# ANOVA with Repeated Measures using SPSS Statistics

## Introduction

An ANOVA with repeated measures is used to compare three or more group means where the participants are the same in each group. This usually occurs in two situations: (1) when participants are measured multiple times to see changes to an intervention; or (2) when participants are subjected to more than one condition/trial and the response to each of these conditions wants to be compared.

For example, you could use a repeated measures ANOVA to understand whether there is a difference in cigarette consumption amongst heavy smokers after a hypnotherapy programme (e.g., with three time points: cigarette consumption immediately before, 1 month after, and 6 months after the hypnotherapy programme). In this example, "cigarette consumption" is your dependent variable, whilst your independent variable is "time" (i.e., with three related groups, where each of the three time points is considered a "related group"). Alternately, you could use a repeated measures ANOVA to understand whether there was a difference in breaking speed in a car based on three different coloured tints of windscreen (e.g., breaking speed under four conditions: no tint, low tint, medium tint and dark tint). In this example, "breaking speed" is your dependent variable, whilst your independent variable is "condition" (i.e., with four related groups, where each of the four conditions is considered a "related group").

Note: Whilst the repeated measures ANOVA is used when you have just "one" independent variable, if you have "two" independent variables (e.g., you measured time and condition), you will need to use a two-way repeated measures ANOVA.

This "quick start" guide shows you how to carry out a repeated measures ANOVA using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a repeated measures ANOVA to give you a valid result. We discuss these assumptions next.

## Assumptions

When you choose to analyse your data using a repeated measures ANOVA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a repeated measures ANOVA. You need to do this because it is only appropriate to use a repeated measures ANOVA if your data "passes" five assumptions that are required for a repeated measures ANOVA to give you a valid result. In practice, checking for these five assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task.

Before we introduce you to these five assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out a repeated measures ANOVA when everything goes well! However, don’t worry. Even when your data fails certain assumptions, there is often a solution to overcome this. First, let’s take a look at these five assumptions:

• Assumption #1: Your dependent variable should be measured at the continuous level (i.e., they are interval or ratio variables). Examples of continuous variables include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. You can learn more about interval and ratio variables in our article: Types of Variable.
• Assumption #2: Your independent variable should consist of at least two categorical, "related groups" or "matched pairs". "Related groups" indicates that the same subjects are present in both groups. The reason that it is possible to have the same subjects in each group is because each subject has been measured on two occasions on the same dependent variable. For example, you might have measured 10 individuals' performance in a spelling test (the dependent variable) before and after they underwent a new form of computerized teaching method to improve spelling. You would like to know if the computer training improved their spelling performance. The first related group consists of the subjects at the beginning (prior to) the computerized spelling training and the second related group consists of the same subjects, but now at the end of the computerized training. The repeated measures ANOVA can also be used to compare different subjects, but this does not happen very often. Nonetheless, to learn more about the different study designs you use with a repeated measures ANOVA, see our enhanced repeated measures ANOVA guide.
• Assumption #3: There should be no significant outliers in the related groups. Outliers are simply single data points within your data that do not follow the usual pattern (e.g., in a study of 100 students' IQ scores, where the mean score was 108 with only a small variation between students, one student had a score of 156, which is very unusual, and may even put her in the top 1% of IQ scores globally). The problem with outliers is that they can have a negative effect on the repeated measures ANOVA, distorting the differences between the related groups (whether increasing or decreasing the scores on the dependent variable), and can reduce the accuracy of your results. Fortunately, when using SPSS Statistics to run a repeated measures ANOVA on your data, you can easily detect possible outliers. In our enhanced repeated measures ANOVA guide, we: (a) show you how to detect outliers using SPSS Statistics; and (b) discuss some of the options you have in order to deal with outliers.
• Assumption #4: The distribution of the dependent variable in the two or more related groups should be approximately normally distributed. We talk about the repeated measures ANOVA only requiring approximately normal data because it is quite "robust" to violations of normality, meaning that the assumption can be a little violated and still provide valid results. You can test for normality using the Shapiro-Wilk test of normality, which is easily tested for using SPSS Statistics. In addition to showing you how to do this in our enhanced repeated measures ANOVA guide, we also explain what you can do if your data fails this assumption (i.e., if it fails it more than a little bit).
• Assumption #5: Known as sphericity, the variances of the differences between all combinations of related groups must be equal. Unfortunately, repeated measures ANOVAs are particularly susceptible to violating the assumption of sphericity, which causes the test to become too liberal (i.e., leads to an increase in the Type I error rate; that is, the likelihood of detecting a statistically significant result when there isn't one). Fortunately, SPSS Statistics makes it easy to test whether your data has met or failed this assumption. Therefore, in our enhanced repeated measures ANOVA guide, we (a) show you how to perform Mauchly's test of sphericity in SPSS Statistics, (b) explain some of the things you will need to consider when interpreting your data, and (c) present possible ways to continue with your analysis if your data fails to meet this assumption.

You can check assumptions #3, #4 and #5 using SPSS Statistics. Before doing this, you should make sure that your data meets assumptions #1 and #2, although you don't need SPSS Statistics to do this. Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running a repeated measures ANOVA might not be valid. This is why we dedicate a number of sections of our enhanced repeated measures ANOVA guide to help you get this right. You can find out about our enhanced content as a whole on our Features: Overview page, or more specifically, learn how we help with testing assumptions on our Features: Assumptions page.

In the section, Test Procedure of SPSS Statistics, we illustrate the SPSS Statistics procedure to perform a repeated measures ANOVA assuming that no assumptions have been violated. First, we set out the example we use to explain the repeated measures ANOVA procedure in SPSS Statistics.

## Example

A researcher wants to understand how exercise might reduce heart disease. The researcher wants to concentrate on a protein called C-Reactive Protein (CRP), which is a marker of chronic inflammation in the body and associated with heart disease: the greater the concentration of CRP, the greater the risk of heart disease. Regular exercise reduces the risk of heart disease. Therefore, the researcher would like to know whether exercise has an effect on CRP concentration because this might indicate that exercise has an anti-inflammatory effect.

To test out this theory, the researcher recruits 10 subjects to undergo a 6-month exercise-training programme. CRP concentration is measured at three different stages within the 6-month exercise-training programme: (1) pre-intervention (i.e., pre); (2) midway through the intervention at 3 months (i.e., mid); and (3) immediately post-intervention (i.e., post). These three time points reflect the three levels of our within-subjects factor, time (i.e., a within-subjects factor that is measured on an ordinal scale, although a within-subjects factor can also be measured on a nominal scale when carrying out a one-way repeated measures ANOVA). The dependent variable is CRP, which is measured in mg/L (i.e., a dependent variable that is measured on a continuous scale).

The CRP concentrations pre-intervention were recorded in the crp_pre variable, the CRP concentrations midway through the intervention in the crp_mid variable and the post-intervention CRP concentrations in the crp_post variable. The researcher would like to know whether there are changes in CRP concentration over time. In variable terms, the researcher would like to know if there are differences between the three variables: crp_pre, crp_mid and crp_post.

In our enhanced repeated measures ANOVA guide, we show you how to correctly enter data in SPSS Statistics to run a repeated measures ANOVA. You can learn about our enhanced data setup content on our Features: Data Setup page. Alternatively, see our generic, "quick start" guide: Entering Data in SPSS Statistics.

## Test Procedure in SPSS Statistics

The General Linear Model > Repeated Measures... procedure below shows you how to analyse your data using a repeated measures ANOVA in SPSS Statistics when the five assumptions in the previous section, Assumptions, have not been violated. At the end of these 13 steps, we show you how to interpret the results from this test. If you are looking for help to make sure your data meets assumptions #3, #4 and #5, which are required when using a repeated measures ANOVA and can be tested using SPSS Statistics, you can learn more in our enhanced guides (see our Features: Overview page to learn more).

Since some of the options in the General Linear Model > Repeated Measures... procedure changed in SPSS Statistics version 25, we show how to carry out a repeated measures ANOVA depending on whether you have SPSS Statistics versions 25, 26, 27 or 28 (or the subscription version of SPSS Statistics) or version 24 or an earlier version of SPSS Statistics. The latest versions of SPSS Statistics are version 28 and the subscription version. If you are unsure which version of SPSS Statistics you are using, see our guide: Identifying your version of SPSS Statistics.

##### SPSS Statistics versions 25, 26, 27 and 28 (and the subscription version of SPSS Statistics)
1. Click Analyze > General Linear Model > Repeated measures... on the top menu, as shown below:

Note: In version 27 and the subscription version, SPSS Statistics introduced a new look to their interface called "SPSS Light", replacing the previous look for versions 26 and earlier versions, which was called "SPSS Standard". Therefore, if you have SPSS Statistics versions 27 or 28 (or the subscription version of SPSS Statistics), the images that follow will be light grey rather than blue. However, the procedure is identical.

Published with written permission from SPSS Statistics, IBM Corporation.

You will be presented with the Repeated Measures Define Factor(s) dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

Explanation: This dialogue box is where you inform SPSS Statistics that the three variables – crp_pre, crp_mid and crp_post – are three levels of the within-subjects factor, time. Without doing this, SPSS Statistics will think that the three variables are just that, three separate variables.

2. In the Within-Subject Factor Name: box, replace "factor1" with a more meaningful name for your within-subjects factor. For example, we replaced "factor1" with "time" because this is the name of our within-subjects factor (i.e., time). Next, enter the number of levels of your within-subjects factor into the Number of Levels: box. For example, our within-subjects factor, time, has three levels, representing the three time points when our dependent variable, CRP, was measured (i.e., pre-intervention, crp_pre, mid-intervention, crp_mid, and post-intervention, crp_post). Therefore, we entered "3" into the Number of Levels: box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

Click on the button and you will be presented with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

3. In the Measure Name: box, enter a name that reflects the name of your dependent variable. Since our dependent variable is CRP, we entered "CRP", as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

Click on the button and you will get the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

4. Click on the button and you will be presented with the Repeated Measures dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

5. Transfer crp_pre, crp_mid and crp_post into the "_?_(1,CRP)", "_?_(2,CRP)" and "_?_(3,CRP)" placeholders respectively in the Within-Subjects Variables (time): box, by highlighting all the variables in the left-hand box (by clicking on them whilst holding down the shift-key), and then clicking on the top button. You will end up with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

6. Click on the button. You will be presented with the Repeated Measures: Profile Plots dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

7. Transfer the within-subjects factor, time, from the Factors: box into the Horizontal Axis: box by clicking on the top button. You will end up with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

8. Click on the button. This will transfer "time" from the Horizontal Axis: box to the Plots: box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

9. Click on the button and you will be returned to the Repeated Measures dialogue box.
10. Click on the button and you will be presented with the Repeated Measures: Estimated Margin Means dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

11. Transfer time from the Factor(s) and Factor Interactions: box to the Display Means for: box using the button. This will activate the Compare main effects checkbox (i.e., it will no longer be greyed out). Tick this checkbox and select from the drop-down menu under Confidence interval adjustment:. You will be presented with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

12. Click on the button and you will be returned to the Repeated Measures dialogue box.
13. Click on the button and you will be presented with the Repeated Measures: Options dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

14. In the –Display– area, tick the Descriptive statistics and Estimates of effect size checkboxes. You will be presented with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

15. Click on the button and you will be returned to the Repeated Measures dialogue box.
16. Click on the button. This will generate the output.

After running the 16-step procedure above, you will have generated the results for a repeated measures ANOVA with a post hoc test. We discuss this output on the next page. You can ignore the first section on the next page, which shows how to carry out a one-way repeated measures ANOVA with a post hoc test when you have SPSS Statistics version 24 or an earlier version of SPSS Statistics.