spss one way anova assignment

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• SPSS Tutorials

One-Way ANOVA

Spss tutorials: one-way anova.

• The SPSS Environment
• The Data View Window
• Using SPSS Syntax
• Data Creation in SPSS
• Importing Data into SPSS
• Variable Types
• Date-Time Variables in SPSS
• Defining Variables
• Creating a Codebook
• Computing Variables
• Computing Variables: Mean Centering
• Computing Variables: Recoding Categorical Variables
• Computing Variables: Recoding String Variables into Coded Categories (Automatic Recode)
• rank transform converts a set of data values by ordering them from smallest to largest, and then assigning a rank to each value. In SPSS, the Rank Cases procedure can be used to compute the rank transform of a variable." href="https://libguides.library.kent.edu/SPSS/RankCases" style="" >Computing Variables: Rank Transforms (Rank Cases)
• Weighting Cases
• Sorting Data
• Grouping Data
• Descriptive Stats for One Numeric Variable (Explore)
• Descriptive Stats for One Numeric Variable (Frequencies)
• Descriptive Stats for Many Numeric Variables (Descriptives)
• Descriptive Stats by Group (Compare Means)
• Frequency Tables
• Working with "Check All That Apply" Survey Data (Multiple Response Sets)
• Chi-Square Test of Independence
• Pearson Correlation
• One Sample t Test
• Paired Samples t Test
• Independent Samples t Test
• How to Cite the Tutorials

Sample Data Files

Our tutorials reference a dataset called "sample" in many examples. If you'd like to download the sample dataset to work through the examples, choose one of the files below:

• Data definitions (*.pdf)
• Data - Comma delimited (*.csv)
• Data - Tab delimited (*.txt)
• Data - Excel format (*.xlsx)
• Data - SAS format (*.sas7bdat)
• Data - SPSS format (*.sav)
• SPSS Syntax (*.sps) Syntax to add variable labels, value labels, set variable types, and compute several recoded variables used in later tutorials.
• SAS Syntax (*.sas) Syntax to read the CSV-format sample data and set variable labels and formats/value labels.

One-Way ANOVA ("analysis of variance") compares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. One-Way ANOVA is a parametric test.

This test is also known as:

• One-Factor ANOVA
• One-Way Analysis of Variance
• Between Subjects ANOVA

The variables used in this test are known as:

• Dependent variable
• This variable divides cases into two or more mutually exclusive levels , or groups

Common Uses

The One-Way ANOVA is often used to analyze data from the following types of studies:

• Field studies
• Experiments
• Quasi-experiments

The One-Way ANOVA is commonly used to test the following:

• Statistical differences among the means of two or more groups
• Statistical differences among the means of two or more interventions
• Statistical differences among the means of two or more change scores

Note: Both the One-Way ANOVA and the Independent Samples t Test can compare the means for two groups. However, only the One-Way ANOVA can compare the means across three or more groups.

Note: If the grouping variable has only two groups, then the results of a one-way ANOVA and the independent samples t test will be equivalent. In fact, if you run both an independent samples t test and a one-way ANOVA in this situation, you should be able to confirm that t 2 = F .

Data Requirements

Your data must meet the following requirements:

• Dependent variable that is continuous (i.e., interval or ratio level)
• Independent variable that is categorical (i.e., two or more groups)
• Cases that have values on both the dependent and independent variables
• subjects in the first group cannot also be in the second group
• no subject in either group can influence subjects in the other group
• no group can influence the other group
• Random sample of data from the population
• Non-normal population distributions, especially those that are thick-tailed or heavily skewed, considerably reduce the power of the test
• Among moderate or large samples, a violation of normality may yield fairly accurate p values
• When this assumption is violated and the sample sizes differ among groups, the p value for the overall F test is not trustworthy. These conditions warrant using alternative statistics that do not assume equal variances among populations, such as the Browne-Forsythe or Welch statistics (available via Options in the One-Way ANOVA dialog box).
• When this assumption is violated, regardless of whether the group sample sizes are fairly equal, the results may not be trustworthy for post hoc tests. When variances are unequal, post hoc tests that do not assume equal variances should be used (e.g., Dunnett’s C ).
• No outliers

Note: When the normality, homogeneity of variances, or outliers assumptions for One-Way ANOVA are not met, you may want to run the nonparametric Kruskal-Wallis test instead.

Researchers often follow several rules of thumb for one-way ANOVA:

• Each group should have at least 6 subjects (ideally more; inferences for the population will be more tenuous with too few subjects)
• Balanced designs (i.e., same number of subjects in each group) are ideal; extremely unbalanced designs increase the possibility that violating any of the requirements/assumptions will threaten the validity of the ANOVA F test

The null and alternative hypotheses of one-way ANOVA can be expressed as:

H 0 : µ 1  = µ 2  = µ 3  = ...   = µ k   ("all k population means are equal") H 1 : At least one µ i different  ("at least one of the k population means is not equal to the others")

• µ i is the population mean of the i th group ( i = 1, 2, ..., k )

Note: The One-Way ANOVA is considered an omnibus (Latin for “all”) test because the F test indicates whether the model is significant overall —i.e., whether or not there are any significant differences in the means between any of the groups. (Stated another way, this says that at least one of the means is different from the others.) However, it does not indicate which mean is different. Determining which specific pairs of means are significantly different requires either contrasts or post hoc (Latin for “after this”) tests.

Test Statistic

The test statistic for a One-Way ANOVA is denoted as F . For an independent variable with k groups, the F statistic evaluates whether the group means are significantly different. Because the computation of the F statistic is slightly more involved than computing the paired or independent samples t test statistics, it's extremely common for all of the F statistic components to be depicted in a table like the following:

SSR = the regression sum of squares

SSE = the error sum of squares

SST = the total sum of squares (SST = SSR + SSE)

df r = the model degrees of freedom (equal to df r = k - 1)

df e = the error degrees of freedom (equal to df e = n - k )

k = the total number of groups (levels of the independent variable)

n = the total number of valid observations

df T = the total degrees of freedom (equal to df T = df r + df e = n - 1)

MSR = SSR/df r = the regression mean square

MSE = SSE/df e = the mean square error

Then the F statistic itself is computed as

$$ F = \frac{\mathrm{MSR}}{\mathrm{MSE}} $$

Note: In some texts you may see the notation df 1 or ν 1 for the regression degrees of freedom, and df 2 or ν 2 for the error degrees of freedom. The latter notation uses the Greek letter nu ( ν ) for the degrees of freedom.

Some texts may use "SSTr" (Tr = "treatment") instead of SSR (R = "regression"), and may use SSTo (To = "total") instead of SST.

The terms Treatment (or Model ) and Error are the terms most commonly used in natural sciences and in traditional experimental design texts. In the social sciences, it is more common to see the terms Between groups instead of "Treatment", and Within groups instead of "Error". The between/within terminology is what SPSS uses in the one-way ANOVA procedure.

Data Set-Up

Your data should include at least two variables (represented in columns) that will be used in the analysis. The independent variable should be categorical (nominal or ordinal) and include at least two groups, and the dependent variable should be continuous (i.e., interval or ratio). Each row of the dataset should represent a unique subject or experimental unit.

Note: SPSS restricts categorical indicators to numeric or short string values only.

Run a One-Way ANOVA

The following steps reflect SPSS’s dedicated One-Way ANOVA procedure. However, since the One-Way ANOVA is also part of the General Linear Model (GLM) family of statistical tests, it can also be conducted via the Univariate GLM procedure (“univariate” refers to one dependent variable). This latter method may be beneficial if your analysis goes beyond the simple One-Way ANOVA and involves multiple independent variables, fixed and random factors, and/or weighting variables and covariates (e.g., One-Way ANCOVA). We proceed by explaining how to run a One-Way ANOVA using SPSS’s dedicated procedure.

To run a One-Way ANOVA in SPSS, click Analyze > Compare Means > One-Way ANOVA .

The One-Way ANOVA window opens, where you will specify the variables to be used in the analysis. All of the variables in your dataset appear in the list on the left side. Move variables to the right by selecting them in the list and clicking the blue arrow buttons. You can move a variable(s) to either of two areas: Dependent List or Factor .

A Dependent List: The dependent variable(s). This is the variable whose means will be compared between the samples (groups). You may run multiple means comparisons simultaneously by selecting more than one dependent variable.

B Factor: The independent variable. The categories (or groups) of the independent variable will define which samples will be compared. The independent variable must have at least two categories (groups), but usually has three or more groups when used in a One-Way ANOVA.

C Contrasts: (Optional) Specify contrasts, or planned comparisons, to be conducted after the overall ANOVA test.

When the initial F test indicates that significant differences exist between group means, contrasts are useful for determining which specific means are significantly different when you have specific hypotheses that you wish to test . Contrasts are decided before analyzing the data (i.e., a priori ). Contrasts break down the variance into component parts. They may involve using weights, non-orthogonal comparisons, standard contrasts, and polynomial contrasts (trend analysis).

Many online and print resources detail the distinctions among these options and will help users select appropriate contrasts. For more information about contrasts, you can open the IBM SPSS help manual from within SPSS by clicking the "Help" button at the bottom of the One-Way ANOVA dialog window.

D Post Hoc: (Optional) Request post hoc (also known as multiple comparisons ) tests. Specific post hoc tests can be selected by checking the associated boxes.

1 Equal Variances Assumed: Multiple comparisons options that assume homogeneity of variance (each group has equal variance). For detailed information about the specific comparison methods, click the Help button in this window.

2 Test: By default, a 2-sided hypothesis test is selected. Alternatively, a directional, one-sided hypothesis test can be specified if you choose to use a Dunnett post hoc test. Click the box next to Dunnett and then specify whether the Control Category is the Last or First group, numerically, of your grouping variable. In the Test area, click either < Control or > Control . The one-tailed options require that you specify whether you predict that the mean for the specified control group will be less than ( > Control ) or greater than ( < Control ) another group.

3 Equal Variances Not Assumed: Multiple comparisons options that do not assume equal variances. For detailed information about the specific comparison methods, click the Help button in this window.

4 Significance level: The desired cutoff for statistical significance. By default, significance is set to 0.05.

When the initial F test indicates that significant differences exist between group means, post hoc tests are useful for determining which specific means are significantly different when you do not have specific hypotheses that you wish to test . Post hoc tests compare each pair of means (like t-tests), but unlike t-tests, they correct the significance estimate to account for the multiple comparisons.

E Options: Clicking Options will produce a window where you can specify which Statistics to include in the output (Descriptive, Fixed and random effects, Homogeneity of variance test, Brown-Forsythe, Welch), whether to include a Means plot , and how the analysis will address Missing Values (i.e., Exclude cases analysis by analysis or Exclude cases listwise ). Click Continue when you are finished making specifications.

Click OK to run the One-Way ANOVA.

To introduce one-way ANOVA, let's use an example with a relatively obvious conclusion. The goal here is to show the thought process behind a one-way ANOVA.

Problem Statement

In the sample dataset, the variable Sprint is the respondent's time (in seconds) to sprint a given distance, and Smoking is an indicator about whether or not the respondent smokes (0 = Nonsmoker, 1 = Past smoker, 2 = Current smoker). Let's use ANOVA to test if there is a statistically significant difference in sprint time with respect to smoking status. Sprint time will serve as the dependent variable, and smoking status will act as the independent variable.

Before the Test

Just like we did with the paired t test and the independent samples t test, we'll want to look at descriptive statistics and graphs to get picture of the data before we run any inferential statistics.

The sprint times are a continuous measure of time to sprint a given distance in seconds. From the Descriptives procedure ( Analyze > Descriptive Statistics > Descriptives ), we see that the times exhibit a range of 4.5 to 9.6 seconds, with a mean of 6.6 seconds (based on n=374 valid cases). From the Compare Means procedure ( Analyze > Compare Means > Means ), we see these statistics with respect to the groups of interest:

Notice that, according to the Compare Means procedure, the valid sample size is actually n=353. This is because Compare Means (and additionally, the one-way ANOVA procedure itself) requires there to be nonmissing values for both the sprint time and the smoking indicator.

Lastly, we'll also want to look at a comparative boxplot to get an idea of the distribution of the data with respect to the groups:

From the boxplots, we see that there are no outliers; that the distributions are roughly symmetric; and that the center of the distributions don't appear to be hugely different. The median sprint time for the nonsmokers is slightly faster than the median sprint time of the past and current smokers.

Running the Procedure

• Click  Analyze > Compare Means > One-Way ANOVA .
• Add the variable Sprint to the Dependent List box, and add the variable Smoking to the Factor box.
• Click Options . Check the box for Means plot , then click Continue .
• Click OK when finished.

Output for the analysis will display in the Output Viewer window.

The output displays a table entitled ANOVA .

After any table output, the Means plot is displayed.

The Means plot is a visual representation of what we saw in the Compare Means output. The points on the chart are the average of each group. It's much easier to see from this graph that the current smokers had the slowest mean sprint time, while the nonsmokers had the fastest mean sprint time.

Discussion and Conclusions

We conclude that the mean sprint time is significantly different for at least one of the smoking groups ( F 2, 350 = 9.209, p < 0.001). Note that the ANOVA alone does not tell us specifically which means were different from one another. To determine that, we would need to follow up with multiple comparisons (or post-hoc ) tests.

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SPSS One-Way ANOVA Tutorial

For reading up on some basics, see ANOVA - What Is It?

One-Way ANOVA - Null Hypothesis

Anova assumptions, spss anova flowchart, spss one-way anova dialog.

• SPSS ANOVA Output

ANOVA - APA Reporting Guidelines

Anova example - effect of fertilizers on plants.

A farmer wants to know which fertilizer is best for his parsley plants. So he tries different fertilizers on different plants and weighs these plants after 6 weeks. The data -partly shown below- are in parsley.sav .

Quick Data Check - Split Histograms

After opening our data in SPSS , let's first see what they basically look like. A quick way for doing so is inspecting a histogram of weights for each fertilizer separately. The screenshot below guides you through.

After following these steps, clicking P aste results in the syntax below. Let's run it.

Importantly, these distributions look plausible and we don't see any outliers: our data seem correct to begin with -not always the case with real-world data! Conclusion: the vast majority of weights are between some 40 and 65 grams and they seem reasonably normally distributed .

Inspecting Sample Sizes and Means

• We have sample sizes of n = 30 for each fertilizer .
• Second, the chemical fertilizer resulted in the highest mean weight of almost 57 grams. “None” performed worst at some 51 grams while “Biological” is in between.
• “Biological” has a slightly higher standard deviation than the other conditions but the difference is pretty small.

Now, this table tells us a lot about our samples of plants. But what do our sample means say about the population means? Can we say anything about the effects of fertilizers on all (future) plants? We'll try to do so by refuting the statement that all fertilizers perform equally: our null hypothesis.

The null hypothesis for ANOVA is that all population means are equal. If this is true, then our sample means will probably differ a bit anyway. However, very different sample means contradict the hypothesis that the population means are equal. In this case, we may conclude that this null hypothesis probably wasn't true after all. ANOVA will basically tells us to what extent our null hypothesis is credible. However, it requires some assumptions regarding our data.

• independent observations : each record in the data must be a distinct and independent entity. Precisely, the assumption is “independent and identically distributed variables” but a thorough explanation is way beyond the scope of this tutorial.
• normality : the dependent variable is normally distributed in the population. Normality is not needed for reasonable sample sizes, say each n ≥ 25.
• homogeneity : the variance of the dependent variable must be equal in each subpopulation. Homogeneity is only needed for (sharply) unequal sample sizes. In this case, Levene's test can be used to see if homogeneity is met.

So how to check if we meet these assumptions? And what to do if we violate them? The simple flowchart below guides us through.

So what about our data?

• Our plants seem to be independent observations : each has a different id value (first variable).
• Our means table shows that each n ≥ 25 so we don't need to meet normality.
• Since our sample sizes are equal, we don't need the homogeneity assumption either.

So why do we inspect our sample sizes based on a means table ? Why didn't we just look at the frequency distribution for fertilizer? Well, our ANOVA uses only cases without missing values on our dependent variable. And our means table shows precisely those. A second reason is that we need to report the means and standard deviations per group. And the means table gives us precisely the statistics we want in the order we want them.

We'll now run a basic ANOVA from the menu. The screenshot below guides you through.

The P aste button creates the syntax below.

One-Way ANOVA Syntax

Spss one-way anova output.

A general rule of thumb is that we reject the null hypothesis if “Sig.” or p < 0.05 which is the case here. So we reject the null hypothesis that all population means are equal. Conclusion : different fertilizers perform differently. The differences between our mean weights -ranging from 51 to 57 grams- are statistically significant .

First and foremost, we'll report our means table . Regarding the significance test, the APA suggests we report

• the F value;
• df1 , the numerator d egrees of f reedom;
• df2 , the denominator degrees of freedom;
• the p value

like so: “our three fertilizer conditions resulted in different mean weights for the parsley plants, F(2,87) = 3.7, p = .028.”

One-Way ANOVA - Next Steps

For this example, there's 2 more things we could take a look at:

• Post hoc tests : our ANOVA results tell us that not all population means are equal. But precisely which mean differs from which other mean? This is answered by running post hoc tests . For an outstanding tutorial, consult SPSS - One Way ANOVA with Post Hoc Tests Example .
• Effect size : we concluded that fertilizers affect mean weights but how strong is this effect? A common effect size measure for ANOVA is partial eta squared . Sadly, effect size is absent from the One-Way dialog. Oddly, MEANS does include eta-squared but lacks other essential options such as Levene’s test. For complete output, you need to run your ANOVA twice from 2 different commands. This really is a major stupidity in SPSS . There. I said it.

ANOVA with Eta-Squared from MEANS

Final Notes

Right, so that's about the most basic SPSS ANOVA tutorial I could come up with. I hope you found it helpful. Let me know what you think by throwing me a comment below. Thanks for reading!

Tell us what you think!

This tutorial has 49 comments:.

By Wiselychong on June 18th, 2020

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By belete on August 20th, 2020

it is very help full tutorial service . keep up with support ,please

By Mustapha Touray on May 8th, 2021

Your explanation is very concise and understandable. Thanks for the efforts, well appreciated.

By Christopher Raj on October 15th, 2021

Excellent presentation

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EZ SPSS Tutorials

One Way ANOVA in SPSS Including Interpretation

In this tutorial, we’ll look at how to perform a one-way analysis of variance (ANOVA) for independent groups in SPSS, and how to interpret the result using Tukey’s HSD.

Quick Steps

• Click on Analyze -> Compare Means -> One-Way ANOVA
• Drag and drop your independent variable into the Factor box and dependent variable into the Dependent List box
• Click on Post Hoc, select Tukey, and press Continue
• Click on Options, select Homogeneity of variance test, and press Continue
• Press the OK button, and your result will pop up in the Output viewer

We’re starting from the assumption that you’ve already got your data into SPSS, and you’re looking at a Data View screen that looks a bit like this.

Our fictitious dataset contains a number of different variables. For the purposes of this tutorial, we’re interested in whether level of education has an effect on the ability of a person to throw a frisbee. Our independent variable, therefore, is Education, which has three levels – High School, Graduate and PostGrad – and our dependent variable is Frisbee Throwing Distance (i.e., the distance a subject throws a frisbee).

The one-way ANOVA test allows us to determine whether there is a significant difference in the mean distances thrown by each of the groups.

One-Way Analysis of Variance (ANOVA)

To start, click on Analyze -> Compare Means -> One-Way ANOVA.

This will bring up the One-Way ANOVA dialog box.

To set up the test, you’ve got to get your independent variable into the Factor box (Education in this case, see above) and dependent variable into the Dependent List box. You can do this by dragging and dropping, or by highlighting a variable, and then clicking on the appropriate arrow in the middle of the dialog.

After you’ve moved the variables over, you should click the Post Hoc button, which will allow you to specify the post hoc test(s) you wish to run.

The ANOVA test will tell you whether there is a significant difference between the means of two or more levels of a variable. However, if you’ve got more than two levels it’s not going to tell you between which of the various pairs of means the difference is significant. You need to do a post hoc test to find this out.

Post Hoc Tests

The Post Hoc dialog box looks like this.

You should select Tukey, as shown above, and ensure that your significance level is set to 0.05 (or whatever alpha level is right for your study).

Now press Continue to return to the previous dialog box.

You should be looking at this dialog box again.

Click Options to bring up the Options dialog box.

At the very least, you should select the Homogeneity of variance test option (since homogeneity of variance is required for the ANOVA test). Descriptive statistics and a Means plot are also useful.

Once you’ve made your selections, click Continue.

At this point, you’re ready to run the test.

Review your options, and click the OK button. You’ll see the result pop up in the Output Viewer.

SPSS produces a lot of data for the one-way ANOVA test. Let’s deal with the important bits in turn.

Descriptives

It’s worth having a quick glance at the descriptive statistics generated by SPSS.

If you look above, you’ll see that our sample data produces a difference in the mean scores of the three levels of our education variable. In particular, the data analysis shows that the subjects in the PostGrad group throw the frisbee quite a bit further than subjects in the other two groups. The key question, of course, is whether the difference in mean scores reaches significance.

Homogeneity of Variances

A requirement for the ANOVA test is that the variances of each comparison group are equal. We have tested this using the Levene statistic. What you’re looking for here is a significance value that is greater than .05. You don’t want a significant result, since a significant result would suggest a real difference between variances.

In our example, as you can see above, the significance value of the Levene statistic based on a comparison of medians is .155. This is  not a significant result, which means the requirement of homogeneity of variance has been met, and the ANOVA test can be considered to be robust.

F Statistic (ANOVA Result)

Now that we know we have equal variances, we can look at the result of the ANOVA test.

The ANOVA result is easy to read. You’re looking for the value of F that appears in the Between Groups row (see above) and whether this reaches significance (next column along).

In our example, we have a significant result. The value of F is 3.50, which reaches significance with a p- value of .038 (which is less than the .05 alpha level). This means there is a statistically significant difference between the means of the different levels of the education variable.

However, as yet we don’t know between which of the various pairs of means the difference is significant. For this we need to look at the result of the post hoc Tukey HSD test.

If you take a look at the Multiple Comparisons table above you’ll see that significance values have been generated for the mean differences between pairs of the various levels of the education variable (Graduate – High School; Graduate – PostGrad; and High School – PostGrad).

In our example, the Tukey HSD (Honest Significant Difference) shows that it is only the mean difference between the High School and PostGrad groups that reaches significance (see the Sig. column, above). The  p -value is .034, which is less than the standard .05 alpha level.

Report the Result

When reporting the result it’s normal to reference both the ANOVA test and the post hoc Tukey HSD test.

Thus, given our example here, you could write something like:

There was a statistically significant difference between groups as demonstrated by one-way ANOVA ( F (2,47) = 3.50, p = .038). A Tukey post hoc test showed that the PostGrad group was able to throw the frisbee statistically significantly further than the High School group ( p = .034). There was no statistically significant difference between the Graduate and High School groups ( p = . 691) or between the Graduate and PostGrad groups ( p = .099).

Alternatively, please see our tutorial on reporting the results of a one-way ANOVA from SPSS in APA style .

***************

Right, that’s it for this tutorial. You should now be able to perform a one-way ANOVA test in SPSS, check the homogeneity of variance assumption has been met, run a post hoc test, and interpret and report your result. Check out our tutorial if you’d like to export the SPSS output for your ANOVA to another application such as Word, Excel, or PDF.

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How to Run a one-way ANOVA in SPSS: A Comprehensive Guide for Beginners

In this comprehensive tutorial, we will explore how you can perform a one-way anova in spss . You will gain an in-depth understanding of one-way anova assumptions, as well as, understanding how to run a one-way anova in SPSS step by step.

What is a One-way ANOVA Test ?

One-way ANOVA also called one-way analysis of variance (ANOVA) test is an inferential statistics test widely used in research. In particular, it is a statistical test used to determine whether there exists any statistically significant differences between two or more independent groups (factors). In other words, a one-way anova test allows you to examine the impact of a categorical variable with three or more groups, referred to as the factor, on a continuous dependent variable. It serves as an extension of the t-test, which is used for comparing means between two independent samples, but ANOVA facilitates the comparison among more than two groups.

One-Way Anova Test Assumptions

Before delving into the practical implementation and interpretation of the One Way ANOVA test, it is important to acknowledge the underlying assumptions associated with this statistical procedure. The most common assumptions for one-way anova are:

• Continuous dependent variable: The dependent variable should be measured in a continuous scale
• Multiple independent groups: The factor being studied should consist of two or more independent groups.
• Independence of observations: Each observation within the study should be independent of the others.
• Absence of outliers: Outliers, which are extreme values that deviate significantly from the rest of the data, should not be present.
• Normal distribution: The dependent variable should follow a normal distribution. It is worth noting that one-way ANOVA is a parametric technique, relying on the assumption of normality. Check out our detailed article on how to run normality test in SPSS .
• Homogeneity of variance: The variance of the dependent variable should be similar across all groups.

One-Way ANOVA test Example Scenario

To better illustrate the implementation of the ANOVA test, let’s consider an example scenario where we want to assess the effect of four different fertilizers on the growth of plants (measured using plant heights). In this case, the four different types fertilizers, say Fertilizer A, B, C and D are the categorical/independent variable (factor). The height of the plants represents the continuous dependent/response variable.

Now, let’s outline the null and alternative hypotheses for our ANOVA test:

Null hypothesis:

There is no significant difference in plant height between the four groups of fertilizers applied to the plants

Alternative hypothesis:

At least any two types of fertilizers yielded significantly different heights

Multiple Comparison Tests in One-Way ANOVA

A one-way ANOVA only informs you whether there exists significant difference between the groups. This means, anova test will not explicitly highlight the groups that differs from each other. To achieve this, post-hoc analysis is performed. There are several tests used in post hoc analysis. Some of these tests include:

• Tukey’s Honestly Significant Difference (HSD): This test is widely used to compare all possible pairs of group means. It helps in controlling the Type 1 error, thus, helping in determining the specific groups that are statistically significant.
• Bonferroni correction: This test adjusts the significance level for multiple comparisons by dividing the given level of significance (alpha) by the number of comparison. This helps in maintaining the overall level of significance.
• Scheffe’s method: Scheffe’s test is a conservative post hoc test that compares all possible group combinations. It provides simultaneous confidence intervals for all possible pairwise comparisons. Thus, it allow the researcher to identify the significant differences between groups while controlling the family-wise error rate.
• Fisher’s Least Significant Difference (LSD): This test compares all possible pairs of group means and determines the significance of the observed differences. It does not control for the family-wise error rate, so caution should be exercised when interpreting the results.
• Dunn’s test: Dunn’s test is a non parametric post hoc test used when the assumptions of ANOVA are violated. It compares group means using rank-based procedures. It is often used in situations, where the data distribution is not normal or when there are unequal variances.
• Games-Howell test: The Games-Howell test is also a non parametric test that does not assume equal variances or normality. It compares all possible pairs of group means and provides adjusted p-values to account for multiple comparisons.

These post hoc tests help researchers determine which specific group differences are statistically significant after an ANOVA analysis. This means, if the ANOVA results are insignificant, there is no need for conducting a post hoc analysis tests. The choice of which post hoc test to use will generally depend on your study design, the assumptions of the data distribution and the specific research questions proposed by the researcher.

Looking to gain a deeper understanding of parametric and non parametric tests? check out this informative guide: difference between parametric and non-parametric tests made easy . You can also hire an expert statistician to help you with statistics homework . Just click the button below.

How to Run One-Way ANOVA in SPSS: Step-by-Step Procedure

Looking for a step by step tutorial on how to run a one-way anova in SPSS? Here you will gain a comprehensive understanding on how you can perform a one-way anova test, followed by a post hoc test. You will also learn how to interpret ANOVA results in APA format.

One-Way ANOVA in SPSS Example

suppose we want to determine whether there is a difference in the mean yield of plants between three types of fertilizers. Here, the dependent variable is yield , whereas the independent variable is types of fertilizers with levels 1, 2, and 3. The data was imported into spss as shown below.

1. Import Data into SPSS

Generally, the data comes in different format. Regardless of how the data is, SPSS provides you with a way to import different data format into spss. Once, you’ve imported the data into spss, it should appear as shown below:

2. From the SPSS menu Select Analyze > Compare Means > One-way ANOVA

3. Add your dependent variable (should be continuous) to the  Dependent List  box, and add the independent variable (should be categorical) to the  Factor  box.

Once you click on one-way anova button, a box with variables will open. Transfer the continuous variable wage into the dependent list box, and factor variable responsibility to factor box.

4. Click  Options . Check the box for  Descriptive , Homogeneity of Variance and Means plot , then click  Continue .

Choose Options, and a new window will appear. Check Descriptive, Homogeneity of variance test and Means plot Click Continue.

5. Click Post Hoc and on the Equal Variances Assumed , click Tukey , then click Continue .

If we assume that we have equal variance across the group so we will use the first box of tests. The Tukey HSD test is the best option for this assumption. On the other hand, if our data does not have equal variance then we can pick up the Games-Howell or the LSD test.

6. One-Way ANOVA SPSS Output

The results will appear in the output window.

Summary of Running Procedure for One-Way ANOVA in SPSS

To run a One-Way ANOVA in SPSS,

• Click  Analyze > Compare Means > One-Way ANOVA .
• Add your dependent variable (should be continuous) to the  Dependent List  box, and add the independent variable (should be categorical) to the  Factor  box.
• Click  Options . Check the box for  Descriptive , Homogeneity of Variance and Means plot , then click  Continue .
• Click Post Hoc and on the Equal Variances Assumed , click Tukey , then click Continue .

Boom! You have successfully performed a one-way ANOVA in SPSS and you’ve SPSS Output

To Learn how to interpret these SPSS Outputs, Check out our step by step guide on reporting one-way anova spss output .

Also, if you’re still struggling with your spss homework or data analysis for your dissertation, worry no more! Online-spss is the best place for reliable spss homework help and spss data analysis services for your dissertation, thesis paper, capstone project or any other business project.

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One Way ANOVA Test in SPSS

Discover One Way ANOVA Test in SPSS ! Learn how to perform, understand SPSS output , and report results in APA style. Check out this simple, easy-to-follow guide below for a quick read!

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Introduction

Welcome to our exploration of the One-Way ANOVA Test , a statistical method that unlocks valuable insights when comparing means across multiple groups. Whether you’re a student engaged in a research project or a seasoned researcher investigating diverse populations, the One-Way ANOVA Test proves indispensable in discerning if there are significant differences among group means. In this blog post, we’ll traverse the fundamentals of the One-Way ANOVA Test , from its definition to the practical application using SPSS . By the end, you’ll possess not only a solid theoretical understanding but also the practical skills to conduct and interpret this powerful statistical analysis.

What is the One-Way ANOVA Test?

ANOVA stands for Analysis of Variance, and the “ One-Way ” denotes a scenario where there is a single independent variable with more than two levels or groups . Essentially, this test assesses whether the means of these groups are significantly different from each other. It’s a robust method for scenarios like comparing the performance of students in multiple teaching methods or examining the impact of different treatments on a medical condition. The One-Way ANOVA Test yields valuable insights into group variations, providing researchers with a statistical lens to discern patterns and make informed decisions. Now, let’s delve deeper into the assumptions, hypotheses, and the step-by-step process of conducting the One-Way ANOVA Test in SPSS .

  Assumption of the One-Way ANOVA Test

Before delving into the intricacies of the One-Way ANOVA Test, let’s outline its critical assumptions:

• Normality : The dependent variable should be approximately normally distributed within each group.
• Homogeneity of Variances : The variances of the groups being compared should be approximately equal. This assumption is crucial for the validity of the test.
• Independence : Observations within each group must be independent of each other.

Adhering to these assumptions ensures the reliability of the One-Way ANOVA Test results, providing a strong foundation for accurate statistical analysis.

Hypothesis of the One-Way ANOVA Test

Moving on to the formulation of hypotheses in the One-Way ANOVA Test,

• The null hypothesis ( H 0): There is no significant difference in the means of the groups.
• The alternative hypothesis ( H 1): there is a significant difference in the means of the groups.

Clear and specific hypotheses are crucial for the subsequent statistical analysis and interpretation.

Post-Hoc Tests for ANOVA

While the One-Way ANOVA is powerful in detecting overall group differences, it doesn’t provide specific information on which pairs of groups differ significantly. Post-hoc tests become essential in this context to conduct pairwise comparisons and identify the specific groups responsible for the observed overall difference. Without post-hoc tests, researchers might miss crucial nuances in the data, leading to incomplete or inaccurate interpretations.

Here are commonly used Post-hoc Tests for One-Way ANOVA:

• Tukey’s Honestly Significant Difference (HSD): Ideal when there are equal sample sizes and variances across groups. It controls the familywise error rate, making it suitable for multiple comparisons.
• Bonferroni Correction : Helpful when conducting numerous comparisons. It’s more conservative, adjusting the significance level to counteract the increased risk of Type I errors.
• Scheffe Test : Useful for unequal sample sizes and variances. It’s more robust but might be conservative in some situations.
• Dunnett’s Test : Designed for comparing each treatment group with a control group. It’s suitable for situations where there is a control group and multiple treatment groups.
• Games-Howell Test: Useful when sample sizes and variances are unequal across groups. It’s a robust option for situations where assumptions of homogeneity are not met.

Choosing the appropriate post-hoc test depends on the characteristics of your data and the specific research context. Consider factors such as sample sizes, homogeneity of variances, and the number of planned comparisons when deciding on the most suitable post-hoc test for your One-Way ANOVA results.

Example of One-Way ANOVA Test

To illustrate the practical application of the One-Way ANOVA Test, let’s consider a hypothetical scenario. Imagine you’re studying the effectiveness of different fertilizers on the growth of plants. You have three groups, each treated with a different fertilizer.

• The null hypothesis: there’s no significant difference in the mean plant growth across the three fertilizers.
• The alternative hypothesis: there is a significant difference in the mean plant growth across the three fertilizers.

By conducting the One-Way ANOVA Test, you can statistically evaluate whether the observed differences in plant growth are likely due to the different fertilizers’ effectiveness or if they could occur by random chance alone. This example demonstrates how the One-Way ANOVA Test can be a valuable tool in diverse fields, providing insights into the impact of various factors on the dependent variable.

How to Perform One-Way ANOVA Test in SPSS

Step by Step: Running One Way ANOVA Test in SPSS Statistics

Let’s delve into the step-by-step process of conducting the One-Way ANOVA Test using SPSS.  Here’s a step-by-step guide on how to perform a One-Way ANOVA Test in SPSS :

• STEP: Load Data into SPSS

Commence by launching SPSS and loading your dataset, which should encompass the variables of interest – a categorical independent variable. If your data is not already in SPSS format, you can import it by navigating to File > Open > Data and selecting your data file.

• STEP: Access the Analyze Menu

In the top menu, locate and click on “ Analyze .” Within the “Analyze” menu, navigate to “ Compare Means ” and choose ” One-Way ANOVA .” Analyze > Compare Means> One-Way ANOVA

• STEP: Specify Variables 

In the dialogue box, move the dependent variable (the variable for which you want to compare means) to the “ Dependent List ” field. Move the variable representing the group or factor to the “ Factor ” field. This is the independent variable with different levels or groups.

• STEP: Post-Hoc Test

Click on the “ Post Hoc ” button, Check “ Tukey ” and Adjust as per your analysis requirements.

• STEP: Options

Click on the “ Options ” button Check “ Descriptive ”, “ Homogeneity of Variance Test ” and “ Mean Plot ”

• STEP: Generate SPSS Output

Once you have specified your variables and chosen options, click the “ OK ” button to perform the analysis. SPSS will generate a comprehensive output, including the requested frequency table and chart for your dataset.

Conducting a One-Way ANOVA test in SPSS provides a robust foundation for understanding the key features of your data. Always ensure that you consult the documentation corresponding to your SPSS version, as steps might slightly differ based on the software version in use. This guide is tailored for SPSS version 25 , and for any variations, it’s recommended to refer to the software’s documentation for accurate and updated instructions.

SPSS Output for One Way ANOVA

How to Interpret SPSS Output of ANOVA Test

SPSS will generate output, including descriptive statistics, the f value, degrees of freedom, and the p-value and post-hoc  

Descriptives Table

• Mean and Standard Deviation : Evaluate the means and standard deviations of each group. This provides an initial overview of the central tendency and variability within each group.
• Sample Size (N): Confirm the number of observations in each group. Discrepancies in sample sizes could impact the interpretation.
• 95% Confidence Interval (CI): Review the confidence interval for the mean difference.

Test of Homogeneity of Variances Table

• Levene’s Test: In the Test of Homogeneity of Variances table, look at Levene’s Test statistic and associated p-value. This test assesses whether the variances across groups are roughly equal. A non-significant p-value suggests that the assumption of homogeneity of variances is met.

ANOVA Table

• Between-Groups and Within-Groups Variability: Move on to the ANOVA table, which displays the Between-Groups and Within-Groups sums of squares, degrees of freedom, mean squares, the F-ratio, and the p-value.
• F-Ratio : Focus on the F-ratio. A higher F-ratio indicates larger differences among group means relative to within-group variability.
• Degrees of Freedom : Note the degrees of freedom for Between-Groups and Within-Groups. These values are essential for calculating the critical F-value.
•   P-Value: Examine the p-value associated with the F-ratio. If the p-value is below your chosen significance level (commonly 0.05), it suggests that at least one group’s mean is significantly different.

Post Hoc Tests Table

• Specific Group Differences: If you conducted post-hoc tests, examine the results. Look for significant differences between specific pairs of groups. Pay attention to p-values and confidence intervals to identify which groups are significantly different from each other.

Effect Size Measures (Optional)

• Eta-squared : If available, consider effect size measures in the ANOVA table. Eta-squared indicates the proportion of variance in the dependent variable explained by the group differences.

How to Report Results of One-Way ANOVA Test in APA

Reporting the results of a One-Way ANOVA Test in APA style ensures clarity and adherence to established guidelines. Begin with a concise description of the analysis conducted, including the test name, the dependent variable, and the independent variable representing the groups.

For instance, “A One-Way Analysis of Variance (ANOVA) was conducted to examine the differences in plant growth across different fertilizers.”

Present the key statistical findings from the ANOVA table, including the F-ratio, degrees of freedom, and p-value. For example, “The results revealed a significant difference in plant growth among the fertilizers, F(df_between, df_within) = [F-ratio], p = [p-value].”

If the p-value is significant, proceed with post-hoc tests (e.g., Tukey’s HSD) to pinpoint specific group differences. Additionally, report effect size measures to provide a comprehensive overview of the results.

Conclude the report by summarising the implications of the findings in relation to your research question or hypothesis. This structured approach to reporting One-Way ANOVA results in APA format ensures transparency and facilitates the understanding of your research outcomes.

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How to Perform a One-Way ANOVA in SPSS

A one-way ANOVA is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups.

This type of test is called a one-way ANOVA because we are analyzing how one  predictor variable impacts a response variable.

If we were instead interested in how two predictor variables impact a response variable, we could conduct a  two-way ANOVA .

This tutorial explains how to conduct a one-way ANOVA in SPSS.

Example: One-Way ANOVA in SPSS

Suppose a researcher recruits 30 students to participate in a study. The students are randomly assigned to use one of three studying techniques for the next month to prepare for an exam. At the end of the month, all of the students take the same test. 

The test scores for the students are shown below:

Use the following steps to perform a one-way ANOVA to determine if the average scores are the same across all three groups.

Step 1: Visualize the data.

First, we’ll create boxplots to visualize the distribution of test scores for each of the three studying techniques. Click the  Graphs  tab, then click  Chart Builder .

Select  Boxplot  in the  Choose from:  window. Then drag the first chart titled  Simple boxplot  into the main editing window. Drag the variable  technique  onto the x-axis and  score  onto the y-axis.

Then click Element Properties , then  Y-axis1 . Change the  minimum  value to 60. Then click  OK .

The following boxplots will appear:

We can see that the distribution of test scores tend to be higher for students who used technique 2 compared to students who used techniques 1 and 3. To determine if these differences in scores are statistically significant, we’ll perform a one-way ANOVA.

Step 2: Perform a one-way ANOVA.

Click the  Analyze  tab, then  Compare Means , then  One-Way ANOVA .

In the new window that pops up, place the variable  score  into the box labelled Dependent list and the variable  technique  into the box labelled Factor.

Then click  Post Hoc  and check the box next to  Tukey . Then click  Continue .

Then click  Options  and check the box next to  Descriptive . Then click  Continue .

Lastly, click  OK .

Step 3: Interpret the output.

Once you click  OK , the results of the one-way ANOVA will appear. Here is how to interpret the output:

Descriptives Table

This table displays descriptive statistics for each of the three groups in our dataset.

The most relevant numbers include:

• N:  The number of students in each group.
• Mean:  The mean test score for each group.
• Std. Deviation:  The standard deviation of test scores for each group.

ANOVA Table

This table displays the results of the one-way ANOVA:

• F:  The overall F-statistic.
• Sig:  The p-value that corresponds to the F-statistic (4.545) with df numerator (2) and df denominator (27). In this case, the p-value turns out to be  .020 .

Recall that a one-way ANOVA uses the following null and alternative hypotheses:

• H 0  (null hypothesis):  μ 1  = μ 2  = μ 3  = … = μ k  (all the population means are equal)
• H A (alternative hypothesis):  at least one population mean is different   from the rest

Since the p-value from the ANOVA table is less than .05, we have sufficient evidence to reject the null hypothesis and conclude that at least one of the group means is different from the rest.

To find out exactly which group means differ from one another, we can refer to the last table in the ANOVA output.

Multiple Comparisons Table

This table displays the Tukey post-hoc multiple comparisons between each of the three groups. We are mostly interested in the  Sig.  column, which displays the p-values for the differences in means between each group:

From the table we can see the p-values for the following comparisons:

• Technique 1 vs. 2: | p-value =  0.024
• Technique 1 vs. 3 | p-value =  0.883
• Technique 2 vs. 3 | p-value =  0.067

The only group comparison that has a p-value less than .05 is between technique 1 and technique 2.

This tells us that there is a statistically significant difference in average test scores between students who used technique 1 compared to students who used technique 2.

However, there is no statistically significant difference between technique 1 and 3, or between technique 2 and 3.

Step 4: Report the results.

Lastly, we can report the results of the one-way ANOVA. Here is an example of how to do so:

A one-way ANOVA was performed to determine if three different studying techniques lead to different test scores.   A total of 10 students used each of the three studying techniques for one month before all taking the same test.   A one-way ANOVA revealed that there was a statistically significant difference in test scores between at least two groups (F(2, 27) = 4.545, p = 0.020).   Tukey’s test for multiple comparisons found that mean test scores were significantly different between students who used technique 1 and technique 2 (p = .024, 95% C.I. = [-14.48, -.92]).   There was no statistically significant difference between scores for techniques 1 and 3 (p=.883) or between scores for techniques 2 and 3 (p = .067).

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One-way ANOVA in SPSS Statistics (cont...)

Spss statistics output of the one-way anova.

SPSS Statistics generates quite a few tables in its one-way ANOVA analysis. In this section, we show you only the main tables required to understand your results from the one-way ANOVA and Tukey post hoc test. For a complete explanation of the output you have to interpret when checking your data for the six assumptions required to carry out a one-way ANOVA, see our Features: One-way ANOVA page. This includes relevant boxplots, and output from the Shapiro-Wilk test for normality and test for homogeneity of variances. Also, if your data failed the assumption of homogeneity of variances, we take you through the results for Welch ANOVA, which you will have to interpret rather than the standard one-way ANOVA in this guide. Below, we focus on the descriptives table, as well as the results for the one-way ANOVA and Tukey post hoc test only. We will go through each table in turn.

SPSS Statistics

Descriptives table.

The descriptives table (see below) provides some very useful descriptive statistics, including the mean, standard deviation and 95% confidence intervals for the dependent variable ( Time ) for each separate group (Beginners, Intermediate and Advanced), as well as when all groups are combined (Total). These figures are useful when you need to describe your data.

Published with written permission from SPSS Statistics, IBM Corporation.

ANOVA Table

This is the table that shows the output of the ANOVA analysis and whether there is a statistically significant difference between our group means. We can see that the significance value is 0.021 (i.e., p = .021), which is below 0.05. and, therefore, there is a statistically significant difference in the mean length of time to complete the spreadsheet problem between the different courses taken. This is great to know, but we do not know which of the specific groups differed. Luckily, we can find this out in the Multiple Comparisons table which contains the results of the Tukey post hoc test.

Multiple Comparisons Table

From the results so far, we know that there are statistically significant differences between the groups as a whole. The table below, Multiple Comparisons , shows which groups differed from each other. The Tukey post hoc test is generally the preferred test for conducting post hoc tests on a one-way ANOVA, but there are many others. We can see from the table below that there is a statistically significant difference in time to complete the problem between the group that took the beginner course and the intermediate course ( p = 0.046), as well as between the beginner course and advanced course ( p = 0.034). However, there were no differences between the groups that took the intermediate and advanced course ( p = 0.989).

It is also possible to run comparisons between specific groups that you decided were of interest before you looked at your results. For example, you might have expressed an interest in knowing the difference in the completion time between the beginner and intermediate course groups. This type of comparison is often called a planned contrast or a simple custom contrast. However, you do not have to confine yourself to the comparison between two time points only. You might have had an interest in understanding the difference in completion time between the beginner course group and the average of the intermediate and advanced course groups. This is called a complex contrast. All these types of custom contrast are available in SPSS Statistics. In our enhanced guide we show you how to run custom contrasts in SPSS Statistics using syntax (or sometimes a combination of the graphical user interface and syntax) and how to interpret and report the results. In addition, we also show you how to "trick" SPSS Statistics into applying a Bonferroni adjustment for multiple comparisons which it would otherwise not do.

Reporting the output of the one-way ANOVA

Based on the results above, you could report the results of the study as follows (N.B., this does not include the results from your assumptions tests or effect size calculations):

There was a statistically significant difference between groups as determined by one-way ANOVA ( F (2,27) = 4.467, p = .021). A Tukey post hoc test revealed that the time to complete the problem was statistically significantly lower after taking the intermediate (23.6 ± 3.3 min, p = .046) and advanced (23.4 ± 3.2 min, p = .034) course compared to the beginners course (27.2 ± 3.0 min). There was no statistically significant difference between the intermediate and advanced groups ( p = .989).

In our enhanced one-way ANOVA guide, we show you how to write up the results from your assumptions tests, one-way ANOVA and Tukey post hoc results if you need to report this in a dissertation, thesis, assignment or research report. We do this using the Harvard and APA styles (see our Features: One-way ANOVA page to learn more). It is also worth noting that in addition to reporting the results from your assumptions, one-way ANOVA and Tukey post hoc test, you are increasingly expected to report an effect size . Whilst there are many different ways you can do this, we show you how to calculate an effect size from your SPSS Statistics results in our enhanced one-way ANOVA guide. Effect sizes are important because whilst the one-way ANOVA tells you whether differences between group means are "real" (i.e., different in the population), it does not tell you the "size" of the difference. Providing an effect size in your results helps to overcome this limitation. You can learn more about our enhanced one-way ANOVA guide on our Features: One-way ANOVA page, or our enhanced content in general on our Features: Overview page.