Repeated Measures ANOVA Tool

Data Analysis Tool

On this webpage, we describe the Real Statistics data analysis tool that supports repeated measures with one within-subjects factor. 

Real Statistics Data Analysis Tool: The One Factor Repeated Measures Anova data analysis tool contained in the Real Statistics Resource Pack can be used to automatically perform analysis of variance for repeated measures, including the calculation of the GG and HF epsilon correction factors.

Example 1: Use the One Factor Repeated Measures Anova data analysis tool to perform the analysis for Example 2 of  Sphericity,

Press Ctrl-m, click on the Anova tab, and select One Repeated Measures Anova.

If using the original user interface (instead of the Multipage interface), then press Ctrl-m and double-click on Analysis of Variance (as shown in Figure 0 of Anova Analysis Tool). Next select Repeated Measures Anova: one factor from the dialog box that appears.

In either case, the dialog box shown in Figure 1 will appear.

Figure 1 – Dialog box for Repeated Measures Anova

Fill in the dialog box as shown in the figure and click on OK. The output is as shown in Figure 2.

Figure 2 – One Factor Repeated Measures Anova

Sphericity Considerations

A rule of thumb is that if sphericity is greater than .75 then the Huynh and Feldt epsilon should be used; otherwise, the Greenhouse and Geisser epsilon should be used. When sphericity is very low, it might be better to use MANOVA since it does not rely on the sphericity assumption. Another rule of thumb is that for sphericity < .7 you should use MANOVA provided your sample size is at least 10 + # of columns; otherwise, you should use ANOVA.

For more information about sphericity, including other ways of calculating Greenhouse and Geisser epsilon, as well as Mauchly’s test for sphericity, click here.

Effect Size

The effect size measure used in Figure 2 is partial eta-squared, which is calculated for the Group factor by SS_G/(SS_G+SS_E). E.g. cell T5 contains the formula =O6/(O6+O7).

We can also use omega-squared as a measure of effect size, although the formula used is different from the one employed for ANOVA with independent factors.

For Example 1, ω² = .14 using the GG epsilon correction factor. As we have noted elsewhere, the effect size for comparisons is more meaningful than the effect size of the omnibus ANOVA.

Post-hoc Tests

As can be seen from the Options on the dialog box in Figure 1, a number of post-hoc tests are available after a significant repeated-measures ANOVA. Click here for a description of these tests and the results of each of these tests on the data in Figure 1.

Reference

Howell, D. C. (2010) Statistical methods for psychology (7^th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf