised by an overall milder IBD severity, a higher prevalence of right-sided predominant pancolitis, rectal sparing, backwash ileitis and an increased risk of developing colorectal neoplasia. 3 5 Even for people with PSC without clinically manifested IBD, we have previously shown that a high proportion exhibits molecular signs of intestinal inflammation, characterised by immune cell infiltration and expression of proinflammatory cytokines in intestinal biopsies. 6

The factors that contribute to the development of PSC-IBD are not yet understood. Previous studies suggest a critical role of CD4 + Foxp3 + regulatory T cells (Foxp3 + Treg) in IBD, as well as PSC. 7–9 In line with these data, reduced Foxp3 + Treg-cell numbers and function were associated with single nucleotide polymorphisms in the IL2RA gene present in people with IBD and PSC. 10–12 Interestingly, the microbiota plays a key role in the emergence of Foxp3 + Treg cells: microbiota-derived short-chain fatty acids (SCFAs) can facilitate the induction of Foxp3 + Treg cells both in in vitro and in animal models. 13 14 Accordingly, aside from genetic predispositions in genes regulating Foxp3 + Treg-cell function, the intestinal microbiota has been suggested to be one of the contributing factors for the close association of IBD and PSC. 15 Indeed, both IBD and PSC are characterised by intestinal dysbiosis. Moreover, direct comparisons revealed distinct microbiota compositions between these diseases. 16–22 Thus, among others, the phylae Veillonella and Escherichia have been reported to be enriched in people with PSC-IBD compared with IBD alone, that are proposed to promote immune cell migration to the gut. In addition, bacteria of the Lachnospiraceae family which produce anti-inflammatory SCFAs were reported to be increased in people with PSC. 23 However, it remains unclear, whether changes in the microbial composition caused by PSC lead to an altered Foxp3 + Treg-cell expansion and function that contributes to the phenotype of IBD in people with PSC.

Taken together, there is a clear connection between IBD and PSC. However, whether PSC increases the risk for IBD but attenuates its phenotype remains to be elucidated. In this study we combined cellular and microbial analyses from experimental mouse models of colitis and sclerosing cholangitis, biopsies and stool samples of people with PSC-IBD and IBD, and then performed human faecal microbiota transplantation (FMT) into gnotobiotic mice to decipher the impact of PSC on IBD.

## Experimental sclerosing cholangitis attenuates colitis severity and increases Foxp3 + Treg-cell frequency in mice

First, we aimed to test the connection between IBD and sclerosing cholangitis in experimental mouse models. To this end, Il10 −/− mice, which develop spontaneous colitis 24 were crossed to Mdr2 −/− mice, a mouse model for experimental sclerosing cholangitis 25 ( figure 1A ). As expected, Il10 −/− Mdr2 −/− mice, but not Il10 −/− mice, developed sclerosing cholangitis based on increased transaminase AST and ALT levels, and fibrosis score ( online supplemental figure S1A,B ). Next, we assessed IBD severity. We found that Il10 −/− and Il10 −/− Mdr2 −/− mice developed an overall mild colitis ( figure 1B,C ). Interestingly, Il10 −/− Mdr2 −/− mice with a concomitant experimental sclerosing cholangitis developed significantly reduced colitis compared with Il10 −/− mice ( figure 1C ). However, there was little impact on weight, despite the differences observed in colitis severity using endoscopy. Of note, we aimed to induce a mild to moderate colitis severity in our experiments in order to limit the suffering of the animals. Thus, all mice showed a relatively mild weight loss, and we therefore may have not observed a difference. Moreover, while colonic CD4 + T-cell infiltration was comparable between the groups ( figure 1D ), the proportion of Foxp3 + Treg cells within the CD4 + T-cell population was significantly increased in the inflamed colon of Il10 −/− Mdr2 −/− compared with Il10 −/− mice ( figure 1D,E ).

## Supplemental material

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Spontaneous colitis is reduced in mice with concomitant experimental primary sclerosing cholangitis in Il10 −/− Mdr2 −/− mice. (A) Graphical breeding scheme for generation of Il10 −/− and Il10 −/− Mdr2 −/− littermates. Mice were bred under specific pathogen-free (SPF) conditions in the local mouse facility (MB1). After weening, litters were separated with respect to their genotype. At an age of 12 weeks, (B) body weight (n=22 Il10 −/− , n=16 Il10 −/− Mdr2 −/− ) and (C) colon inflammation was assessed by mouse colonoscopy (n=25 Il10 −/− , n=13 Il10 −/− Mdr2 −/− ), as described in material and methods. (D, E) Flow cytometry analysis of colon infiltrating CD4 + T-cell (n=17 Il10 −/− , n=13 Il10 −/− Mdr2 −/− ) and Foxp3 + Treg-cell frequencies of 12 weeks old mice (n=12 Il10 −/− , n=10 Il10 −/− Mdr2 −/− ). (F) Graphical breeding scheme for generation of Il10 −/− and Il10 −/− Mdr2 −/− littermates bred in the presence of a colitogenic SPF microbiome (MB2) containing Helicobacter hepaticus , that was transferred to the founding animals. After weening, litters were separated with respect to their genotype. At the age of 12 weeks (G) body weight (n=8 Il10 −/− , n=13 Il10 −/− Mdr2 −/− ), (H) colonoscopy (n=8 Il10 −/− , n=12 Il10 −/− Mdr2 −/− ) and (I, J) frequencies of colon infiltrating CD4 + T cells and Foxp3 + Treg cells (n=6 Il10 −/− , n=11 Il10 −/− Mdr2 −/− ) were analysed. For statistical analysis, Mann-Whitney U test was performed.

The intestinal microbiota composition is known to impact colitis-susceptibility 26 . Therefore the colitis development we observed in Il10 −/− mice under specific pathogen-free (SPF) conditions of the local mouse facility (referred to as MB1) was generally mild. To this end, we next aimed to determine spontaneous colitis development in Il10 −/− mice bred in the presence of a colitogenic SPF microbiota, that showed a distinct beta diversity compared with MB1, including an enrichment of Helicobacter on genus level (referred to as MB2) ( online supplemental figure S2A,B ; figure 1F ). As expected, the mice bred under MB2 conditions showed an overall increased susceptibility to developing colitis compared with mice with MB1 microbiota ( figure 1C,H ). Comparisons between Il10 −/− and Il10 −/− Mdr2 −/− mice bred under MB2 conditions revealed no differences in body weight between the groups ( figure 1G ). However, colitis severity in Il10 −/− Mdr2 −/− mice with concomitant sclerosing cholangitis ( online supplemental figure S1C,D ) was significantly reduced compared with Il10 −/− mice ( figure 1H ). Moreover, Il10 −/− Mdr2 −/− mice bred under MB2 condition showed reduced colonic CD4 + T-cell infiltration and increased Foxp3 + Treg-cell accumulation compared with Il10 −/− mice ( figure 1I,J ).

Next, we aimed to validate our observation in Il10 −/− Mdr2 −/− mice using a second model of experimental sclerosing cholangitis. To this end, we fed Il10 −/− mice a 3,5-diethoxycarbonyl-1,4-dihydrocollidine (DDC) diet. 27 We used mice with the more colitogenic MB2 microbiota ( figure 2A ). DDC diet-induced sclerosing cholangitis in Il10 −/− mice as determined by blood transaminase levels and fibrosis development ( online supplemental figure S3A,B ). In line with our results in Il10 −/− Mdr2 −/− mice, colitis severity and CD4 + T-cell infiltration in the inflamed colon of Il10 −/− mice was attenuated under the DDC diet ( figure 2B ), and frequencies of colonic Foxp3 + Treg cells were increased compared with the regular chow diet ( figure 2C,D ).

Spontaneous colitis is reduced in Il10 −/− mice with concomitant 3,5-diethoxycarbonyl-1,4-dihydrocollidine (DDC)-mediated liver cholestasis. (A) Graphical scheme of the experimental setup. At an age of 6–8 weeks Il10 −/− mice were gavaged with MB2. Four weeks after reconstitution, liver cholestasis was induced by 0.1% DDC feeding supplemented into the normal chow diet. After 8 days, (B) colonic inflammation was analysed by mouse colonoscopy (n=22 mice per group). (C, D) On day 9, mice were sacrificed and frequencies of colon infiltrating CD4 + T cells and Foxp3 + Treg cells were analysed using flow cytometry (8=mice per group). For statistical analysis Mann-Whitney U test was performed.

Thus, sclerosing cholangitis attenuates colitis severity in mouse models and is associated with an increased colonic Foxp3 + Treg-cell frequency.

## Attenuated colitis severity in mice with sclerosing cholangitis is dependent on Foxp3 + Treg cells

Since the reduced colitis severity was associated with a shift of CD4 + T-cell infiltration towards Foxp3 + Treg cells, we hypothesised that Foxp3 + Treg cells contribute to the limitation of colonic inflammation. Foxp3 + Treg cells are well known for their capacity to limit intestinal inflammation and restore immune homeostasis. 28 Thus, to define the contribution of Foxp3 + Treg cells to the PSC-mediated attenuation of colitis, we used the T-cell transfer colitis model, in which Foxp3 + Treg cells are largely absent. 29 To that end, we induced colitis in lymphopenic Rag1 −/− and Rag1 −/− Mdr2 −/− mice, by transfer of naïve CD4 + Foxp3 − CD45RB high cells ( figure 3A ). As expected, Rag1 −/− Mdr2 −/− mice, but not Rag1 −/− mice developed concomitant sclerosing cholangitis ( online supplemental figure S4,B ). Next, we assessed colitis severity and found it not to be attenuated in Rag1 −/− Mdr2 −/− mice, but in fact to be significantly increased compared with Rag1 −/− based on weight loss and endoscopic score ( figure 3B,C ). As expected, no considerable Foxp3 + Treg-cell levels were detectable among CD4 + T-cell infiltrating cells ( figure 3D,E ).

Increased colitis manifestation in Rag1 −/− Mdr2 −/− mice after Foxp3 − CD45RB high T-cell transfer. (A) Graphical scheme of the experimental setup. (B) At an age of 8–10 weeks Rag1 −/− and Rag1 −/− Mdr2 −/− mice were gavaged with MB2. After 4 weeks of reconstitution, colitis was induced on transfer of flow cytometry sorted Foxp3 − CD45RB high CD4 + T cells, isolated from Foxp3-RFP reporter mice. After 13 days of T-cell reconstitution, (B) weight loss and (C) colonic inflammation by colonoscopy were analysed (n=13 Rag1 −/− , n=12 Rag1 −/− Mdr2 −/− ). (D, E) At day 14, mice were sacrificed and frequencies of colon infiltrating CD4 + T cells and Foxp3 + Treg cells were analysed by flow cytometry in one of three experiments (n=4 Rag1 −/− n=4 Rag1 −/− Mdr2 −/− ). For statistical analysis Mann-Whitney U test was performed.

Taken together, the protective effect of sclerosing cholangitis on colitis appears to be dependent on the presence of Foxp3 + Treg cells.

## FMT from Mdr2 −/− mice into germ-free wild-type mice attenuates colitis severity

Alterations in the intestinal microbiota are a hallmark of IBD. 30 Moreover, the intestinal microbiota is known to impact Foxp3 + Treg-cell differentiation and expansion. 31 We therefore hypothesised that sclerosing cholangitis may alter the intestinal microbiota, and thus, reduce colitis severity. In order to test this hypothesis, we profiled the microbiota of stool samples collected from mice suffering from colitis alone (eg, Il10 −/− mice and Rag1 −/− mice on colitis induction via transfer of CD45Rb high cells) and with concomitant sclerosing cholangitis (eg, Il10 −/− Mdr2 −/− mice and Rag1 −/− Mdr2 −/− mice on colitis induction via transfer of CD45Rb high cells) ( online supplemental figure S5 ). Comparison of beta diversities revealed clustering with some overlap of both experimental groups ( online supplemental figure S5A,C ), although a spread of samples between the groups was detected in both models. Of note, on the genus level, we found several taxa that significantly differed in abundance between the groups in the transfer colitis model ( online supplemental figure S5D ), but only one taxon in the Il10 −/− model ( online supplemental figure S5B ). Most notably, an enrichment of genera of the Lachnospiraceae family was found in stool samples of mice suffering from colitis with concomitant liver inflammation in transfer colitis ( online supplemental figure S5D ).

To decipher the functional relevance of the observed PSC-induced microbiota alterations on colitis severity, we next reconstituted germ-free wild-type mice with stool derived from mice with sclerosing cholangitis ( Mdr2 −/− mice) or without sclerosing cholangitis (wild-type mice), respectively, and induced colitis in these mice using a blocking anti-IL10Rα mAb 32 ( figure 4A ). In accordance with our above-mentioned results ( figure 1B,G ), a mild weight loss was observed on colitis induction, that did not differ between the groups ( figure 4B ). However, endoscopic colitis severity was reduced in germ-free mice reconstituted with microbiota derived from Mdr2 −/− mice compared with wild-type mice ( figure 4C ).

Reduced colitis severity in germ-free wild-type mice after transfer of Mdr2 −/− microbiota. (A) Graphical scheme of the experimental procedure. In brief, faecal microbiota obtained from wild-type and Mdr2 −/− mice, harbouring MB2 microbiome, was gavaged into germ-free wild-type mice. One day later, colitis was induced in these mice by intraperitoneal injection of 0.25 mg anti-IL10Rα antibody per mouse two times a week. After 13 days of colitis induction, (B) weight loss was determined and (C) colonic inflammation was analysed by colonoscopy (n=9 WT-FMT, n=10 Mdr2 −/− -FMT). FMT, faecal microbiota transplantation; WT, wild-type.

Taken together, these results indicate that sclerosing cholangitis leads to alterations in the intestinal microbiota, in particular to an enrichment in genera of the Lachnospiraceae family. Furthermore, this altered intestinal microbiota of Mdr2 −/− mice suffering from sclerosing cholangitis is protective against colitis, when compared with wild-type mice.

## Colitis severity in germ-free mice is attenuated after FMT from people with PSC-IBD compared with IBD

Based on the data obtained in the murine system, we next characterised FOXP3 mRNA expression levels in intestinal biopsies taken from a cohort of people with CD (n=29), UC (n=22) and PSC-IBD (n=41). We observed increased FOXP3 mRNA expression in the intestinal tissue of people with PSC-IBD compared with both, individuals with CD and UC ( figure 5A ). Within the cohort, we found milder IBD severity in people with concomitant PSC compared with people with CD and to a lesser extent to people with UC, as described previously ( figure 5B ). 5 To account for this bias in disease severity, we next compared only those individuals with a clinically active disease as assessed by their physician. We again found an increased FOXP3 mRNA expression in the intestinal tissue of people with PSC-IBD compared with both individuals with CD and UC ( figure 5C ). Of note, the mean IBD score in all three groups was low and comparable (mean IBD-score for PSC-IBD: 0.48, CD: 0.52, UC: 0.78). To further test, if this decrease is biased by biopsies from a certain location, we plotted all biopsies from the same location for all patients. We found the same trend in all locations analysed: individuals with PSC-IBD having a higher FOXP3 mRNA expression compared with people with IBD without PSC ( online supplemental figure S6A , online supplemental table S2 ). Next, we measured FOXP3 protein levels in tissue sections using immunohistochemistry. To this end we focused on biopsies from the terminal ileum and sigma/rectum. In line with the mRNA expression, we found an increased number of FOXP3 + cells in people with PSC-IBD compared with IBD without PSC ( online supplemental figure S6B,C ).

FOXP3 mRNA expression and endoscopic IBD scoring reveal reduced clinical manifestation of IBD in people with primary sclerosing cholangitis (PSC-IBD). Description of a cohort including 29 people with Crohn’s disease (CD), 22 with Ulcerative colitis (UC) and 41 with PSC-IBD. (A) FOXP3 mRNA expression levels were analysed from intestinal biopsies taken from the terminal ileum, ascending and descending colon and sigma/rectum from every person. (B) IBD severity was determined based on CDAI (persons with CD) and Mayo score (all other persons). Both scores were merged into a unified IBD score (healthy/remission: 0, mild: 1, moderate: 2, severe: 3 points). (C) FOXP3 mRNA expression levels were analysed from intestinal biopsies taken from the terminal ileum, ascending and descending colon and sigma/rectum from every person with clinically active disease. To test for significance MLEM, post hoc Dunnett test was used for (A and C). Fisher’s exact test was used for (B).

Next, we aimed to test whether the microbiota from people with PSC would protect against the development of concomitant IBD. Thus, we first performed microbiota profiling of mucosa-adherent bacteria isolated from intestinal biopsies derived from our IBD and PSC-IBD cohort, that has been partially published in Wittek et al, 2023. Sequencing of faecal microbiota revealed a large overlap, but also some differences in the microbiota composition of people with IBD and those with PSC-associated IBD. However, it is important to note that our study was not powered to decipher detailed microbiota differences between PSC-IBD and IBD as this point has been addressed by previous larger studies. 23 33 Beta diversity comparison revealed a large overlap between people with IBD and PSC-IBD ( figure 6A ). In fact, on the genus level only a few taxa differed in abundance between both groups ( figure 6B ). Interestingly, genera of the Lachnospiraceae family were enriched in intestinal biopsies from people with PSC-IBD compared with IBD. To test the functional relevancy of this finding, we reconstituted germ-free wild-type mice with faecal microbiota samples derived from people with IBD or PSC-IBD and induced DSS colitis on reconstitution ( figure 6C ). Weight loss was comparable in both groups ( figure 6D ). However, the colitis severity as assessed by endoscopy was significantly reduced in mice reconstituted with faecal microbiota from people with PSC-IBD compared with IBD alone ( figure 6E,F ). To address whether ursodeoxycholic acid (UDCA) treatment mediates the observed effect, we performed a gnotobiotic mouse experiment. Specifically, a faecal microbiota transfer from healthy control (HC), without UDCA treatment, and primary biliary cholangitis (PBC) patients, with UDCA treatment, into germ-free mice was performed. People with PBC with mild cholestasis comparable to that of people with PSC-IBD were selected as cholestatic controls ( online supplemental figure S7A,B ). On engraftment, DSS-colitis was induced. A comparable colitis severity was observed between these groups, indicating that UDCA does not per se influence the colitis activity ( online supplemental figure S7C,D ). Next, we analysed whether the observed protection of these PSC-IBD-specific gnotobiotic mice is associated with an enrichment of genera of the Lachnospiraceae family on FMT. Microbiota profiling of donors (see online supplemental table S1 for the clinical information) and recipient mice was performed and can be found in online supplemental figure S8A . A Permanova analysis showed a significant contribution of disease, group (donor vs recipient) and donor on the variation observed in the data ( online supplemental figure S8B ). The abundance of bacteria in the different donors is comparable to a cross-sectional cohort ( online supplemental figure S8C ). When looking at the 10 highest abundant families, we observed that these were in most cases distributed similarly between recipients of the same donor, although at different proportions compared with the donor ( online supplemental figure S8D ). Beta diversities showed some overlapping of clusters representing each of the groups ( figure 6G ). Indeed, a strong enrichment of genera of the Lachnospiraceae family was detectable in faecal samples of mice that had been reconstituted with PSC-IBD stool compared with IBD stool ( figure 6H ).

Colitis severity in germ-free mice is attenuated after FMT from people with primary sclerosing cholangitis and colitis (PSC-IBD), enriched for genera of the Lachnospiraceae family. Microbiota profiling was performed on mucosal tissue samples of our IBD and PSC-IBD cohort, as described in the material and methods. (A) PCoA of Bray-Curtis dissimilarities shows beta diversity across people with IBD and PSC-IBD. (B) Genera with significantly different abundance between people with IBD and PSC-IBD. (C) Graphical scheme of the protocol for faecal microbiota transplantation of stool derived from IBD or PSC-IBD patients into germ-free wild-type mice, and subsequent DSS colitis induction. After 9 days of colitis induction, (D) weight loss was determined and (E and F) colonic inflammation was analysed by colonoscopy (each dot represents one mouse). IBD activity of the donor is shown as: remission (black), mild (green), moderate (blue) and severe (red). (G and H) Microbiota profiling from stool samples collected from mice after reconstitution with stool samples from our IBD and PSC-IBD cohort. (D–H) n=21 mice transplanted with IBD stool; n=21 mice transplanted with PSC-IBD stool were used in four independent experiments.

In conclusion, these data indicate that PSC induces alterations of the intestinal microbiota, in particular an enrichment of genera of the Lachnospiraceae family, which in turn attenuate colitis susceptibility.

In line with previous reports, 3 5 we found that people with PSC-IBD present with milder colitis severity compared with people with IBD without PSC in our cohort. Likewise, we found a lower IBD susceptibility in a genetic ( Mdr2 −/− ) and an induced (DDC-diet) mouse model of sclerosing cholangitis.

Alterations in the intestinal microbiota of people with PSC-IBD and IBD without PSC have been documented in various studies. These studies have yielded somewhat divergent findings, 19 33 possibly due to variations in participant selection criteria, sampling locations and sample processing. Our study, along with several others, consistently identified an elevation in Lachnospiraceae among people with PSC-IBD compared with those with IBD without PSC. 17 23 It could be possible that cholestasis, which is observed in people with PSC mediates the observed effects on the intestinal microbiota. In this case a similar effect should be observed in people and mouse models with cholestasis even in the absence of PSC. Further studies will be critical to address this point.

We observed that the protective effect of sclerosing cholangitis on colitis susceptibility was transferable on faecal microbiota transfer from Mdr2 −/− mice and people with PSC-IBD into germ-free mice. Overall, we found genera of the Lachnospiraceae family to be abundant in the faecal samples of people with PSC used for the faecal microbiota transfer experiment. This finding is in line with a previous study by our group. 6 Importantly, genera of the Lachnospiraceae family were over-presented in faecal samples after engraftment of the germ-free mice, supporting the notion that these could be involved in the protective effect. However, there is still the limitation that the number of donors may not fully capture the range of microbiota variability in people with PSC. In line with this finding, a previous publication has reported that Mdr2 −/− mice treated with vancomycin, which reduced Lachnospiraceae and Clostridiaceae , had an increased liver pathology. Supplementation of these mice after antibiotic treatment with a 23 strain Lachnospiraceae consortium reduced histological liver inflammation and fibrosis. 22 Conversely, in people with PSC, the Lachnospiraceae Blautia (genus), Lachnospiraceae bacterium 1_4_56FAA was negatively correlated with the Mayo risk score. 22

Another important observation of this study is the association between increased Foxp3 + Treg-cell accumulation in the colon and over-representation of Lachnospiraceae in faecal samples. This has been observed in our mouse models of experimental sclerosing cholangitis with concomitant colitis, and in people with PSC-IBD compared with people suffering from IBD without PSC. Lachnospiraceae have indeed been associated with the production of SCFAs, 34 35 which in turn have been linked to the induction of Foxp3 + Treg cells. 35–38 Therefore, further assessment of SCFAs from faecal samples of our IBD and PSC-IBD cohort and mouse models of sclerosing cholangitis is required to test whether the enrichment in Lachnospiraceae is indeed associated with increased SCFA levels and subsequently increased Foxp3 + Treg-cell numbers.

One limitation of this study is that the role of Lachnospiraceae remains controversial. While some taxa produce butyrate, which can strengthen the intestinal barrier, others produce propionate, which can drive mucin degradation. 34 More in-depth analysis of this family of bacteria in people with PSC-IBD, for example, through metagenomics, could help to identify which taxa are involved and how their metabolites could influence IBD development. Similarly, another publication 39 showed an increase of Lachnospiraceae in faecal samples of Mdr2 −/− mice. Transfer of the dysbiotic Mdr2 −/− microbiota into healthy wild-type mice induced NLRP3 activation in the gut and the liver, which sustained liver injury and promoted disease progression. It would be important to further investigate the role of different taxa of Lachnospiraceae in the relationship of PSC and IBD.

Interestingly, a recent study identified Klebsiella pneumoniae in mesenteric lymph nodes of people with PSC, and also in faecal samples. 40 Subsequent studies revealed that K. pneumoniae causes disruption in the epithelial barrier, resulting in the translocation of bacteria and subsequent inflammation in the liver. These discoveries emphasise how pathobionts contribute to dysfunction in the intestinal barrier and inflammation in the liver. 40 Given the crucial role of the microbiome, it would be of interest to study whether the PSC microbiota can also modify complications of IBD in PSC, such as cancer risk.

The observation that people with PSC-IBD have a lower IBD activity on average, compared with people with IBD, 6 is also reflected in our selected donors for the faecal microbiota experiments ( online supplemental table S1 ). However, it appears that the observed protective effect was not linked to this difference. Of note, neither Mdr2 -deficient mice nor control mice, which were used as donors for the FMT experiment, developed spontaneous colitis. This strengthens the observation that the IBD activity of the microbiota donor on the IBD susceptibility of the recipient does not play a key role for the observed protective effect.

Another interesting question that arose during this study is whether the protective effect observed is related to the UDCA treatment that people with PSC commonly receive. Thus, we compared colitis susceptibility of germ-free wild-type mice on transfer of faecal microbiota from PBC patients, who also commonly receive UDCA, to faecal microbiota from HCs. We could not find a difference between these two groups. In addition, we transferred faecal microbiota from Mdr2 -deficient mice, which had not received UDCA, into germ-free mice. In this set of experiments, we also observed a protective effect of the microbiota from Mdr2 -deficient mice compared with control mice on colitis susceptibility. Therefore, our data argue against a beneficial effect of the UDCA treatment on the IBD susceptibility after FMT of PSC-IBD microbiota. However, we were not able to compare cholestatic cohorts with or without UDCA treatment and therefore, we cannot exclude an additional effect of UDCA on colitis severity mediated by the microbiota composition as it has been shown recently by He et al . 41

Interestingly, we found an increased FOXP3 mRNA and protein expression in the colon of people with active PSC-IBD, compared with active IBD without PSC. In addition, we identified an increased infiltration of Foxp3 + Treg cells in the inflamed colon of mice with concomitant sclerosing cholangitis in our mouse models. Interestingly, patients with genetic mutations 42 in the FOXP3 gene, that have no or non-functional Treg cells, develop severe intestinal inflammation. Furthermore, adoptive transfer of autologous OVA-specific or polyclonal Treg cells has been shown to reduce CD and PSC-associated UC. 43 Therefore, our data argue for the involvement of Foxp3 + Treg cells in the protective effect of PSC on IBD in humans and mice. This hypothesis is supported by our finding that the protective effect of liver cholestasis on colitis severity was not detectable in the CD4 + CD45RB high T-cell transfer colitis model, 44 45 in which Foxp3 + Treg cells are largely absent. One limitation of this experiment is that, although Foxp3 + Treg cells were depleted before the transfer into the recipient mice, there is the possibility of inducing peripheral Foxp3 + iTreg cells. However, colon infiltrating Foxp3 + Treg cells were hardly detectable in our study. Furthermore, the factors that control colonic Treg-cell accumulation during sclerosing cholangitis with concomitant colitis revealed that sclerosing cholangitis per se did not promote Treg-cell infiltration in the absence of intestinal inflammation. In fact, an increase in colonic Treg-cell accumulation was only observed in a colitogenic environment during sclerosing cholangitis. This finding is in line with a recent study by Shaw et al which showed that FOXP3 + Treg-cell frequencies gradually increase with colitis severity in intestinal biopsies of people with PSC-IBD. 46 Nevertheless, potential differences in the suppressive capabilities of colonic FOXP3 + Treg cells from people with IBD and PSC-IBD have not been assessed in this study and by Shaw et al . 46 Thus further studies will be essential to decipher the mechanism how PSC influences Foxp3 + Treg-cell expression and function in the setting of intestinal inflammation.

Overall, it remains to be elucidated what mechanism drives the increased accumulation of colonic Foxp3 + Treg cells during PSC-associated IBD. Beyond a participation of SCFAs in Foxp3 + Treg-cell differentiation in the colon, it is also tempting to speculate that the differentiation and expansion of Foxp3 + Treg cells already occurs in the cholestatic liver, and that consequently increased numbers of Foxp3 + Treg cells traffic from the liver to the colon. Indeed, increased Foxp3 + Treg-cell frequencies have been found in livers with different diseases like chronic viral hepatitis and hepatocellular carcinoma compared with healthy livers. 47 Further studies will be essential to test these hypotheses.

Interestingly, it is well known that there are shared genetic risk loci between PSC and IBD, however it is also well established that the co-occurrence is far too extensive to be explained by genetics alone. 48 Overall, our study provides novel insights into the relationship between PSC and IBD. We found that despite the common co-occurrence of both diseases, PSC can actually modify the severity of IBD to a better outcome. This effect is mediated by changes in the microbiota, which promotes the expansion of the Foxp3 + Treg-cell pool. A recently published report showed that IBD also ameliorates PSC. 49 Therefore, our data suggest that disease in one organ, for example, the liver, may modify the disease in the other, for example, the intestine, in this case limiting the disease severity in both organs. Thus, we believe that our study might serve as a basis for further investigations on the molecular mechanisms underlying these processes, and could therefore lead to the discovery of novel therapeutic targets for PSC and IBD.

## Ethics statements

Patient consent for publication.

Consent obtained directly from patient(s).

## Ethics approval

This study involves human participants and was approved by Ethical commission of the medical association Hamburg (PV4444, PV7106). Participants gave informed consent to participate in the study before taking part.

## Acknowledgments

The authors thank Morsal Sabihi for carefully proof-reading the manuscript, and also Cathleen Haueis, Sandra Wende, Amanda Pidgornji and Saskia Domanig for technical support.

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## Supplementary materials

Supplementary data.

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

• Data supplement 1
• Data supplement 2
• Data supplement 3
• Data supplement 4

TB, FS and MT are joint first authors.

PP and SH are joint senior authors.

Contributors TB, FS, MT and BS collaboratively conceived, designed and carried out most of the experiments, analysed the data, provided critical intellectual input and drafted the manuscript. RJ, SB, DR and AF performed experiments and analysed data. JK provided critical intellectual input and aided in drafting the manuscript. MB and SW performed histological analysis of colon and liver pathology. ML, TC and GS performed immunohistochemistry staining of FOXP3 in human. NG, SC and GT provided critical intellectual input. TB, PP and SH collaboratively conceived and designed most experiments, supervised the study, drafted the manuscript and provided critical intellectual input. SH is acting as guarantor.

Funding This work was supported by the Deutsche Forschungsgemeinschaft (CRU306 to SH and SC (290522633 and 426581255), SFB841 to SH). SH has an endowed Heisenberg-Professorship awarded by the Deutsche Forschungsgemeinschaft.

Competing interests None declared.

Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

• Open access
• Published: 18 June 2024

## Measurement properties of the Iranian version of the breast cancer perception scale (BCPS) according to the COSMIN checklist

• Sepideh Mashayekh-Amiri 1 ,
• Elham seyed Kanani 6 &
• Mojgan Mirghafourvand 7 , 8

BMC Cancer volume  24 , Article number:  743 ( 2024 ) Cite this article

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Metrics details

Breast cancer is a prevalent cancer characterized by its aggressive nature and potential to cause mortality among women. The rising mortality rates and women’s inadequate perception of the disease’s severity in developing countries highlight the importance of screening using conventional methods and reliable scales. Since the validity and reliability of the breast cancer perception scale (BCPS) have not been established in the Iranian context. Therefore, this study aimed to determine the measurement properties of the BCPS in women residing in Tabriz, Iran.

The present study comprised a cross-sectional design, encompassing a sample of 372 Iranian women. The participants were selected through a multi-stage cluster random sampling technique conducted over a period spanning from November 2022 to February 2023. The measurement properties of the Iranian version of BCPS were assessed following the guidelines outlined in the COSMIN checklist. This involved conducting various steps, including the translation process, reliability testing (internal consistency, test-retest reliability, and measurement error), and methodological tests for validity (content validity, face validity, construct validity, and hypothesis testing). The study also investigated the factors of responsiveness and interpretability. The presence of floor and ceiling effects was assessed.

The internal consistency of the scale was assessed using Cronbach’s alpha, yielding a satisfactory value of 0.68. Additionally, McDonald’s omega (95% CI) was computed, resulting in a value of 0.70 (0.66 to 0.74). Furthermore, the test-retest reliability was evaluated, revealing a high intraclass correlation coefficient (ICC) of 0.97 (95% CI: 0.94 to 0.99). The CVI, CVR, and impact scores of the BCPS were determined to be 0.98, 0.95, and 3.70, respectively, indicating favorable levels of content and face validity. To assess construct validity, an examination of the Exploratory Factor Analysis (EFA) was conducted on a set of 24 items. This analysis revealed the presence of six distinct factors, which collectively accounted for 52% of the cumulative variance. The fit indices of the validity model (CFI = 0.91, NFI = 0.96, RFI = 0.94, TLI = 0.90, χ 2 /df = 2.03, RMSEA = 0.055 and SRMR = 0.055) were confirmed during the confirmatory factor analysis (CFA). The overall score of BCPS exhibited a ceiling effect of 0.3%. The floor effect observed in the overall score (BCPS) was found to be 0.5%. Concerning the validation of the hypothesis, Spearman’s correlation coefficient of 0.55 was obtained between the BCPS and the QLICP-BR V2.0. This correlation value signifies a statistically significant association. Furthermore, it is worth noting that the minimum important change (MIC) of 3.92 exhibited a higher value compared to the smallest detectable change (SDC) of 3.70, thus suggesting a satisfactory level of response.

## Conclusions

The obtained findings suggest that the Iranian version of the BCPS demonstrates satisfactory psychometric properties for assessing the perception of breast cancer among Iranian women. Furthermore, it exhibits favorable responsiveness to clinical variations. Consequently, it can serve as a screening instrument for healthcare professionals to comprehend breast cancer and as a reliable tool in research endeavors.

Peer Review reports

Breast cancer is a significant global health issue [ 1 ], accounting for approximately 30% of cancer cases among women [ 2 ]. It is recognized as the second-leading cause of mortality in developed nations and the third-leading cause of mortality in less developed nations [ 3 ]. Based on the findings of the Global Cancer Incidence, Mortality and Prevalence (GLOBOCAN) report in 2020, it was determined that there were an estimated 2,261,419 million new cases (1 in 4 new cancer cases) (11.7%), and 684,996 (1 in 6 deaths) (6.9%) fatalities [ 4 ]. It is also predicted that these figures will reach 2,964,197 in 2040 (31% rise from 2018) [ 5 ], and 4.4 million in 2070 (110% rise from 2018) [ 6 ]. According to the report of the American Cancer Society in 2024, the number of new cases of female breast cancer in the United States was 310,720 and the number of deaths was 42,250 [ 7 ]. Approximately two-thirds of these fatalities are documented in regions with lower levels of development [ 4 ]. Alternatively, based on the projection provided by the World Health Organization (WHO), it is anticipated that by 2050, approximately 2.3 million women will receive a diagnosis of breast cancer [ 8 ]. Breast cancer is recognized as a highly costly form of cancer on a global scale, with an estimated annual expenditure of approximately 88 billion dollars. Failing to promptly diagnose and conduct screening examinations, coupled with the consequential impact on the entire family unit, imposes substantial financial burdens on society [ 9 ].

Breast cancer exhibits the highest prevalence and mortality rates among women in the Eastern Mediterranean region (EMR), encompassing Iran when compared to other forms of cancer. Breast cancer is widely recognized as the predominant form of cancer in Iran, ranking as the fifth-highest cause of mortality among women in the country [ 10 ]. The Age-standardized rate (ASR) incidence rate is approximately 28 per 100,000 individuals, exhibiting a recent upward trend [ 11 ]. Based on a systematic review, it has been documented that the incidence rate of breast cancer in Iran stands at 23.6% [ 12 ]. The reported prevalence of this cancer in the United States (US) is approximately 13%, indicating that one out of every eight individuals is affected [ 13 ].

Breast cancer is correlated with numerous risk factors, a significant proportion of which remain unidentified. The findings of a systematic review conducted in 2020 in Iran reveal various risk factors associated with breast cancer. These factors include family history, hormone replacement therapy (HRT), exposure to passive smoking, advanced maternal age during pregnancy, history of abortion, consumption of sweets, and possession of the Arg/Arg genotype. These factors have been found to potentially elevate the risk of developing breast cancer. Conversely, certain factors such as the late onset of menstruation, nulliparity, breastfeeding for a duration of 13 to 24 months, regular physical exercise, and consumption of vegetables have been observed to have a protective effect against the incidence of breast cancer [ 14 ].

It is noteworthy that the incidence of breast cancer among Iranian women occurs at an age approximately 10 years earlier compared to women in other developed nations. According to various studies, there has been a documented increase in the prevalence of breast cancer among women under the age of 40 in recent years [ 15 ]. The rise in its occurrence in developing nations is primarily attributed to alterations in lifestyle and reproductive behaviors [ 16 ]. The majority of female individuals afflicted with breast cancer receive a diagnosis during the later stages of the ailment, thereby correlating with an elevated mortality rate. Hence, it has been observed that early detection of breast cancer leads to a significant improvement in both survival rates and treatment outcomes, with a reported increase of 90% [ 17 ].

The United States Office of Disease Prevention and Health Promotion’s Healthy People 2020 initiative has as its goals the improvement of breast cancer diagnostic procedures for women, a decrease in the prevalence of cases of end-stage cancer, and a reduction in breast cancer mortality rates. Conversely, in the case of cancers that exhibit both genetic and environmental risk factors, it is imperative to adopt strategies that prioritize modifiable risk factors and early detection. Hence, the implementation of a preventive strategy aimed at early detection, which incorporates the evaluation of knowledge on breast cancer and its associated risks, assumes paramount significance [ 18 ].

The perception of breast cancer is a crucial subjective psychological phenomenon that is associated with the evaluation of potential threats. This evaluation is linked to an individual’s assessment of their susceptibility to the disease and the probability of gaining advantages from engaging in preventive measures [ 15 ]. Various studies have indicated that risk perception is a significant determinant of preventive health-related behaviors, such as screening. The motivation to undergo screening tests can be influenced by individuals’ perceptions of the risk associated with breast cancer [ 16 ]. According to the literature, screening tests play a crucial role in mitigating complications and mortality associated with breast cancer [ 17 ].

Various studies have documented divergent findings regarding the correlation between the perception of breast cancer risk and the utilization of screening tests, such as mammography [ 18 ]. Research findings indicate that the implementation of mammography screening during the age range of 40 to 49 years has been associated with a reduction in mortality rates of approximately 15 to 20% [ 19 ].

According to a study conducted on families to assess their perception of breast cancer risk, the rate of adherence to screening tests in Germany was found to be 83% [ 20 ]. Conversely, a research study conducted in Iran examined the adherence rate of women aged 35 to 69 years to mammography, as recommended by screening programs. The findings revealed that in urban areas, the adherence rate was 8.3%, while in rural areas, it was 3.16% [ 1 ]. Therefore, the perception level that women possess regarding breast cancer has the potential to influence their subsequent actions, such as seeking medical evaluation and undergoing screening procedures like breast self-examination (BSE), clinical breast examination (CBE), and mammography. Therefore, it is imperative to assess the perception of breast cancer in women using a multidimensional approach [ 20 ].

Numerous methodologies have been suggested for assessing the perception of breast cancer risk, which can be categorized into two distinct types: evaluation of the objective perception of risk (i.e., actual risk) and evaluation of the subjective perception of risk [ 21 ]. Currently, Gill’s model predominantly serves as a tool for conducting quantitative risk assessments. This approach aims to objectively evaluate the actual risk by considering the attributes of risk factors [ 22 ]. The second method entails the assessment of self-perceived risk, which can be anticipated by gauging individuals’ mental perceptions using a visual analog scale (VAS). Despite the presence of a multitude of tools within this domain, their practicality appears to be limited as they do not provide comprehensive coverage of all the factors that influence behaviors related to the diagnosis of breast cancer [ 23 ].

Taylan et al. (2021) developed the BCPS in Turkey, considering the health belief model for the first time. This scale encompasses various domains, including Perceived knowledge, Perceived treatment belief, Perceived need for health check, Perceived stigma, Perceived fear and Perceived risk. The utilization of this scale offers several benefits in assessing women’s perceptions regarding the factors influencing breast cancer diagnostic behavior comprehensively. Furthermore, it is worth noting that the extent of women’s perceived knowledge of breast cancer has not been quantitatively evaluated thus far. Consequently, this tool serves as a distinctive scale specifically designed to measure women’s knowledge regarding cancer. Additionally, it quantifies the dimensions of the breast [ 23 ].

The Health Belief Model (HBM) was initially formulated by Becker et al., in 1974 to comprehend health-related protective behaviors [ 24 ]. The evaluation of perceived risk, employing the HBM, has been validated in various studies examining screening behaviors, such as those related to breast cancer diagnostics [ 25 , 26 , 27 ]. The model encompasses various dimensions, namely perceived sensitivity, perceived severity, perceived benefits, perceived barriers, self-efficacy, and guidance for action. Based on the presented model, individuals’ healthcare behaviors can be subject to influence from factors such as perception, beliefs, values, and attitudes. By identifying and modifying an individual’s perceptions, beliefs, and attitudes, the effectiveness of healthcare education or treatment can be enhanced [ 26 ].

However, it is crucial to assess the methodological rigor of studies that evaluate the measurement properties of instruments used to measure health-related patient-reported outcomes (HR-PROs) [ 28 ]. The Consensus-Based Standards for the Selection of Health Status Measurement Instruments (COSMIN) checklist was developed by Mokkink et al. in 2010 through a consensus-based approach utilizing the Delphi method [ 28 ]. The COSMIN list is widely regarded as a highly comprehensive set of criteria for selecting an appropriate tool. It serves as a valuable guide for researchers, offering a range of logical indicators that aid in the process of tool selection [ 29 ].

Given the rising incidence of breast cancer, the significance of early screening, and the potential influence of risk perception on women’s adoption of preventive behaviors, such as breast screening methods, it is pertinent to assess the level of knowledge regarding breast cancer when devising interventions aimed at modifying health behaviors. It is worth noting that the validity and reliability of the aforementioned assessment tool have not been established in Iran. The present study was undertaken to conduct a measurement propertice of the BCPS in women residing in Tabriz city-Iran, by using the COSMIN checklist.

The present study was conducted with the aim of determining the measurement properties of the breast cancer risk perception scale (BCPS) in according to COSMIN checklist in women in Tabriz, Iran.

## Validity procedure

The measurement properties of the Iranian version of BCPS were assessed following the guidelines outlined in the COSMIN checklist [ 29 ]. This involved conducting various steps, including the translation process, reliability testing (internal consistency, test-retest reliability, and measurement error), and methodological tests for validity (content validity, face validity, construct validity, and hypothesis testing). The study also investigated the factors of responsiveness and interpretability. The presence of floor and ceiling effects was assessed.

## Translation process

Initially, permission to use the BCPS was obtained by sending an email from the original designer of the instrument (Taylan et al.) [ 23 ]. Efforts were made to maintain the integrity of the original intent during the translation process. Following the recommendations made by the WHO, EORTC Quality of Life Group Translation Procedure Guidelines and expert panel review, this was performed [ 30 ]. The translation process involves the utilization of two distinct methods. The two methods utilized in this study are the Forward-Backward method (FB) and the Dual Panel method (DP), which were implemented throughout four distinct stages. The process consisted of four stages: forward translation, backward translation, pre-testing and cognitive interviewing, and the final version.

During the initial phase of translation, the original English version of the instrument was administered to two individuals who were native Persian speakers, proficient in English, and possessed expertise in the development of the instrument as well as knowledge in the field of breast cancer. Translators were subsequently instructed to translate the tool in a fully autonomous and individual manner, with a focus on conceptual rather than literal translations. Additionally, they were encouraged to use language that would be comprehensible to the majority of the target audience. Ultimately, two translators looked into the discrepancies between the two translated versions, which led to a reconciled translation. Subsequently, the identified issues were addressed, leading to the presentation of a unified version [ 31 ]. Subsequently, the backward translation method was employed to guarantee a comprehensive correspondence between the Persian translation and the original version. The translated questionnaire from the preceding stage was administered to two individuals who are native English speakers. These individuals were not involved in the forward translation process and had no prior exposure to the original version of the questionnaire. They were instructed to retranslate the questionnaire back into English. The concluding report at the culmination of this phase encompassed the following components: two forward translations from the English language to Farsi, a reconciled translation, two backward translations from Farsi to English, and the incorporation of any supplementary remarks regarding the translations provided by the panel of experts. Ultimately, before implementing the tool in the intended population, it is imperative to conduct a pilot study. To achieve the intended objective, a questionnaire was administered to a sample of ten qualified female participants. Based on the feedback received from these participants regarding the ease of completing the instrument, grammar, comprehensibility, and writing style, modifications were made to the Persian version, and the revised version was finalized and presented [ 31 ].

## Validation study

This cross-sectional study aimed to assess the measurement properties of the Iranian version of the BCPS among a sample of 372 Iranian women who sought healthcare services at Tabriz health centers affiliated with Tabriz University of Medical Sciences in two separate secondary samples (172 participants via exploratory factor analysis and 200 participants via confirmatory factor analysis). The study was conducted following the approval of the Ethics Committee of Tabriz University of Medical Sciences (ref: IR.TBZMED.REC.1401.390) from November 2022 to February 2023. It is important to acknowledge that informed consent was obtained from all participants. The study was conducted in adherence to the applicable regulations of the Ethics Committee of the University of Medical Sciences and the Declaration of Helsinki.

Among the 410 women, it was found that 16 participants did not satisfy the predetermined eligibility criteria, leading to their exclusion from the research investigation. Out of the remaining 394 participants who met the eligibility criteria, a total of 22 participants expressed their unwillingness to participate in the study. Ultimately, a total of 372 participants were incorporated into the research investigation. The response rate for the study was 94%, (372/394). In the sampling procedure, the cluster method was employed to randomly select a quarter of the 92 health centers in Tabriz City. The selection process was facilitated through the utilization of the website ( www.random.org ). In addition to their contact information, which was obtained from the SIB system (integrated health system), women were selected at random from the compiled list. To clarify, the selection of women from each center was determined based on the proportional sampling method, and the process of randomly selecting women was carried out utilizing the aforementioned website. Following a telephone conversation with the participants, wherein the researcher offered a concise overview of the research, the researcher proceeded to invite the women to attend the designated health center within the specified timeframe. The purpose of this visit was to provide additional explanations and administer the questionnaires. Upon conducting a visit and assessing the fundamental aspects such as basic information and inclusion and exclusion criteria, the individual proceeded to furnish the concerned parties with extensive details related to the research, its advantages, outcomes, and the confidentiality of the data. It is important to acknowledge that the random selection of participants was conducted before the assessment of their eligibility criteria. Following their visit to the health center, participants underwent a comprehensive evaluation to gather baseline data and determine their eligibility. Full information regarding the research objectives and methodology was exclusively provided to individuals who satisfied the predetermined eligibility criteria, and only they were extended an invitation to participatein the study. After agreeing to participate in the study, the participants proceeded to complete the informed consent form, the questionnaire of socio-demographic characteristics, and the BCPS.

The study’s inclusion criteria encompassed women who were at least 20 years old, exhibited no indications of abnormal breast lesions during clinical examination, and possessed the necessary literacy skills to complete the questionnaire. The study excluded individuals who met the following criteria: a confirmed diagnosis of breast cancer as documented in medical records, a history of cosmetic breast surgery, and impairment in communication skills related to hearing and speaking, and an inability to physically, cognitively, or mentally respond to questions.

## Socio-demographic questionnaire

The questionnaire included questions regarding socio-demographic factors such as age, spouse age, marital status, educational level, job, income, breast cancer history, history of hormone therapy, family history of breast cancer and menopause status.

## Breast cancer perception scale

Taylan et al. (2021) in Turkey [ 23 ] developed the BCPS. The present tool is grounded in the theoretical framework of the HBM and comprises a set of 24 items designed to assess women’s perceptions of breast cancer. The construct comprises six sub-dimensions, including Perceived knowledge, Perceived treatment belief, Perceived need for health check, Perceived stigma, Perceived fear and Perceived risk, which are assessed using a five-point Likert scale. The responses span a spectrum from strongly disagree (1) to strongly agree (5). The scale’s validity and reliability have been empirically established within the specific demographic of Turkish women in 2021. The lower bound of the scoring range for this questionnaire is 24, while the upper bound is set at 120. A positive correlation exists between higher scores and a greater level of women’s perception of breast cancer [ 23 ].

## Sample size determination

It is imperative to ascertain the appropriate sample size to conduct the factor analysis procedure. According to a rule of thumb, the classification of sample size for EFA is as follows: a sample size of 50 is considered very poor, 100 is poor, 200 is fair, 300 is good, 500 is very good, and 1000 is excellent [ 32 ]. To ensure the reliability and validity of the results, it is necessary to have an appropriate sample size when conducting factor analysis. This study incorporated the guidelines proposed by Nunnally [ 33 ], which recommend a sample size of 5 to 10 samples for each instrument question to facilitate the generalizability of the findings to the broader community. Under these guidelines, it was deemed appropriate to utilize a sample size of 10 samples for each case, taking into account that the tool consisted of 24 items. Therefore, initially, a minimum of 240 samples were considered necessary. Nevertheless, it is imperative to take into account the effectof the cluster sampling technique employed in the research. The cluster sampling method introduces a factor of intra-cluster correlation that necessitates its inclusion in the calculation of the sample size [ 33 ]. To address this issue, a design effect of 1.5 was employed to modify the sample size. Due to a 10% attrition rate, the sample size has consequently expanded to encompass a total of 372 participants.

## Statistical analysis

The statistical analysis was conducted using the SPSS software package (version 16, IBM Corp., Armonk, NY, USA), STATA14 (Statcorp, College Station, Texas, USA), and R software 4.2 (Psych package). To examine socio-demographic data, descriptive statistics were employed, including frequency (percentage) for qualitative variables, minimum and maximum values, and mean ± standard deviation (SD) for quantitative variables. The evaluation encompassed methodological testing, which involved the assessment of reliability, validity, and responsiveness. Exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) techniques were employed to assess construct validity on a larger scale. The direct oblimin method was employed in the EFA. Bartlett’s test for sphericity and KMO’s test for assessing the adequacy of scale content and sample size were conducted. The CFA methodology was employed to assess the factor structure and factor loadings of the scale. In conclusion, an assessment was conducted to evaluate the reliability of the study, specifically focusing on internal consistency, test-retest reliability, and measurement error. Finally, the presence of ceiling and floor effects was assessed.

## Methodological testing according to the COSMIN checklist

• Reliability

Reliability refers to the extent to which a measurement is devoid of any errors that may arise during the measurement process. The evaluation of reliability primarily involves the assessment of three key characteristics: internal consistency, test-retest reliability, and measurement error [ 29 ].

## Internal consistency

Internal consistency refers to the extent of interconnectedness among items. It serves as an estimation of the correlation level between the variables that constitute the intended structure or instrument [ 29 ]. The internal consistency of the instrument as a whole and its six subscales was assessed using both Cronbach’s alpha coefficient and McDonald’s omega coefficient. A minimum threshold of 0.7 was deemed necessary for both Cronbach’s alpha and MacDonald’s Omega coefficients to establish satisfactory internal consistency [ 34 ].

## Test–retest reliability

Test-retest reliability refers to the extent to which the outcomes of a patient with identical health conditions remain consistent over a while [ 29 ]. Following the guidelines outlined in the COSMIN manual, a test-retest procedure was conducted with a minimum interval of two weeks. This time frame was chosen to prevent participants from recalling their previous responses and to account for any potential changes in their health status [ 29 ]. To achieve the intended objective, a survey was administered to a cohort of 30 female participants on two separate occasions, with a 14-day gap between each administration. The resulting scores were subsequently utilized to assess the reliability of the survey instrument through the application of the intraclass correlation coeficient (ICC). A reliability coefficient greater than 0.7 was deemed advantageous [ 34 ].

## Measurement error

Measurement error is considered one of the key indicators of measurement and test reliability. In essence, it refers to the presence of both systematic and random errors in the patient’s score, which cannot be attributed to genuine variations in the construct under consideration. The calculation of the standard error of measurement (SEM) involves the use of the formula (SEM = SD√1-ICC), where SD represents the standard deviation [ 34 ]. The concept of the smallest detectable change (SDC) pertains to the minimum magnitude of an individual score change that can be accurately interpreted as a genuine change. The calculation of the SDC is determined by employing the formula (SDC = SEM*1.96*√2). A reduced level of the SDC corresponds to an increased level of measurement sensitivity [ 34 ].

Validity refers to the extent to which a given instrument accurately measures the specific characteristic it is designed to assess [ 29 ].

## Face validity

Face validity is a concept that pertains to the extent to which the items within an instrument, specifically the HR-PRO, accurately represent the underlying construct that is intended to be measured [ 29 ]. The researchers conducted an assessment of face validity using both qualitative and quantitative methods. To conduct a qualitative assessment of face validity, a sample of 10 women from health centers in Tabriz City was selected using a convenience sampling method. This sample then examined the initial questionnaire. The participants assessed the quality, level of difficulty, lack of relevance, and degree of ambiguity of the items. To evaluate the face validity, item impact scores were quantitatively computed. During this phase, the aforementioned participants assessed each item on a 5-point Likert scale, ranging from “completely important” to “not at all important,” with scores ranging from 5 to 1 (representing “completely important,” “important,” “moderately important,” “slightly important,” and “not important,” respectively). The impact score is calculated by multiplying the Frequency (expressed as a percentage) by the Importance (Impact Score = Frequency (%) × Importance). Items with an impact score exceeding 1.5 were deemed appropriate and were subsequently retained for further stages of analysis [ 35 ].

## Content validity

The degree to which the content of an HR-PRO instrument effectively represents the construct that is intended to be assessed [ 29 ]. Both qualitative and quantitative methods were used to examine the validity of the content of the questionnaire. To assess the credibility of the qualitative content, a group of ten experts, including three experts in reproductive health, two specialists in midwifery, three specialists in medical-surgical nursing, and two specialists in community health nursing, were invited to provide their insights and opinions on topics considering grammar, vocabulary choice, item arrangement, and scoring.

The inclusion criteria of the experts to determine content validity include voluntary participation, faculty members with the rank of assistant professor and above, PhDs of midwifery/nursing and individuals with clinical experience in breast cancer. The process of assessing quantitative content validity involves the calculation of two measures: the content validity ratio (CVR) and the content validity index (CVI) [ 36 ]. To fulfill the objective, a questionnaire comprising questions organized into two overarching categories was distributed to each expert. In the initial phase, the participants assessed the items using a 3-point Likert scale (necessary, useful but not necessary, not necessary) to ascertain the CVR, which was computed using the following mathematical expression:

CVR= (Ne-N/2)/ (N/2).

Where, “Ne” represents the count of experts who have chosen the “necessary” option, and N denotes the total number of experts. Regarding Lawshe table, a CVR > 0.62 for a sample size of 10 individuals, confirms the essentiality of the items under investigation [ 37 ].

Subsequently, the CVI review underwent evaluation by an identical group of 10 experts. Concerning this matter, questions have been raised regarding the three criteria of relevance, clarity, and simplicity for each item. These criteria have been assessed using a four-point Likert scale, which includes options such as irrelevant, somewhat relevant, relevant, and completely relevant. The assessment is based on the content validity index [ 38 ] developed by Waltz and Basel. The level of relevance, clarity, and simplicity was assessed by experts based on their subjective evaluation, and then the CVI was computed using the following formula:

CVI = number of experts giving a rating of 3 and 4 / total number of experts.

CVIs higher than 0.79, between 0.70 and 0.79, and less than 0.70 were considered acceptable, in need of correction, and unacceptable, respectively [ 39 ].

## Construct validity

The concept of construct validity pertains to the extent to which the scores obtained from an HR-PRO instrument align with the anticipated hypotheses. This alignment can be observed in terms of internal relationships, relationships with scores obtained from other instruments, or differences between relevant groups. This assessment is contingent upon the assumption that the HR-PRO instrument possesses validity. The concept of validity pertains to the extent to which a given measure accurately assesses the construct it is intended to measure. The three aspects encompassed in this study are as follows: structural validity, which pertains to the internal relationships within the construct; hypothesis testing; and cross-cultural validity, which focuses on the relationships with scores on other instruments or differences between relevant groups [ 29 ].

## Structural validity

The suitability of the data for EFA was assessed by employing the Kaiser-Meyer Olkin (KMO) criterion and Bartlett’s test of sphericity. The KMO test is a statistical measure that quantifies the proportion of variance in the questions that can be attributed to the primary factors. Typically, values falling within the range of 0.8–1 are indicative of adequate data sampling to conduct factor analysis. However, when the value of the statistic falls below 0.7, it indicates that the sample size is insufficient, necessitating the implementation of corrective actions [ 40 ].

Bartlett’s test of sphericity is a frequently employed statistical test to assess the appropriateness of data for factor analysis. The significance of this test serves as an indicator of the suitability of the data for factor analysis [ 40 ]. The process of extracting factors from the 24 items of the questionnaire was conducted using the principal component analysis method, employing varimax rotation (direct oblimin). The determination of the number of factors was based on the criterion of an Eigenvalue greater than 1 and the examination of the Scree plot. In this analysis, a minimum factor loading threshold of 0.3 was utilized for the extraction of factors. In contrast, CFA employs the maximum likelihood method to estimate the model’s fit indices, and a range of indices are utilized to assess the appropriateness of the model. This study assessed the adequacy of the model by employing the indicators outlined below [ 41 ]:

Root mean score error of approximation (RMSEA < 0.08), standardized root mean square residual (SRMR < 0.10), normed Chi 2 (x 2 / df) < 5, comparative fit indices including comparative fit index (CFI > 0.90), Bentler-Bonett Normed Fit Index (NFI) > 0.90, Relative fit index (RFI) > 0.90 and Tucker-Lewis Index (TLI) > 0.90.

## Hypothesis testing

The process of hypothesis testing is characterized by its continuous and iterative nature. Hypotheses serve as a means to express the anticipated direction and magnitude of correlations or differences between the construct under investigation and other constructs. As the number of hypotheses tested regarding the alignment between the data and pre-existing hypotheses increases, a greater amount of evidence supporting construct validity is accumulated [ 29 ]. To assess construct validity, an analysis of the hypotheses that were previously formulated was conducted. In this study, it was postulated that the BCPS would exhibit a strong correlation with other subjective scales, such as quality-of-life instruments for cancer patients (QLICP-BR V2.0). Hence, confirmation of the desired hypothesis can be achieved when the Pearson correlation coefficient exceeds 0.5. Furthermore, the study computed the floor and ceiling effect (F/C) as well as the proportion of women who achieved the minimum and maximum scores. F/C effects refer to the percentage of individuals who achieve the highest (ceiling) or lowest (floor) possible scores within a specific domain. These effects serve as indicators of a questionnaire’s sensitivity and coverage at the extreme ends of the scale. In the context of this study, a problematic scenario is defined as a situation where 15% or more of the respondents fall into either the ceiling or floor category [ 42 ].

## Responsiveness

Measurement instruments should possess a high degree of sensitivity to detect and accurately capture changes, while also demonstrating a responsive nature to promptly reflect these changes. According to the COSMIN checklist, responsiveness refers to the capacity of an HR-PRO instrument to accurately identify alterations in the construct being assessed over a while [ 29 ]. Terwee et al. [ 34 ] argue that responsiveness can be assessed by examining the relationship between the smallest detectable change (SDC) and the minimally important change (MIC). If the value of SDC is less than MIC, then the responsiveness is confirmed.

## Interpretability

Interpretability refers to the extent of qualitative significance, specifically the minimally important changes (MIC) within the instrument. The extent to which quantitative instrument scores or changes in scores can be attributed to qualitative meaning, such as clinical or commonly understood meanings, has been discussed [ 29 ]. The estimation of the minimum important change (MIC) was conducted by dividing the standard deviation (SD) by two, as outlined in the study conducted by Norman et al. [ 43 ].

## Descriptive characteristics of participants

This study involved the participation of 372 women. The participants were randomly split into two groups, one group of 172 participants for EFA and another group of 200 participants for CFA. The average age was 52.7 and 52.3 years with a standard deviation of 9.5 and 8.5 years in EFA and CFA group, respectively. A significant majority of the individuals surveyed were married (78.5%, 80.5% in EFA and CFA group, respectively), and 73.8%, 61.0% of them identified themselves as housewives in EFA and CFA group, respectively. Table  1 provides a summary of the additional socio-demographic characteristics of the two groups of participants.

In the present study, the mean (SD) of the entire BCPS scale was 61.66 (8.44), with a range of obtainable scores from 24 to 120. The mean (SD) for the six extracted factors, namely Perceived fear, Perceived knowledge, Perceived treatment belief, Perceived risk, Perceived need for a health check, and Perceived stigma, were respectively 8.28 (4.02), 11.63 (3.79), 10.5 (2.41), 9.37 (2.12), 10.19 (3.22), and 12.15 (2.65).

The values of Cronbach’s alpha and McDonald’s omega (95% CI) were found to be 0.68 and 0.70 (0.66 to 0.74), respectively. These results suggest that the questionnaire exhibits satisfactory internal consistency. Also, the ICC (95% CI) gave a value of 0.97 (0.94 to 0.99). Standard error of measurment is a statistical metric utilized to assess the accuracy and consistency of a given measurement. The SEM value in this study was determined to be 1.36. This implies that upon conducting multiple iterations of the measurement, it is anticipated that the recorded values will fall within a range of ± 1.36 units with the actual score. Moreover, the SDC denotes the smallest detectable change that can be consistently detected by the measuring apparatus. Within the given framework, the value of SDC was ascertained to be 3.73 units. This implies that any deviation in the measured quantity that is less than 3.73 units may not be discernible due to measurement errors and can be regarded as insignificant (Table  2 ).

The tool’s content and face validity were assessed using the CVI (CVI range: 0.87–1.00), CVR (CVR range: 0.75–1.00), and impact scores (3.06–4.00), which yielded values of 0.98, 0.95, and 3.70, respectively.

The construct validity investigation involved conducting an EFA on a set of 24 items. The resulting Kaiser-Meyer-Olkin (KMO) value of 0.71 was obtained at a statistically significant level of less than 0.001, indicating that the sample size in the current study was sufficient. Furthermore, the statistical analysis revealed that Bartlett’s test of sphericity yielded a significant result ( p  ≤ 0.001), indicating that factor analysis was appropriately conducted based on the correlation matrix in the sample under investigation.

The scree plot displayed the results of EFA, revealing six factors with eigenvalues > 1. These factors collectively accounted for 52% of the variance (Fig.  1 ). Table  3 presents the extracted components alongside the corresponding items associated with each factor. The initial factor examined in this study was Perceived fear, comprising a set of four questions that contributed to 13.60% of the overall variance. The second factor, referred to as Perceived knowledge, comprises a set of four questions that collectively account for 11.00% of the overall variance. The third and fourth factors were Perceived treatment belief and Perceived risk, respectively. These factors consisted of four and two questions, respectively, and accounted for 8.9% and 6.4% of the variance. The fifth factor, referred to as Perceived need for a health check, consists of four questions with a variance of 6.3%. Additionally, the sixth factor, known as “Perceived stigma,” comprises four questions that account for 5.8% of the total variance (Fig.  2 ). After preliminary psychometric testing, 24 items were factor-analysed providing a 22-item, six-factor scale. It is important to highlight that, in the original instrument, questions 9 and 23, respectively addressed the notions that “Breast cancer treatment does not change the outcome” and “The risk for breast cancer is higher in those with a family history of breast cancer,” were excluded from the EFA in the present study due to their factor loadings being less than 0.3. Consequently, there was a reduction in the number of instrument questions from 24 items in the original instrument to 22 items.

Factor load scree plot of the items for determining the number of extracted factors of the Iranian version of BCPS

Factor structure model of the BCPS based on CFA. All factor-item relationships were significant ( P  < 0.05). Fc1: Perceived fear, Fc2: Perceived knowledge, Fc3: Perceived treatment belief, Fc4: Perceived risk, Fc5: Perceived need for health check, Fc6: Perceived stigma

CFA was employed to examine the six factors that were derived from EFA. The findings indicate that the model has attained a level of fit that is considered optimal, thereby providing support for confirming the factor structure. The indicator $$\raisebox{1ex}{{x}^{2}}\!\left/ \!\raisebox{-1ex}{df}\right.$$ is found to be 2.029 (χ2 = 393.781, df = 194, P-value < 0.001). Additionally, the fit indexes TLI, CFI, NFI, and RFI all exceed the threshold of 0.9. Furthermore, the RMSEA and SRMR index values are both equal to 0.055, indicating a valid model.

## Hypothesis testing, responsiveness and interpretability

The hypothesis confirmation involved the computation of Spearman’s correlation coefficient between the BCPS and QLICP-BR V2.0, and the resulting coefficient of 0.55 indicated a statistically significant correlation. To assess the feasibility of the tool, the ceiling effect in the overall score of BCPS was found to be 0.3%. In the sub-domains, the ceiling effects for Perceived fear, Perceived knowledge, Perceived treatment belief, Perceived risk, Perceived need for a health check, and Perceived stigma were determined to be 2.2%, 0.4%, 0.3%, 1.1%, 0.3%, and 0.8%, respectively. The floor effect in the overall score of BCPS was observed to be 0.5%, while in the specific subdomains, it was found to be 26.9%, 3.5%, 3.2%, 1.3%, 4.6%, and 0.8%, respectively. It is noteworthy to mention that the MIC refers to a specific threshold value that delineates the smallest alteration in the measured parameter that holds clinical or practical significance. In this particular instance, the MIC was determined to be 3.92 units. Specifically, the study reveals that the MIC value surpasses the SDC value by 3.73 units. This observation indicates that the Iranian version of the measurement tool is sufficiently responsive. Put simply, the measurement tool can accurately identify and assess changes that hold significance or relevance within the given measurement framework. SEM of this study’s findings generally implies that the measuring device used exhibits a satisfactory level of precision. The comparison between the SDC and the MIC values further demonstrates the instrument’s capacity to consistently identify significant variations in the measured variable (Table  2 ).

The aim of this study was to assess the measurment properties of the Breast Cancer Perception Scale (BCPS) in Iranian women, according to the COSMIN checklist for the first time. The findings of the research substantiate the validity, reliability, responsiveness, and interpretability of the BCPS, which is grounded in the health belief model (HBM) when applied to Iranian women.

The HBM has been widely employed in the study of breast cancer diagnostic behaviors for an extended period [ 25 , 26 , 27 ]. The BCPS is a novel screening tool for breast cancer that has been developed utilizing the HBM [ 23 ]. Despite the presence of various tools in this domain, such as “belief in mammography” and “breast self-examination,” “perceived sensitivity toward breast cancer,” “perceived benefits and obstacles of mammography usage,” “fear of breast cancer (FBC)”, and “fatalism regarding cancer “, these instruments appear to lack practicality as they assess factors individually and fail to encompass all relevant domains. The BCPS demonstrates utility in its comprehensive coverage of various domains, particularly in assessing previously unmeasured aspects such as perceived knowledge, and mental measurements, including the perceived need for a health check, perceived stigma, perceived fear, and perceived risk [ 23 ].

Breast cancer perception is one of the most important indicators for preventing breast cancer and adopting protective behaviors against breast cancer. Proper perception of breast cancer serves as a motivator for women to adhere to breast cancer prevention methods. Despite the existence of various preventive and diagnostic methods for breast cancer, none of these methods will be effective until there is a proper perception of breast cancer. Therefore, the BCPS scale, considering important dimensions such as Perceived knowledge, Perceived treatment belief, Perceived need for health check, Perceived stigma, Perceived fear and Perceived risk, can play an important role in creating preventive behaviors against breast cancer [ 23 ].

In the current investigation, EFA was conducted on a set of 24 items of the instrument. The analysis yielded six factors, namely Perceived fear, Perceived knowledge, Perceived treatment belief, Perceived risk, Perceived need for a health check, and Perceived stigma. These factors aligned with the original instrument and collectively accounted for approximately 52% of the variance, while in the original instrument, they accounted for 74.36% of the variance [ 23 ]. To assess the validity of the instrument, the KMO measure was computed, yielding a value of 0.71. Additionally, the adequacy of the model was verified through Bartlett’s test, which yielded a significance level of 0.77 in the original study [ 23 ]. Furthermore, the reliability of the instrument was obtained ranging from 0.64 to 0.94 by using Cronbach’s alpha, and these values align with the original study’s reported range of 0.81 to 0.95 [ 23 ].

In the present study, the initial factor extracted during the exploratory EFA was identified as perceived fear. The influence of perceived fear on women’s adoption of protective behaviors against breast cancer can be observed. The findings of various studies indicate that a significant majority of women encounter fear regarding the potential diagnosis of breast cancer and the subsequent possibility of undergoing a mastectomy, either unilaterally or bilaterally, at some point in their lives [ 44 , 45 ]. In a similar vein, a separate study indicated that women who exhibited a heightened FBC were found to undergo mammograms less frequently within a one-year timeframe in comparison to their counterparts [ 46 ]. In the study conducted by Aguirre et al., it was observed that young Spanish women exhibited a notable level of fear towards breast cancer, despite not expressing a general sense of concern regarding the disease. According to the study [ 47 ], it was found that 25.3% of the participants reported above-average FBC, while 59.7% reported high FBC. This finding implies that breast cancer may elicit a particularly strong sense of fear, even among young women who do not have significant health issues and have a low objective risk. This observation aligns with the findings of previous research [ 48 , 49 ]. Furthermore, when comparing the findings of this study to previous research conducted within the past two decades, it becomes evident that the extent of fear induced by breast cancer has remained relatively stable despite favorable epidemiological advancements such as reduced mortality rates and enhanced treatment options [ 50 ].

The second factor that was extracted in this study related to perceived knowledge. Perceived knowledge encompasses biases, such as unrealistic optimism and implicit confidence [ 51 ]. The concept of perceived knowledge pertains to an individual’s level of knowledge and is not directly associated with one’s knowledge, specifically regarding breast cancer. The WHO has advocated for the adoption of breast cancer knowledge and awareness as a viable medical strategy for the management of breast cancer. This approach is deemed essential and should be universally implemented, irrespective of financial constraints. In this regard, Izanloo et al. demonstrated that a significant majority of the participants, totaling over 84%, exhibited a lack of knowledge regarding breast cancer and screening tests among 14- to 84-year-old Iranian women. The primary factors cited by women as barriers to undergoing screening tests were the absence of discernible symptoms or issues and their perception of the test’s necessity. A significant difference was observed in the level of women’s knowledge of breast cancer and screening tests concerning factors such as employment status, education level, and family history of breast cancer. However, no significant difference was found in the level of knowledge among women based on their marital status or income level [ 52 ]. Moreover, a study conducted by Mehejabin et al. sought to examine the level of knowledge regarding various aspects of breast cancer among women in Bangladesh. The findings revealed that a majority of the participants, exceeding 50%, possessed a limited understanding of the risk factors associated with breast cancer, indicating a significant lack of knowledge [ 53 ].

Perceived treatment beliefs constituted an additional factor. Perceived belief in treatment can be influenced by various factors, including women’s spiritual and religious beliefs, familial history of breast cancer treatment, and prior experiences with breast cancer treatment [ 45 ]. Concerning this matter, individuals’ perceptions of their treatment beliefs have the potential to influence their engagement in protective behaviors. The findings of the study conducted by Mehejabin et al. indicate that a considerable proportion of women hold the belief that breast cancer can be detected at a young age. Furthermore, the participants held the belief that early diagnosis of the disease could lead to its potential cure [ 53 ]. The aforementioned findings align with the results obtained from a research study carried out at Dhaka Medical College Hospital in Bangladesh, wherein 51.43% of female participants indicated that early detection of breast cancer leads to a potential cure [ 54 ]. Suwankhong and Liamputtong have posited that religious belief significantly influences individuals’ decision-making processes concerning treatment options and risk factors associated with breast cancer [ 55 ]. Yew et al., found a significant difference in the perceptions of breast cancer risk with religious affiliations, specifically between the Muslim and Buddhist cohorts. The impact of Islam and Buddhism on individuals’ lifestyles and health-related behaviors has been significant. Muslim women exhibited a profound conviction in the authority of God (Allah), whereas Buddhist women commonly invoked their karma [ 56 ].

Perceived risk, identified as an additional extracted factor, holds a significant influence over breast cancer protective behavior [ 45 ]. Observing the challenges and distress experienced by our beloved individuals throughout breast cancer treatment amplifies both the perceived fear and the perceived risk of breast cancer [ 57 ]. The primary determinant of health behaviors for breast cancer prevention, diagnosis, and control is the perceived risk. Conversely, establishing concordance between the perceived risk and the objective risk of developing breast cancer results in a more accurate and actual perception of the risk. Consequently, it can serve as motivation for fostering suitable health behaviors [ 58 ]. Hajian et al. [ 59 ], examined the perceived risk of breast cancer among 800 Iranian women about the actual risk. The findings of the study revealed that both women with a low and high risk of breast cancer exhibited a significantly higher perceived risk of the disease compared to their actual risk. This finding suggests a significant inclination towards pessimism in the assessment of breast cancer risk, consistent with previous research conducted in this domain [ 60 , 61 ].

The results of this study also identified the perceived need for a health check as an additional extracted factor. One of the main obstacles to breast cancer screening among women is a diminished perception of the necessity for health screening. Women typically do not perceive the necessity of seeking medical attention unless they possess knowledge regarding the specific symptoms associated with a particular ailment [ 62 ]. Research findings indicate that women residing in developing nations often tend to decline the notion of early diagnosis and screening for breast cancer, primarily influenced by their cultural and personal beliefs. The aforementioned factor has a detrimental impact on the implementation of preventive measures aimed at mitigating the risk of breast cancer [ 63 ]. Therefore, variations in the perceived need for health screening can potentially impact individuals’ engagement in breast cancer protective behaviors. The scoping review study conducted by Omidi et al. examined the current status of breast cancer screening strategies and indicators among Iranian women. The study findings revealed that the prevalence rates of screening methods, including BSE, CBE, and mammography, among Iranian women were reported as 0-79.4%, 4.1–41.1%, and 1.3–45%, respectively [ 64 ].

Based on the HBM theory, Darvishpour et al. [ 25 ] posited that the decision of women to engage in breast cancer screening is influenced by factors such as self-efficacy and perceived benefits. Conversely, the presence of perceived barriers diminishes the likelihood of self-examination. According to Khazir et al., individuals who perceive fewer barriers are more likely to engage in breast cancer screening programs [ 65 ]. Abdel-Aziz et al. conducted a study utilizing EFA to examine the perceived barriers faced by women with breast cancer. Their findings indicate that personal fears, specifically fear of doctors/examiners, fear of screening results, and fear of the hospital environment, are the primary obstacles preventing women from utilizing free screening. These fears were identified as the main barriers based on their eigenvalue values, which exceeded 3.335, representing 30.4% of the barriers identified [ 66 ].

The final factor that was extracted pertains to the concept of perceived stigma. The symbolic significance of breasts for women stems from their association with childbirth, breastfeeding, childrearing, and sexual desires. Consequently, the symbolic significance associated with this phenomenon may impede women from accessing necessary healthcare services, interventions, or diagnostic procedures [ 67 ]. Furthermore, the absence of discussion regarding breast cancer and screening behaviors may be associated with societal stigmatization and cultural taboos surrounding the topic of breasts [ 68 ]. It is well known that stigma plays a significant role in the psychological distress that breast cancer-diagnosed women experience. The occurrence of rejection, blame, or devaluation is what defines the social phenomenon known as stigma. This arises from the personal experience, perception, or rational expectation of an unfavorable social evaluation directed toward an individual or a collective entity [ 69 ]. It was found that around 76.7% and 8.7% of breast cancer survivors reported moderate and high levels of stigma, respectively [ 70 ]. Based on prior research, it has been established that the perceived stigma among individuals diagnosed with breast cancer has significant adverse consequences for their overall well-being and health-related outcomes. These repercussions encompass various aspects such as sexual dysfunction, depressive symptoms, compromised sleep quality, reduced inclination to seek medical assistance, and diminished quality of life [ 71 ].

In terms of clinical application, the use of this scale is considered to save time and enable early detection of breast cancer during assessment. Utilizing this screeninig tool by health care providers improves a quick and comprehensive attitude toward breast cancer perception among women. The main advantage of BCPS is that it helps more subjective measurements compared to other scales in this area. In addition, its goal is to evaluate the relationship between breast cancer and diagnostic behaviors for breast cancer (such as maintaining healthy behaviors like diet, physical activity, mammography, breast self-examination, and clinical breast examination), knowledge about breast cancer, and family history of breast cancer [ 23 ].

## Strength and limitation

The present study possesses several notable strengths. Firstly, it is the first study to assess BCPS among Iranian women. Secondly, the study adheres to the COSMIN checklist, ensuring methodological rigor. Additionally, the study incorporates both the DP and FB methods for the translation process, effectively addressing the limitations associated with the FB method. Lastly, the study includes a comparative analysis of BCPS with other versions.

However, it is important to acknowledge the limitations of the current study. These limitations include the lack of criterion validity calculations due to the lack of a gold standard, the lack of an assessment of cross-cultural validity and the possibility of bias from participants’ tendency to give socially desirable answers when using self-reported measures. As we conducted this study in Tabriz-Iran, should be cautious about the generalizability of findings. In conclusion, it is recommended that future research endeavors employ a larger sample sizeand assess the measurment properties in diverse contexts.

The obtained findings suggest that the Iranian version of the BCPS demonstrates satisfactory measurment properties for assessing the perception of breast cancer among Iranian women. Furthermore, it exhibits favorable responsiveness to clinical variations. The assessment of women’s perceptions of breast cancer is imperative for the advancement of preventive behaviors against this disease. The present scale can be employed for the assessment of the association between breast cancer and behaviors related to breast cancer diagnosis, including breast self-examination, clinical breast examination, mammography, and the adoption of healthy behaviors such as diet and exercise. Finally, it can be utilized to investigate the correlation between breast cancer knowledge and family history.

## Data availability

The datasets generated and/or analyzed during the current study are not publicly available due to the limitations of ethical approval involving the patient data and anonymity, but are available from the corresponding author upon reasonable requests.

## Abbreviations

Breast Cancer Perception Scale

Consensus-Based Standards for the Selection of Health Status Measurement Instruments

Breast Cancer

Global Cancer Incidence Mortality and Prevalence

World health organization

Eastern Mediterranean Region

Age-standardized rate

Hormone replacement therapy

Visual Analouge Scale

Health Belief Model

Breast self-examination

Clinical Breast Examination

Health related-patient reported outcomes

Dual pannel

Forward-backward

Exploratory factor analysis

Confirmatory factor analysis

Intra-class Correlation Coefficient

standard deviation

Content validity index

Content validity ratio

Standard error of measurment

Smallest detectable change

Minimal important change

Degree of freedom

Average variance extracted

Kaiser-Meyer-Olkin

Root mean squared error of approximation

Comparative fit index

Tucker–Lewis index

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## Acknowledgements

We should thank the Vice-chancellor for Research of Tabriz University of Medical Sciences for their financial support and the invaluable participation of women would be appreciated.

This Study is funded by Tabriz University of Medical Sciences (grant number: 69930). The funding source had no role in the design and conduct of the study, and decision to this manuscript writing and submission.

## Author information

Authors and affiliations.

Students Research Committee, Midwifery Department, Faculty of Nursing and Midwifery, Tabriz University of Medical sciences, Tabriz, Iran

Sepideh Mashayekh-Amiri

Cabrini Research, Cabrini Health, Melbourne, VIC, 3144, Australia

School of Public Health and Preventative Medicine, Faculty of Medicine, Nursing and Health Sciences, Monash University, VIC 3800, Melbourne, Australia

Road Traffic Injury Research Center, Tabriz University of Medical Sciences, Tabriz, Iran

Department of Community Health Nursing, Nursing and Midwifery Faculty, Tabriz University of Medical Sciences, Tabriz, Iran

Department of Community Health Nursing, Faculty of Nursing and Midwifery, Tabriz University of Medical sciences, Tabriz, Iran

Elham seyed Kanani

Social Determinants of Health Research Center, Department of Midwifery, Faculty of Nursing and Midwifery, Tabriz University of Medical Sciences, Tabriz, Iran

Mojgan Mirghafourvand

Medical Philosophy and History Reseach Center, Tabriz University of Medical Sciences, Tabriz, Iran

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## Contributions

MM, SMA, MH contributed to the design of the study. SMA, ESK, MM has written the first draft of this article and MAJ Analyzed and data. All authors have critically read the text and contributed with inputs and revisions, and all authors read and approved the final manuscript.

## Corresponding author

Correspondence to Mojgan Mirghafourvand .

## Ethics declarations

Ethics approval and consent to participate.

The current study was approved by the Ethics Committee of Tabriz University of Medical Sciences [ref: IR.TBZMED.REC.1401.390]. Written Informed consent to participate in the study was obtained from all the participants before enrolment. Permission to use the BCPS was obtained by sending an email from the original designer of the instrument. All methods were carried out in accordance with relevant guidelines and regulations.

Not applicable.

## Competing interests

The authors declare no competing interests.

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Reprints and permissions

Mashayekh-Amiri, S., Jafarabadi, M.A., Hosseinzadeh, M. et al. Measurement properties of the Iranian version of the breast cancer perception scale (BCPS) according to the COSMIN checklist. BMC Cancer 24 , 743 (2024). https://doi.org/10.1186/s12885-024-12493-2

Accepted : 10 June 2024

Published : 18 June 2024

DOI : https://doi.org/10.1186/s12885-024-12493-2

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• Breast cancer
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3. Conclusion and Hypothesis Writing

4. Writing the Final Conclusion for the Hypothesis Testing

5. Identifying Hypothesis and Conclusion (Easier)

6. Module8: Hypothesis Testing Sigma Unknown

1. How to Write Hypothesis Test Conclusions (With Examples)

When writing the conclusion of a hypothesis test, we typically include: Whether we reject or fail to reject the null hypothesis. The significance level. A short explanation in the context of the hypothesis test. For example, we would write: We reject the null hypothesis at the 5% significance level.

2. How to Write a Strong Hypothesis

5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.

3. Hypothesis Testing

There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1 ). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ...

4. 6a.1

The first step in hypothesis testing is to set up two competing hypotheses. The hypotheses are the most important aspect. If the hypotheses are incorrect, your conclusion will also be incorrect. The two hypotheses are named the null hypothesis and the alternative hypothesis. The null hypothesis is typically denoted as H 0.

5. How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.. To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:. Null Hypothesis (H 0): The sample data occurs purely from chance.

6. Hypothesis Testing: Uses, Steps & Example

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it.

7. 6a.2

Below these are summarized into six such steps to conducting a test of a hypothesis. Set up the hypotheses and check conditions: Each hypothesis test includes two hypotheses about the population. One is the null hypothesis, notated as H 0, which is a statement of a particular parameter value. This hypothesis is assumed to be true until there is ...

8. 6.6

The conclusion drawn from a two-tailed confidence interval is usually the same as the conclusion drawn from a two-tailed hypothesis test. In other words, if the the 95% confidence interval contains the hypothesized parameter, then a hypothesis test at the 0.05 $$\alpha$$ level will almost always fail to reject the null hypothesis.

9. Drawing Conclusions

State a conclusion to a hypothesis test in statistical terms and in context; Establishing the type of distribution, sample size, and known or unknown standard deviation can help you figure out how to go about a hypothesis test. However, there are several other factors you should consider when working out a hypothesis test.

10. 8.1: Steps in Hypothesis Testing

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will: Set up two contradictory hypotheses. Collect sample data (in homework problems, the data or summary statistics will be given to you).

11. 9.1: Introduction to Hypothesis Testing

In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted $$H_0$$ while the alternative hypothesis is usually denoted $$H_1$$. An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...

12. What is a Hypothesis

Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion. Relevant: A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

13. 8.6: Hypothesis Test of a Single Population Mean with Examples

Compare the preconceived α with the p-value, make a decision (reject or do not reject H 0), and write a clear conclusion using English sentences. Notice that in performing the hypothesis test, you use $$\alpha$$ and not $$\beta$$. $$\beta$$ is needed to help determine the sample size of the data that is used in calculating the $$p\text{-value}$$.

14. Hypothesis: Definition, Examples, and Types

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...

15. How to Write a Hypothesis 101: A Step-by-Step Guide

In conclusion, understanding how to write a hypothesis is crucial for conducting successful scientific research. By focusing on your research question and carefully building relationships between variables, you will lay a strong foundation for advancing research and knowledge in your field.

16. Making Valid Conclusions about a Hypothesis Test for a Mean

Make a valid conclusion based on this p-value. Step 1: State the null and alternative hypotheses for the mean. The null hypothesis is that the mean vehicle price is equal to \$15,000. The ...

17. Using P-values to make conclusions (article)

Onward! We use p -values to make conclusions in significance testing. More specifically, we compare the p -value to a significance level α to make conclusions about our hypotheses. If the p -value is lower than the significance level we chose, then we reject the null hypothesis H 0 in favor of the alternative hypothesis H a .

18. How to Write a Thesis or Dissertation Conclusion

Step 1: Answer your research question. Step 2: Summarize and reflect on your research. Step 3: Make future recommendations. Step 4: Emphasize your contributions to your field. Step 5: Wrap up your thesis or dissertation. Full conclusion example. Conclusion checklist. Other interesting articles.

19. How to Write Discussions and Conclusions

Begin with a clear statement of the principal findings. This will reinforce the main take-away for the reader and set up the rest of the discussion. Explain why the outcomes of your study are important to the reader. Discuss the implications of your findings realistically based on previous literature, highlighting both the strengths and ...

20. 5 Ways to Write a Good Lab Conclusion in Science

1. Introduce the experiment in your conclusion. Start out the conclusion by providing a brief overview of the experiment. Describe the experiment in 1-2 sentences and discuss the objective of the experiment. Also, make sure to include your manipulated (independent), controlled and responding (dependent) variables. [3] 2.

21. What Is a Hypothesis and How Do I Write One?

Merriam Webster defines a hypothesis as "an assumption or concession made for the sake of argument.". In other words, a hypothesis is an educated guess. Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it's true or not.

22. What Is a Hypothesis? The Scientific Method

A hypothesis (plural hypotheses) is a proposed explanation for an observation. The definition depends on the subject. In science, a hypothesis is part of the scientific method. It is a prediction or explanation that is tested by an experiment. Observations and experiments may disprove a scientific hypothesis, but can never entirely prove one.

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24. The Influence of Individualism/Collectivism Orientation on University

In conclusion, university teachers' bootleg innovation is beneficial in some way (Criscuolo et al., 2014; Globocnik & Salomo, 2015). On the one hand, it can reduce costs in the context of limited resources ( Mainemelis, 2010 ); on the other hand, it can enhance personal improvement and promote more open innovative development systems in ...

25. How to Conclude an Essay

Step 1: Return to your thesis. To begin your conclusion, signal that the essay is coming to an end by returning to your overall argument. Don't just repeat your thesis statement —instead, try to rephrase your argument in a way that shows how it has been developed since the introduction. Example: Returning to the thesis.

26. Protective function of sclerosing cholangitis on IBD

Objective There is a strong clinical association between IBD and primary sclerosing cholangitis (PSC), a chronic disease of the liver characterised by biliary inflammation that leads to strictures and fibrosis. Approximately 60%-80% of people with PSC will also develop IBD (PSC-IBD). One hypothesis explaining this association would be that PSC drives IBD. Therefore, our aim was to test this ...

27. Measurement properties of the Iranian version of the breast cancer

Background Breast cancer is a prevalent cancer characterized by its aggressive nature and potential to cause mortality among women. The rising mortality rates and women's inadequate perception of the disease's severity in developing countries highlight the importance of screening using conventional methods and reliable scales. Since the validity and reliability of the breast cancer ...