Repeated-measures ANOVA
Compare three observations of a continuous outcome, after meeting statistical assumptions
Repeated-measures ANOVA is used to compare three or more observations of a continuous outcome across time or within-subjects. The assumption of normality of difference scores and the assumption of sphericity must be met before running a repeated-measures ANOVA. The p-value for a repeated-measures ANOVA is always interpreted within the context of the means and standard deviations of the observations of the outcome.
Here is a figure depicting the use of a repeated-measures ANOVA. There are three observations of a continuous outcome and the assumptions of normality of difference scores and sphericity have been met. If a significant main effect is found for the repeated-measures ANOVA, then post hoc tests must be run to explain the differences between observations of the outcome.
The steps for conducting a repeated-measures ANOVA in SPSS
1. The data is entered in a within-subjects fashion.
2. Click Analyze.
3. Drag the cursor over the General Linear Model drop-down menu.
4. Click Repeated Measures.
5. Type the number of observations of the continuous outcome being collected into the Number of Levels: box.
6. In the Within-Subject Factor Name: box, give the outcome variable a name. Example: "Outcome"
7. Click the Add button.
8. Click the Define button.
9. Click on the first observation of the continuous outcome.
10. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
11. Click on the second observation of the continuous outcome.
12. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
13. Click on the third observation of the continuous outcome.
14. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
15. Click on the Options button.
16. Click on the outcome variable to highlight it.
17. Click on the arrow to move the outcome into the Display Means for: box.
18. Click on the Compare main effects box to select it.
19. Click on the Descriptive statistics box to select it.
20. Click on the Estimates of effect size box to select it.
21. Click on the Observed power box to select it.
22. Click Continue.
23. Click on the Plots button.
24. Click on the outcome variable to highlight it.
25. Click on the arrow to move your outcome into the Horizontal Axis: box.
26. Click the Add button.
27. Click Continue.
28. Click OK.
2. Click Analyze.
3. Drag the cursor over the General Linear Model drop-down menu.
4. Click Repeated Measures.
5. Type the number of observations of the continuous outcome being collected into the Number of Levels: box.
6. In the Within-Subject Factor Name: box, give the outcome variable a name. Example: "Outcome"
7. Click the Add button.
8. Click the Define button.
9. Click on the first observation of the continuous outcome.
10. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
11. Click on the second observation of the continuous outcome.
12. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
13. Click on the third observation of the continuous outcome.
14. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
15. Click on the Options button.
16. Click on the outcome variable to highlight it.
17. Click on the arrow to move the outcome into the Display Means for: box.
18. Click on the Compare main effects box to select it.
19. Click on the Descriptive statistics box to select it.
20. Click on the Estimates of effect size box to select it.
21. Click on the Observed power box to select it.
22. Click Continue.
23. Click on the Plots button.
24. Click on the outcome variable to highlight it.
25. Click on the arrow to move your outcome into the Horizontal Axis: box.
26. Click the Add button.
27. Click Continue.
28. Click OK.
The steps for interpreting the SPSS output for a repeated-measures ANOVA
1. In the Multivariate Tests table, look under the Sig. column. This is the p-value that is interpreted. In the Partial Eta Squared column, there is a measure of effect size for your analysis. Under Observed Power, the achieved power after conducting the study is presented.
If the p-value is LESS THAN .05, then researchers have evidence of a statistically significant main effect amongst the observations of the outcome or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence of that a significant main effect does NOT exist amongst the observations of the outcome or within-subjects.
If the p-value is LESS THAN .05, then researchers have evidence of a statistically significant main effect amongst the observations of the outcome or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence of that a significant main effect does NOT exist amongst the observations of the outcome or within-subjects.
Repeated-measures ANOVA and post hoc testing
If a significant main effect is found for a repeated-measures ANOVA, then pairwise comparisons should be used in a post hoc fashion to explain within-subjects differences between the observations of the outcome. The figure below shows the three observations being compared to each other.
The steps for interpreting the SPSS output for post hoc tests
In the Pairwise Comparisons table, look under the Sig. column.
If the p-value is LESS THAN .05, then there is a statistically significant difference between the two observations identified in the (I) Outcome and (J) Outcome columns.
If the p-value is MORE THAN .05, then there is NOT a statistically significant difference between the two observations identified in the (I) Outcome and (J) Outcome columns.
If the p-value is LESS THAN .05, then there is a statistically significant difference between the two observations identified in the (I) Outcome and (J) Outcome columns.
If the p-value is MORE THAN .05, then there is NOT a statistically significant difference between the two observations identified in the (I) Outcome and (J) Outcome columns.
Interpreting p-values must be done within the context of the means and standard deviations. For example, researchers would say, there was a significant main effect for the outcome, p < .05. Post hoc comparisons were conducted. There were significant differences between "Observation 1" (mean and standard deviation), "Observation 2" (mean and standard deviation), and "Observation 3" (mean and standard deviation), p = .01.
It is HIGHLY IMPORTANT to interpret the p-values within the context of your means and standard deviations that are presented in the Descriptive Statistics table.
It is HIGHLY IMPORTANT to interpret the p-values within the context of your means and standard deviations that are presented in the Descriptive Statistics table.
Click on the Download Database and Download Data Dictionary buttons for a pre-configured database and data dictionary for repeated-measures ANOVA. Click on the Adjusting for Multiple Comparisons button to learn more about Bonferroni, Tukey's HSD, and Scheffe's test. Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.
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