hypothesis testing design

InVisionApp, Inc.

Inside Design

5 steps to a hypothesis-driven design process

  •   mar 22, 2018.

S ay you’re starting a greenfield project, or you’re redesigning a legacy app. The product owner gives you some high-level goals. Lots of ideas and questions are in your mind, and you’re not sure where to start.

Hypothesis-driven design will help you navigate through a unknown space so you can come out at the end of the process with actionable next steps.

Ready? Let’s dive in.

Step 1: Start with questions and assumptions

On the first day of the project, you’re curious about all the different aspects of your product. “How could we increase the engagement on the homepage? ” “ What features are important for our users? ”

Related: 6 ways to speed up and improve your product design process

To reduce risk, I like to take some time to write down all the unanswered questions and assumptions. So grab some sticky notes and write all your questions down on the notes (one question per note).

I recommend that you use the How Might We technique from IDEO to phrase the questions and turn your assumptions into questions. It’ll help you frame the questions in a more open-ended way to avoid building the solution into the statement prematurely. For example, you have an idea that you want to make riders feel more comfortable by showing them how many rides the driver has completed. You can rephrase the question to “ How might we ensure rider feel comfortable when taking ride, ” and leave the solution part out to the later step.

“It’s easy to come up with design ideas, but it’s hard to solve the right problem.”

It’s even more valuable to have your team members participate in the question brainstorming session. Having diverse disciplines in the room always brings fresh perspectives and leads to a more productive conversation.

Step 2: Prioritize the questions and assumptions

Now that you have all the questions on sticky notes, organize them into groups to make it easier to review them. It’s especially helpful if you can do the activity with your team so you can have more input from everybody.

When it comes to choosing which question to tackle first, think about what would impact your product the most or what would bring the most value to your users.

If you have a big group, you can Dot Vote to prioritize the questions. Here’s how it works: Everyone has three dots, and each person gets to vote on what they think is the most important question to answer in order to build a successful product. It’s a common prioritization technique that’s also used in the Sprint book by Jake Knapp —he writes, “ The prioritization process isn’t perfect, but it leads to pretty good decisions and it happens fast. ”

Related: Go inside design at Google Ventures

Step 3: Turn them into hypotheses

After the prioritization, you now have a clear question in mind. It’s time to turn the question into a hypothesis. Think about how you would answer the question.

Let’s continue the previous ride-hailing service example. The question you have is “ How might we make people feel safe and comfortable when using the service? ”

Based on this question, the solutions can be:

• Sharing the rider’s location with friends and family automatically
• Displaying more information about the driver
• Showing feedback from previous riders

Now you can combine the solution and question, and turn it into a hypothesis. Hypothesis is a framework that can help you clearly define the question and solution, and eliminate assumption.

From Lean UX

We believe that [ sharing more information about the driver’s experience and stories ] For [ the riders ] Will [ make riders feel more comfortable and connected throughout the ride ]

4. Develop an experiment and testing the hypothesis

Develop an experiment so you can test your hypothesis. Our test will follow the scientific methods, so it’s subject to collecting empirical and measurable evidence in order to obtain new knowledge. In other words, it’s crucial to have a measurable outcome for the hypothesis so we can determine whether it has succeeded or failed.

There are different ways you can create an experiment, such as interview, survey , landing page validation, usability testing, etc. It could also be something that’s built into the software to get quantitative data from users. Write down what the experiment will be, and define the outcomes that determine whether the hypothesis is valids. A well-defined experiment can validate/invalidate the hypothesis.

In our example, we could define the experiment as “ We will run X studies to show more information about a driver (number of ride, years of experience), and ask follow-up questions to identify the rider’s emotion associated with this ride (safe, fun, interesting, etc.). We will know the hypothesis is valid when we get more than 70% identify the ride as safe or comfortable. ”

After defining the experiment, it’s time to get the design done. You don’t need to have every design detail thought through. You can focus on designing what is needed to be tested.

When the design is ready, you’re ready to run the test. Recruit the users you want to target , have a time frame, and put the design in front of the users.

5. Learn and build

You just learned that the result was positive and you’re excited to roll out the feature. That’s great! If the hypothesis failed, don’t worry—you’ll be able to gain some insights from that experiment. Now you have some new evidence that you can use to run your next experiment. In each experiment, you’ll learn something new about your product and your customers.

“Design is a never-ending process.”

What other information can you show to make riders feel safe and comfortable? That can be your next hypothesis. You now have a feature that’s ready to be built, and a new hypothesis to be tested.

Principles from from The Lean Startup

We often assume that we understand our users and know what they want. It’s important to slow down and take a moment to understand the questions and assumptions we have about our product.

After testing each hypothesis, you’ll get a clearer path of what’s most important to the users and where you need to dig deeper. You’ll have a clear direction for what to do next.

by Sylvia Lai

Sylvia Lai helps startup and enterprise solve complex problems through design thinking and user-centered design methodologies at Pivotal Labs . She is the biggest advocate for the users, making sure their voices are heard is her number one priority. Outside of work, she loves mentoring other designers through one-on-one conversation. Connect with her through LinkedIn or Twitter .

Collaborate in real time on a digital whiteboard Try Freehand

Get awesome design content in your inbox each week, give it a try—it only takes a click to unsubscribe., thanks for signing up, you should have a thank you gift in your inbox now-and you’ll hear from us again soon, get started designing better. faster. together. and free forever., give it a try. nothing’s holding you back..

• How it works

Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing  is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.  

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

• Clear and precise
• Capable of being tested
• Able to relate to a variable
• Stated in simple terms
• Consistent with known facts
• Limited in scope and specific
• Tested in a limited timeframe
• Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A  null hypothesis  is a hypothesis when there is no significant relationship between the dependent and the participants’ independent  variables . 

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

Hire an Expert Researcher

Orders completed by our expert writers are

• Formally drafted in academic style
• 100% Plagiarism free & 100% Confidential
• Never resold
• Include unlimited free revisions
• Completed to match exact client requirements

How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to  gather the data  obtained through a large number of samples from a specific population. 

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many  types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study 

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance. 

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

Get statistical analysis help at an affordable price

• An expert statistician will complete your work
• Rigorous quality checks
• Confidentiality and reliability
• Any statistical software of your choice
• Free Plagiarism Report

Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the  significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided. 

If the significance level is minimum, then it prevents the researchers from false claims. 

The significance level is denoted by  P,  and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the  outcomes of your study . You need to ensure whether you have met the objectives of your research or not. 

In the discussion section and  conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis? 

Always remember that you either conclude to reject Ho in favor of Haor   do not reject Ho . It would help if you never rejected  Ha  or even  accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude  reject Ho in favor of Haor   do not reject Ho,  then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

• One-Sample Test : Compare sample data to a known population value.
• Two-Sample Test : Compare means between two sample groups.
• ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

You May Also Like

Experimental research refers to the experiments conducted in the laboratory or under observation in controlled conditions. Here is all you need to know about experimental research.

This post provides the key disadvantages of secondary research so you know the limitations of secondary research before making a decision.

What are the different types of research you can use in your dissertation? Here are some guidelines to help you choose a research strategy that would make your research more credible.

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

• How It Works

Advisory boards aren’t only for executives. Join the LogRocket Content Advisory Board today →

• Product Management
• Solve User-Reported Issues
• Find Issues Faster
• Optimize Conversion and Adoption

How to create a perfect design hypothesis

A design hypothesis is a cornerstone of the UX and UI design process. It guides the entire process, defines research needs, and heavily influences the final outcome.

Doing any design work without a well-defined hypothesis is like riding a car without headlights. Although still possible, it forces you to go slower and dramatically increases the chances of unpleasant pitfalls.

The importance of a hypothesis in the design process

Design change for your hypothesis, the objective of your hypothesis, mapping underlying assumptions in your hypothesis, example 1: a simple design hypothesis, example 2: a robust design hypothesis.

There are three main reasons why no discovery or design process should start without a well-defined and framed hypothesis. A good design hypothesis helps us:

• Guide the research
• Nail the solutions
• Maximize learnings and enable iterative design

A design hypothesis guides research

A good hypothesis not only states what we want to achieve but also the final objective and our current beliefs. It allows designers to assess how much actual evidence there is to support the hypothesis and focus their research and discovery efforts on areas they are least confident about.

Research for the sake of research brings waste. Research for the sake of validating specific hypotheses brings learnings.

A design hypothesis influences the design and solution

Design hypothesis gives much-needed context. It helps you:

• Ideate right solutions
• Focus on the proper UX
• Polish UI details

The more detailed and robust the design hypothesis, the more context you have to help you make the best design decisions.

A design hypothesis maximizes learnings and enables iterative design

If you design new features blindly, it’s hard to truly learn from the launch. Some metrics might go up. Others might go down, so what?

With a well-defined design hypothesis, you can not only validate whether the design itself works but also better understand why and how to improve it in the future. This helps you iterate on your learnings.

Components of a good design hypothesis

I am not a fan of templatizing how a solid design hypothesis should look. There are various ways to approach it, and you should choose whatever works for you best. However, there are three essential elements you should include to ensure you get all the benefits mentioned earlier of using design hypotheses, that is:

• Design change
• The objective
• Underlying assumptions

The fundamental part is the definition of what you are trying to do. If you are working on shortening the onboarding process, you might simply put “[…] we’d like to shorten the onboarding process […].”

The goal here is to give context to a wider audience and be able to quickly reference that the design hypothesis is concerning. Don’t fret too much about this part; simply boil the problem down to its essentials. What is frustrating your users?

In other words, the objective is the “why” behind the change. What exactly are you trying to achieve with the planned design change? The objective serves a few purposes.

Over 200k developers and product managers use LogRocket to create better digital experiences

First, it’s a great sanity check. You’d be surprised how many designers proposed various ideas, changes, and improvements without a clear goal. Changing design just for the sake of changing the design is a no-no.

It also helps you step back and see if the change you are considering is the best approach. For instance, if you are considering shortening the onboarding to increase the percentage of users completing it, are there any other design changes you can think of to achieve the same goal? Maybe instead of shortening the onboarding, there’s a bigger opportunity in simply adjusting the copy? Defining clear objectives invites conversations about whether you focus on the right things.

Additionally, a clearly defined objective gives you a measure of success to evaluate the effectiveness of your solution. If you believed you could boost the completion rate by 40 percent, but achieved only a 10 percent lift, then either the hypothesis was flawed (good learning point for the future), or there’s still room for improvements.

Last but not least, a clear objective is essential for the next step: mapping underlying assumptions.

Now that you know what you plan to do and which goal you are trying to achieve, it’s time for the most critical question.

Why do you believe the proposed design change will achieve the desired objective? Whether it’s because you heard some interesting insights during user interviews or spotted patterns in users’ behavioral data, note it down.

Even if you don’t have any strong justification and base your hypothesis on pure guesses (we all do that sometimes!), clearly name these beliefs. Listing out all your assumption will help you:

• Focus your discovery efforts on validating these assumptions to avoid late disappointments
• Better analyze results post-launch to maximize your learnings

You’ll see exactly how in the examples of good design hypotheses below.

Examples of good design hypotheses

Let’s put it all into practice and see what a good design hypothesis might look like.

I’ll use two examples:

• A simple design hypothesis
• A robust design hypothesis

You should still formulate a design hypothesis if you are working on minor changes, such as changing the copy on buttons. But there’s also no point in spending hours formulating a perfect hypothesis for a fifteen-minute test. In these cases, I’d just use a simple one-sentence hypothesis.

Yet, suppose you are working on an extensive and critical initiative, such as redesigning the whole conversion funnel. In that case, you might want to put more effort into a more robust and detailed design hypothesis to guide your entire process.

A simple example of a design hypothesis could be:

Moving the sign-up button to the top of the page will increase our conversion to registration by 10 percent, as most users don’t look at the bottom of the page.

Although it’s pretty straightforward, it still can help you in a few ways.

First of all, it helps prioritize experiments. If there is another small experiment in the backlog, but with the hypothesis that it’ll improve conversion to registration by 15 percent, it might influence the order of things you work on.

Impact assessments (where the 10 percent or 15 percent comes from) are another quite advanced topic, so I won’t cover it in detail, but in most cases, you can ask your product manager and/or data analyst for help.

It also allows you to validate the hypothesis without even experimenting. If you guessed that people don’t look at the bottom of the page, you can check your analytics tools to see what the scroll rate is or check heatmaps.

Lastly, if your hypothesis fails (that is, the conversion rate doesn’t improve), you get valuable insights that can help you reassess other hypotheses based on the “most users don’t look at the bottom of the page” assumption.

Now let’s take a look at a slightly more robust assumption. An example could be:

Shortening the number of screens during onboarding by half will boost our free trial to subscription conversion by 20 percent because:

• Most users don’t complete the whole onboarding flow
• Shorter onboarding will increase the onboarding completion rate
• Focusing on the most important features will increase their adoption
• Which will lead to aha moments and better premium retention
• Users will perceive our product as simpler and less complex

The most significant difference is our effort to map all relevant assumptions.

Listing out assumptions can help you test them out in isolation before committing to the initiative.

For example, if you believe most users don’t complete the onboarding flow , you can check self-serve tools or ask your PM for help to validate if that’s true. If the data shows only 10 percent of users finish the onboarding, the hypothesis is stronger and more likely to be successful. If, on the other hand, most users do complete the whole onboarding, the idea suddenly becomes less promising.

The second advantage is the number of learnings you can get from the post-release analysis.

Say the change led to a 10 percent increase in conversion. Instead of blindly guessing why it didn’t meet expectations, you can see how each assumption turned out.

It might turn out that some users actually perceive the product as more complex (rather than less complex, as you assumed), as they have difficulty figuring out some functionalities that were skipped in the onboarding. Thus, they are less willing to convert.

Not only can it help you propose a second iteration of the experiment, that learning will help you greatly when working on other initiatives based on a similar assumption.

Closing thoughts

Ensuring everything you work on is based on a solid design hypothesis can greatly help you and your career.

It’ll guide your research and discovery in the right direction, enable better iterative design, maximize learning, and help you make better design decisions.

Some designers might think, “Hypotheses are the job of a product manager, not a designer.”

While that’s partly true, I believe designers should be proactive in working with hypotheses.

If there are none set, do it yourself for the sake of your own success. If all your designs succeed, or worse, flunk, no one will care who set or didn’t set the hypotheses behind these decisions. You’ll be judged, too.

If there’s a hypothesis set upfront, try to understand it, refine it, and challenge it if needed.

Most senior and desired product designers are not just pixel-pushers that do what they are being told to do, but they also play an active role in shaping the direction of the product as a whole. Becoming fluent in working with hypotheses is a significant step toward true seniority.

Header image source: IconScout

LogRocket : Analytics that give you UX insights without the need for interviews

LogRocket lets you replay users' product experiences to visualize struggle, see issues affecting adoption, and combine qualitative and quantitative data so you can create amazing digital experiences.

See how design choices, interactions, and issues affect your users — get a demo of LogRocket today .

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Reddit (Opens in new window)
• Click to share on LinkedIn (Opens in new window)
• Click to share on Facebook (Opens in new window)
• #ux research

Stop guessing about your digital experience with LogRocket

Recent posts:.

Color and culture: How color language changes by background

Color variance across cultures and perceptions can impact the way UX design is interpreted and how effective it is.

How to run one-on-one meetings with a design team

Let’s talk about the purpose of a one-on-one meeting, what makes a successful one, and strategies to plan and run one effectively.

Why you shouldn’t use vertical trim in Figma (yet)

Did you know about the vertical trim setting in Figma? Here’s what it does and why it’s awesome but why you shouldn’t use it yet.

Using the similarity matrix to surface card sorting insights (+template)

Analyzing a similarity matrix can help you identify patterns that tend to be grouped together by participants in card sorting.

Leave a Reply Cancel reply

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Korean Med Sci
• v.36(50); 2021 Dec 27

Formulating Hypotheses for Different Study Designs

Durga prasanna misra.

1 Department of Clinical Immunology and Rheumatology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, India.

Armen Yuri Gasparyan

2 Departments of Rheumatology and Research and Development, Dudley Group NHS Foundation Trust (Teaching Trust of the University of Birmingham, UK), Russells Hall Hospital, Dudley, UK.

Olena Zimba

3 Department of Internal Medicine #2, Danylo Halytsky Lviv National Medical University, Lviv, Ukraine.

Marlen Yessirkepov

4 Department of Biology and Biochemistry, South Kazakhstan Medical Academy, Shymkent, Kazakhstan.

Vikas Agarwal

George d. kitas.

5 Centre for Epidemiology versus Arthritis, University of Manchester, Manchester, UK.

Generating a testable working hypothesis is the first step towards conducting original research. Such research may prove or disprove the proposed hypothesis. Case reports, case series, online surveys and other observational studies, clinical trials, and narrative reviews help to generate hypotheses. Observational and interventional studies help to test hypotheses. A good hypothesis is usually based on previous evidence-based reports. Hypotheses without evidence-based justification and a priori ideas are not received favourably by the scientific community. Original research to test a hypothesis should be carefully planned to ensure appropriate methodology and adequate statistical power. While hypotheses can challenge conventional thinking and may be controversial, they should not be destructive. A hypothesis should be tested by ethically sound experiments with meaningful ethical and clinical implications. The coronavirus disease 2019 pandemic has brought into sharp focus numerous hypotheses, some of which were proven (e.g. effectiveness of corticosteroids in those with hypoxia) while others were disproven (e.g. ineffectiveness of hydroxychloroquine and ivermectin).

Graphical Abstract

DEFINING WORKING AND STANDALONE SCIENTIFIC HYPOTHESES

Science is the systematized description of natural truths and facts. Routine observations of existing life phenomena lead to the creative thinking and generation of ideas about mechanisms of such phenomena and related human interventions. Such ideas presented in a structured format can be viewed as hypotheses. After generating a hypothesis, it is necessary to test it to prove its validity. Thus, hypothesis can be defined as a proposed mechanism of a naturally occurring event or a proposed outcome of an intervention. 1 , 2

Hypothesis testing requires choosing the most appropriate methodology and adequately powering statistically the study to be able to “prove” or “disprove” it within predetermined and widely accepted levels of certainty. This entails sample size calculation that often takes into account previously published observations and pilot studies. 2 , 3 In the era of digitization, hypothesis generation and testing may benefit from the availability of numerous platforms for data dissemination, social networking, and expert validation. Related expert evaluations may reveal strengths and limitations of proposed ideas at early stages of post-publication promotion, preventing the implementation of unsupported controversial points. 4

Thus, hypothesis generation is an important initial step in the research workflow, reflecting accumulating evidence and experts' stance. In this article, we overview the genesis and importance of scientific hypotheses and their relevance in the era of the coronavirus disease 2019 (COVID-19) pandemic.

DO WE NEED HYPOTHESES FOR ALL STUDY DESIGNS?

Broadly, research can be categorized as primary or secondary. In the context of medicine, primary research may include real-life observations of disease presentations and outcomes. Single case descriptions, which often lead to new ideas and hypotheses, serve as important starting points or justifications for case series and cohort studies. The importance of case descriptions is particularly evident in the context of the COVID-19 pandemic when unique, educational case reports have heralded a new era in clinical medicine. 5

Case series serve similar purpose to single case reports, but are based on a slightly larger quantum of information. Observational studies, including online surveys, describe the existing phenomena at a larger scale, often involving various control groups. Observational studies include variable-scale epidemiological investigations at different time points. Interventional studies detail the results of therapeutic interventions.

Secondary research is based on already published literature and does not directly involve human or animal subjects. Review articles are generated by secondary research. These could be systematic reviews which follow methods akin to primary research but with the unit of study being published papers rather than humans or animals. Systematic reviews have a rigid structure with a mandatory search strategy encompassing multiple databases, systematic screening of search results against pre-defined inclusion and exclusion criteria, critical appraisal of study quality and an optional component of collating results across studies quantitatively to derive summary estimates (meta-analysis). 6 Narrative reviews, on the other hand, have a more flexible structure. Systematic literature searches to minimise bias in selection of articles are highly recommended but not mandatory. 7 Narrative reviews are influenced by the authors' viewpoint who may preferentially analyse selected sets of articles. 8

In relation to primary research, case studies and case series are generally not driven by a working hypothesis. Rather, they serve as a basis to generate a hypothesis. Observational or interventional studies should have a hypothesis for choosing research design and sample size. The results of observational and interventional studies further lead to the generation of new hypotheses, testing of which forms the basis of future studies. Review articles, on the other hand, may not be hypothesis-driven, but form fertile ground to generate future hypotheses for evaluation. Fig. 1 summarizes which type of studies are hypothesis-driven and which lead on to hypothesis generation.

STANDARDS OF WORKING AND SCIENTIFIC HYPOTHESES

A review of the published literature did not enable the identification of clearly defined standards for working and scientific hypotheses. It is essential to distinguish influential versus not influential hypotheses, evidence-based hypotheses versus a priori statements and ideas, ethical versus unethical, or potentially harmful ideas. The following points are proposed for consideration while generating working and scientific hypotheses. 1 , 2 Table 1 summarizes these points.

Evidence-based data

A scientific hypothesis should have a sound basis on previously published literature as well as the scientist's observations. Randomly generated (a priori) hypotheses are unlikely to be proven. A thorough literature search should form the basis of a hypothesis based on published evidence. 7

Unless a scientific hypothesis can be tested, it can neither be proven nor be disproven. Therefore, a scientific hypothesis should be amenable to testing with the available technologies and the present understanding of science.

Supported by pilot studies

If a hypothesis is based purely on a novel observation by the scientist in question, it should be grounded on some preliminary studies to support it. For example, if a drug that targets a specific cell population is hypothesized to be useful in a particular disease setting, then there must be some preliminary evidence that the specific cell population plays a role in driving that disease process.

Testable by ethical studies

The hypothesis should be testable by experiments that are ethically acceptable. 9 For example, a hypothesis that parachutes reduce mortality from falls from an airplane cannot be tested using a randomized controlled trial. 10 This is because it is obvious that all those jumping from a flying plane without a parachute would likely die. Similarly, the hypothesis that smoking tobacco causes lung cancer cannot be tested by a clinical trial that makes people take up smoking (since there is considerable evidence for the health hazards associated with smoking). Instead, long-term observational studies comparing outcomes in those who smoke and those who do not, as was performed in the landmark epidemiological case control study by Doll and Hill, 11 are more ethical and practical.

Balance between scientific temper and controversy

Novel findings, including novel hypotheses, particularly those that challenge established norms, are bound to face resistance for their wider acceptance. Such resistance is inevitable until the time such findings are proven with appropriate scientific rigor. However, hypotheses that generate controversy are generally unwelcome. For example, at the time the pandemic of human immunodeficiency virus (HIV) and AIDS was taking foot, there were numerous deniers that refused to believe that HIV caused AIDS. 12 , 13 Similarly, at a time when climate change is causing catastrophic changes to weather patterns worldwide, denial that climate change is occurring and consequent attempts to block climate change are certainly unwelcome. 14 The denialism and misinformation during the COVID-19 pandemic, including unfortunate examples of vaccine hesitancy, are more recent examples of controversial hypotheses not backed by science. 15 , 16 An example of a controversial hypothesis that was a revolutionary scientific breakthrough was the hypothesis put forth by Warren and Marshall that Helicobacter pylori causes peptic ulcers. Initially, the hypothesis that a microorganism could cause gastritis and gastric ulcers faced immense resistance. When the scientists that proposed the hypothesis themselves ingested H. pylori to induce gastritis in themselves, only then could they convince the wider world about their hypothesis. Such was the impact of the hypothesis was that Barry Marshall and Robin Warren were awarded the Nobel Prize in Physiology or Medicine in 2005 for this discovery. 17 , 18

DISTINGUISHING THE MOST INFLUENTIAL HYPOTHESES

Influential hypotheses are those that have stood the test of time. An archetype of an influential hypothesis is that proposed by Edward Jenner in the eighteenth century that cowpox infection protects against smallpox. While this observation had been reported for nearly a century before this time, it had not been suitably tested and publicised until Jenner conducted his experiments on a young boy by demonstrating protection against smallpox after inoculation with cowpox. 19 These experiments were the basis for widespread smallpox immunization strategies worldwide in the 20th century which resulted in the elimination of smallpox as a human disease today. 20

Other influential hypotheses are those which have been read and cited widely. An example of this is the hygiene hypothesis proposing an inverse relationship between infections in early life and allergies or autoimmunity in adulthood. An analysis reported that this hypothesis had been cited more than 3,000 times on Scopus. 1

LESSONS LEARNED FROM HYPOTHESES AMIDST THE COVID-19 PANDEMIC

The COVID-19 pandemic devastated the world like no other in recent memory. During this period, various hypotheses emerged, understandably so considering the public health emergency situation with innumerable deaths and suffering for humanity. Within weeks of the first reports of COVID-19, aberrant immune system activation was identified as a key driver of organ dysfunction and mortality in this disease. 21 Consequently, numerous drugs that suppress the immune system or abrogate the activation of the immune system were hypothesized to have a role in COVID-19. 22 One of the earliest drugs hypothesized to have a benefit was hydroxychloroquine. Hydroxychloroquine was proposed to interfere with Toll-like receptor activation and consequently ameliorate the aberrant immune system activation leading to pathology in COVID-19. 22 The drug was also hypothesized to have a prophylactic role in preventing infection or disease severity in COVID-19. It was also touted as a wonder drug for the disease by many prominent international figures. However, later studies which were well-designed randomized controlled trials failed to demonstrate any benefit of hydroxychloroquine in COVID-19. 23 , 24 , 25 , 26 Subsequently, azithromycin 27 , 28 and ivermectin 29 were hypothesized as potential therapies for COVID-19, but were not supported by evidence from randomized controlled trials. The role of vitamin D in preventing disease severity was also proposed, but has not been proven definitively until now. 30 , 31 On the other hand, randomized controlled trials identified the evidence supporting dexamethasone 32 and interleukin-6 pathway blockade with tocilizumab as effective therapies for COVID-19 in specific situations such as at the onset of hypoxia. 33 , 34 Clues towards the apparent effectiveness of various drugs against severe acute respiratory syndrome coronavirus 2 in vitro but their ineffectiveness in vivo have recently been identified. Many of these drugs are weak, lipophilic bases and some others induce phospholipidosis which results in apparent in vitro effectiveness due to non-specific off-target effects that are not replicated inside living systems. 35 , 36

Another hypothesis proposed was the association of the routine policy of vaccination with Bacillus Calmette-Guerin (BCG) with lower deaths due to COVID-19. This hypothesis emerged in the middle of 2020 when COVID-19 was still taking foot in many parts of the world. 37 , 38 Subsequently, many countries which had lower deaths at that time point went on to have higher numbers of mortality, comparable to other areas of the world. Furthermore, the hypothesis that BCG vaccination reduced COVID-19 mortality was a classic example of ecological fallacy. Associations between population level events (ecological studies; in this case, BCG vaccination and COVID-19 mortality) cannot be directly extrapolated to the individual level. Furthermore, such associations cannot per se be attributed as causal in nature, and can only serve to generate hypotheses that need to be tested at the individual level. 39

IS TRADITIONAL PEER REVIEW EFFICIENT FOR EVALUATION OF WORKING AND SCIENTIFIC HYPOTHESES?

Traditionally, publication after peer review has been considered the gold standard before any new idea finds acceptability amongst the scientific community. Getting a work (including a working or scientific hypothesis) reviewed by experts in the field before experiments are conducted to prove or disprove it helps to refine the idea further as well as improve the experiments planned to test the hypothesis. 40 A route towards this has been the emergence of journals dedicated to publishing hypotheses such as the Central Asian Journal of Medical Hypotheses and Ethics. 41 Another means of publishing hypotheses is through registered research protocols detailing the background, hypothesis, and methodology of a particular study. If such protocols are published after peer review, then the journal commits to publishing the completed study irrespective of whether the study hypothesis is proven or disproven. 42 In the post-pandemic world, online research methods such as online surveys powered via social media channels such as Twitter and Instagram might serve as critical tools to generate as well as to preliminarily test the appropriateness of hypotheses for further evaluation. 43 , 44

Some radical hypotheses might be difficult to publish after traditional peer review. These hypotheses might only be acceptable by the scientific community after they are tested in research studies. Preprints might be a way to disseminate such controversial and ground-breaking hypotheses. 45 However, scientists might prefer to keep their hypotheses confidential for the fear of plagiarism of ideas, avoiding online posting and publishing until they have tested the hypotheses.

SUGGESTIONS ON GENERATING AND PUBLISHING HYPOTHESES

Publication of hypotheses is important, however, a balance is required between scientific temper and controversy. Journal editors and reviewers might keep in mind these specific points, summarized in Table 2 and detailed hereafter, while judging the merit of hypotheses for publication. Keeping in mind the ethical principle of primum non nocere, a hypothesis should be published only if it is testable in a manner that is ethically appropriate. 46 Such hypotheses should be grounded in reality and lend themselves to further testing to either prove or disprove them. It must be considered that subsequent experiments to prove or disprove a hypothesis have an equal chance of failing or succeeding, akin to tossing a coin. A pre-conceived belief that a hypothesis is unlikely to be proven correct should not form the basis of rejection of such a hypothesis for publication. In this context, hypotheses generated after a thorough literature search to identify knowledge gaps or based on concrete clinical observations on a considerable number of patients (as opposed to random observations on a few patients) are more likely to be acceptable for publication by peer-reviewed journals. Also, hypotheses should be considered for publication or rejection based on their implications for science at large rather than whether the subsequent experiments to test them end up with results in favour of or against the original hypothesis.

Hypotheses form an important part of the scientific literature. The COVID-19 pandemic has reiterated the importance and relevance of hypotheses for dealing with public health emergencies and highlighted the need for evidence-based and ethical hypotheses. A good hypothesis is testable in a relevant study design, backed by preliminary evidence, and has positive ethical and clinical implications. General medical journals might consider publishing hypotheses as a specific article type to enable more rapid advancement of science.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Data curation: Gasparyan AY, Misra DP, Zimba O, Yessirkepov M, Agarwal V, Kitas GD.

• Urgent Support

Engineering Graduate Studies

Hypothesis and Experimental Design

Jump to: Activity Examples | Resources

Two important elements of The Scientific Method that will help you design your research approach more efficiently are “Generating Hypotheses” and “Designing Controlled Experiments” to test these hypotheses. A well-designed experiment that you deeply understand will save time and resources and facilitate easier data analysis/interpretation. Many people reading this may be working on a project that focuses on designing a product, or discovery research where the hypothesis it is not immediately obvious. We encourage you to read on however as the exercise of generating a hypothesis will likely help you think about the assumptions you are making in your research and the physical principles your work builds upon.     

These activities will help you …  

• Begin formulating an appropriate hypothesis related to your research.  
• Apply a systematic process for designing experiments.  

What is a Hypothesis?  

A hypothesis is an “educated guess/prediction”  or  “ proposed explanation ”  of how a system will behave based on the available evidence .  A hypothesis is a starting point for further investigation and testing   because a hypothesis makes a prediction about the behavior of a measurable outcome of an experiment.  A hypothesis should be:  

• Testable – you can design an experiment to test it  
• Falsifiable – it can be proven wrong (note it cannot be “proved”)  
• Useful – the outcome must give valuable information  

A useful hypothesis may relate to the underlying question of your research. For example:  

“We hypothesize that therapy resistant cell populations will be enriched in hypoxic microenvironments. “  

“We hypothesize that  increasing the number of boreholes simulated in 3D geological models minimizes the variation of the geological model results.”    

Some research projects do not have an obvious hypothesis to test, but the design strategy/concept chosen is based on an underlying assumption about how the system being designed works (i.e. the hypothesis). For example:  

“We hypothesize that decreasing the baking temperature of the photoresist layer will reduce thermal expansion and device cracking”   

In this case the researcher is troubleshooting poor device quality and is proposing to vary different fabrication parameters (one being baking temperature). Understanding the assumptions (working hypotheses) of why different variables might improve device quality is useful as it provides a basis to prioritize what variables to focus on first. The core goal of this research is not to test a specific hypothesis, but using the scientific method to troubleshoot a design challenge will enable the researcher to understand the parameters that control the behavior of different designs and to identify a design that is successful more efficiently.  

In all the examples above, the hypothesis helps to guide the design of a useful and interpretable experiment with appropriate controls that rule out alternative explanations of the experimental observation. Hypotheses are therefore likely essential and useful parts of all research projects.  

Suggested Activity – Create a Hypothesis for Your Research  

Estimated time: 30 mins    

• Write down the parameters you are varying or testing in your experimental system or model and how you think the behaviour of the system is going to vary with these parameters.   
• (Alternative) If your project goal is to design a device, write down the parameters you believe control whether the device will work.  
• (Alternative) If your project goal involves optimizing a process,  write down the underlying physics or chemistry controlling the process you are studying.  
• With these parameters in mind, write down the key assumption(s) you are making about how your system works. 
• Try to formulate each one of these assumptions into a hypothesis that might be useful for your research project.  If you have multiple aims each one may have a separate hypothesis. Make sure the hypothesis meets each of the three key elements above.
• Share your hypothesis with a peer or your supervisor to discuss if this is a good hypothesis – is it testable? Does it make a useful prediction? Does it capture the key underlying assumptions your research is based upon?  

Remember that writing a good research hypothesis is challenging and will take a lot of careful thought about the underlying science that governs your system.  

Designing Experiments  

Designing experiments appropriately is very important to avoid wasting resources (time!) and to ensure results can be interpreted correctly. It is often very useful to discuss the design of your planned experiments in your meetings with your supervisor to get feedback before you start doing experiments. This will also ensure you and your supervisor have a consistent understanding of experimental design and that all the appropriate controls required to interpret your data have been considered.  

The factors that must be considered when you design experiments is going to depend on your specific area of research. S ome important things to think about when designing experiments include:  

Rationale:  What is the purpose of this experiment? Is this the best experiment I can do?  Does my experiment answer  any question ?  Does this experiment help answer  the question  I am trying to ask?  What hypothesis am I trying to test?  

Will my experiment be interpretable?   What controls can I use to distinguish my results from other potential explanations? Can I add a control to distinguish between explanations? Can I add a control to further test my hypothesis?  

Is my experiment/model rigorous?   What is the  sensitivity of the method  I am using and can it measure accurately what I want to measure? What  outcomes  (metrics) will I measure and is this measurement appropriate?  How many  replicates  (technical replicates versus independent replicates) will I do?  Am I only changing the  variable  that I am testing? What am I keeping constant? What  statistical tests  do I plan to carry out and what considerations are needed? Is my statistical design appropriate (power analysis, sufficient replicates)?  

What logistics do I need to consider?  Are the equipment/resources I need available? Do I need additional training or equipment access? Are there important safety or ethical issues/permits to consider? Are pilot experiments needed to assess feasibility and what would these be? What is my planned experimental protocol and are there important timing issues to consider? What experimental outputs and parameters need to be documented throughout experiment?  

This list is not exhaustive and you should consider what is missing for your particular situation.  

Suggested Activity – Design an Experiment Using a Template  

Estimated time: 45 min  

• Explore the excel template for experimental design ( Resource 1 )   or modelling  ( Resource 2 ).  A template like this is very useful for keeping track of protocols as well as improving the reproducibility of your experiments. Note this template is simply a  starting point  to get you thinking systematically and should be adapted to best suit  your  needs.   
• Fill out the template for an experiment or modelling project you are planning to complete soon.  
• Consider how you can modify this template to be more applicable to your specific project.  
• Using the template document, explain your experimental design/model design to a peer or your supervisor. Let them ask questions to understand your design and provide feedback. Alternatively, if there is a part of your design that you are unclear about this is a great starting point for a targeted and efficient discussion with your supervisor.   
• Revise your design based on feedback.  

Activity Examples

© 2024 Faculty of Applied Science and Engineering

• U of T Home
• Accessibility
• Student Data Practices
• Website Feedback

• 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.

1.2: The 7-Step Process of Statistical Hypothesis Testing

• Last updated
• Save as PDF
• Page ID 33320

• Penn State's Department of Statistics
• The Pennsylvania State University

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

We will cover the seven steps one by one.

Step 1: State the Null Hypothesis

The null hypothesis can be thought of as the opposite of the "guess" the researchers made: in this example, the biologist thinks the plant height will be different for the fertilizers. So the null would be that there will be no difference among the groups of plants. Specifically, in more statistical language the null for an ANOVA is that the means are the same. We state the null hypothesis as: \[H_{0}: \ \mu_{1} = \mu_{2} = \ldots = \mu_{T}\] for \(T\) levels of an experimental treatment.

Why do we do this? Why not simply test the working hypothesis directly? The answer lies in the Popperian Principle of Falsification. Karl Popper (a philosopher) discovered that we can't conclusively confirm a hypothesis, but we can conclusively negate one. So we set up a null hypothesis which is effectively the opposite of the working hypothesis. The hope is that based on the strength of the data, we will be able to negate or reject the null hypothesis and accept an alternative hypothesis. In other words, we usually see the working hypothesis in \(H_{A}\).

Step 2: State the Alternative Hypothesis

\[H_{A}: \ \text{treatment level means not all equal}\]

The reason we state the alternative hypothesis this way is that if the null is rejected, there are many possibilities.

For example, \(\mu_{1} \neq \mu_{2} = \ldots = \mu_{T}\) is one possibility, as is \(\mu_{1} = \mu_{2} \neq \mu_{3} = \ldots = \mu_{T}\). Many people make the mistake of stating the alternative hypothesis as \(mu_{1} \neq mu_{2} \neq \ldots \neq \mu_{T}\), which says that every mean differs from every other mean. This is a possibility, but only one of many possibilities. To cover all alternative outcomes, we resort to a verbal statement of "not all equal" and then follow up with mean comparisons to find out where differences among means exist. In our example, this means that fertilizer 1 may result in plants that are really tall, but fertilizers 2, 3, and the plants with no fertilizers don't differ from one another. A simpler way of thinking about this is that at least one mean is different from all others.

Step 3: Set \(\alpha\)

If we look at what can happen in a hypothesis test, we can construct the following contingency table:

You should be familiar with type I and type II errors from your introductory course. It is important to note that we want to set \(\alpha\) before the experiment ( a priori ) because the Type I error is the more grievous error to make. The typical value of \(\alpha\) is 0.05, establishing a 95% confidence level. For this course, we will assume \(\alpha\) =0.05, unless stated otherwise.

Step 4: Collect Data

Remember the importance of recognizing whether data is collected through an experimental design or observational study.

Step 5: Calculate a test statistic

For categorical treatment level means, we use an \(F\) statistic, named after R.A. Fisher. We will explore the mechanics of computing the \(F\) statistic beginning in Chapter 2. The \(F\) value we get from the data is labeled \(F_{\text{calculated}}\).

Step 6: Construct Acceptance / Rejection regions

As with all other test statistics, a threshold (critical) value of \(F\) is established. This \(F\) value can be obtained from statistical tables or software and is referred to as \(F_{\text{critical}}\) or \(F_{\alpha}\). As a reminder, this critical value is the minimum value for the test statistic (in this case the F test) for us to be able to reject the null.

The \(F\) distribution, \(F_{\alpha}\), and the location of acceptance and rejection regions are shown in the graph below:

Step 7: Based on steps 5 and 6, draw a conclusion about H0

If the \(F_{\text{\calculated}}\) from the data is larger than the \(F_{\alpha}\), then you are in the rejection region and you can reject the null hypothesis with \((1 - \alpha)\) level of confidence.

Note that modern statistical software condenses steps 6 and 7 by providing a \(p\)-value. The \(p\)-value here is the probability of getting an \(F_{\text{calculated}}\) even greater than what you observe assuming the null hypothesis is true. If by chance, the \(F_{\text{calculated}} = F_{\alpha}\), then the \(p\)-value would exactly equal \(\alpha\). With larger \(F_{\text{calculated}}\) values, we move further into the rejection region and the \(p\) - value becomes less than \(\alpha\). So the decision rule is as follows:

If the \(p\) - value obtained from the ANOVA is less than \(\alpha\), then reject \(H_{0}\) and accept \(H_{A}\).

If you are not familiar with this material, we suggest that you review course materials from your basic statistics course.

Elektrostal

City in moscow oblast, russia / from wikipedia, the free encyclopedia, dear wikiwand ai, let's keep it short by simply answering these key questions:.

Can you list the top facts and stats about Elektrostal?

Summarize this article for a 10 year old

Current time by city

For example, New York

Current time by country

For example, Japan

Time difference

For example, London

For example, Dubai

Coordinates

For example, Hong Kong

For example, Delhi

For example, Sydney

Geographic coordinates of Elektrostal, Moscow Oblast, Russia

City coordinates

Coordinates of Elektrostal in decimal degrees

Coordinates of elektrostal in degrees and decimal minutes, utm coordinates of elektrostal, geographic coordinate systems.

WGS 84 coordinate reference system is the latest revision of the World Geodetic System, which is used in mapping and navigation, including GPS satellite navigation system (the Global Positioning System).

Geographic coordinates (latitude and longitude) define a position on the Earth’s surface. Coordinates are angular units. The canonical form of latitude and longitude representation uses degrees (°), minutes (′), and seconds (″). GPS systems widely use coordinates in degrees and decimal minutes, or in decimal degrees.

Latitude varies from −90° to 90°. The latitude of the Equator is 0°; the latitude of the South Pole is −90°; the latitude of the North Pole is 90°. Positive latitude values correspond to the geographic locations north of the Equator (abbrev. N). Negative latitude values correspond to the geographic locations south of the Equator (abbrev. S).

Longitude is counted from the prime meridian ( IERS Reference Meridian for WGS 84) and varies from −180° to 180°. Positive longitude values correspond to the geographic locations east of the prime meridian (abbrev. E). Negative longitude values correspond to the geographic locations west of the prime meridian (abbrev. W).

UTM or Universal Transverse Mercator coordinate system divides the Earth’s surface into 60 longitudinal zones. The coordinates of a location within each zone are defined as a planar coordinate pair related to the intersection of the equator and the zone’s central meridian, and measured in meters.

Elevation above sea level is a measure of a geographic location’s height. We are using the global digital elevation model GTOPO30 .

Elektrostal , Moscow Oblast, Russia