What is Repeated Measures ANOVA and How to Perform It in SPSS?

Repeated measures ANOVA

Repeated measures ANOVA is a specialized statistical test used when you take multiple measurements from the same subjects or experimental units. For example, suppose you want to evaluate the effect of a training program by measuring students’ test scores before the program, right after the program, and three months later. In this case, each student has three measurements over time. To determine whether there are statistically significant differences among these repeated measurements, you can use a repeated measures ANOVA. This method appropriately analyzes within-subject designs by controlling for variability between subjects. Additionally, repeated measures ANOVA allows you to evaluate all time points in one model, reducing the Type I error risk compared to performing multiple separate tests.

What Is Repeated Measures ANOVA?

Repeated measures ANOVA is used to compare measurements taken from the same group under different times or conditions. A standard one-way ANOVA compares means across independent groups, whereas a repeated measures ANOVA examines how a single group’s mean changes under different conditions or over time. By using each subject as their own control, this approach generally increases statistical power.

There are a few versions of repeated measures ANOVA:

• One-factor repeated measures ANOVA: There is only one within-subject factor (for example, time).

• Two-way repeated measures ANOVA: There are two factors with repeated measurements (for instance, different time points and different task conditions). This is more complex but can be done in SPSS. Note: If you only have two repeated measurements for the same subjects (e.g., pre-test and post-test), a repeated measures ANOVA is not necessary; you would use a paired samples t-test instead.

• Mixed-design ANOVA: One factor is repeated (within-subjects) and another factor is between-subjects (e.g., treatment group vs. control group measured over time). This design can also be handled in SPSS under the General Linear Model procedure.

How to Perform a Repeated Measures ANOVA in SPSS

Before running a repeated measures ANOVA in SPSS, set up your data correctly. Typically, you will have a wide-format dataset where each subject is a single row and each measurement time/condition is a separate column. For example, if there are three time points, you might have columns like "Time1", "Time2", and "Time3" for the scores.

Step-by-step SPSS procedure:

1. Data Preparation: Organize your dataset so that each row corresponds to one subject (with a unique ID), and the repeated measurements appear in separate columns.

2. Choosing the Analysis: In SPSS, go to Analyze > General Linear Model > Repeated Measures.... In the dialog box, provide a name for the within-subject factor (e.g., "Time") and specify the number of levels (e.g., 3 for three time points).

3. Defining Measures: Click "Define" and assign the variables in your dataset (e.g., Time1, Time2, Time3) to the corresponding factor levels (1, 2, 3).

4. Options and Plots: (Optional) Under the Plots tab, you can add the factor to create a profile plot of means. Under Options, you might select Descriptive statistics, Estimates of effect size, and Pairwise comparisons (with Bonferroni adjustment) to obtain additional output.

5. Run the Analysis: Click OK to run the repeated measures ANOVA.

Note: If any subject is missing one of the repeated measurements, SPSS will by default exclude that subject’s data from the analysis. Be sure to handle missing data appropriately before running the ANOVA (e.g., through imputation or by excluding that subject entirely).

Interpreting the Results

Once the analysis is complete, one key output is the Tests of Within-Subjects Effects table. This table shows the F-test for your repeated factor (e.g., "Time"), with degrees of freedom (df) and the significance value (p).

Significance: If p < 0.05, then there is a statistically significant difference across the measurements. For example, F(2, 28) = 5.12, p = 0.010 would indicate significant differences among the time points. You could report this as, "There was a significant main effect of Time, F(2, 28) = 5.12, p = 0.010." Additionally, check the partial eta-squared (partial η²) value in the output to gauge the effect size. For instance, partial η² = 0.25 would mean the time factor explains about 25% of the variance. If p ≥ 0.05, you conclude that there is no statistically significant change across the time points or conditions.

Sphericity Assumption: Repeated measures ANOVA requires an assumption called sphericity (homogeneity of variances of the differences). In the SPSS output, Mauchly's Test of Sphericity checks this assumption. If Mauchly’s test is significant (p < 0.05), the sphericity assumption is violated. In that case, SPSS provides corrected results (e.g., Greenhouse-Geisser or Huynh-Feldt adjustments) for the F-test. Use the F and p-values from the row with the appropriate correction (often Greenhouse-Geisser when sphericity is violated) to determine significance.

Post-hoc Pairwise Comparisons: If the ANOVA shows a significant effect, the next step is to find out between which specific time points or conditions the differences lie. Check the Pairwise Comparisons section of the output for the p-values of comparisons (e.g., Time 1 vs Time 2, Time 1 vs Time 3, etc.). If you are doing multiple comparisons, apply a Bonferroni or similar adjustment to the p-values to control for Type I error.

Example Scenario

Imagine you conducted a study on 30 participants’ weight, measuring each person before a fitness program, right after the program, and again 6 months later. A repeated measures ANOVA finds a significant effect of time (e.g., F(2, 58) = 10.5, p < 0.001), indicating that weight changed significantly over the three time points. Further pairwise comparisons show a significant weight drop from Pre-Program to Post-Program (p < 0.01), but no significant difference between Post-Program and 6-Month Follow-Up (p > 0.05). In other words, participants lost a significant amount of weight during the program and, on average, maintained most of that loss six months later. (For example, the average weight went from 80 kg pre-program to 75 kg post-program, then to 76 kg at follow-up — a notable initial drop with a slight increase later that was not statistically significant.)

Conclusion: Repeated measures ANOVA is a powerful technique for analyzing multiple measurements on the same subjects. SPSS makes it straightforward to examine how a group changes over time or under different conditions in a statistically rigorous way. Just remember to check assumptions like sphericity and apply corrections if needed (e.g., use Greenhouse-Geisser adjusted results if Mauchly’s test is significant). By using this method properly, you can derive strong and meaningful insights from your data. If you need expert support in performing a repeated measures ANOVA or interpreting the results, our professional statistical consulting services are here to help.