# MASH : Maths and Stats Help

### One-Way Repeated Measures ANOVA

#### Introduction

A One-Way Repeated-Measures ANOVA compares the difference between more than two related groups, such as comparing the difference between three time-points. If your data only has two groups such as a pre/post-test you should consider the Paired-Samples t-Test.

It is considered a parametric test and is only suitable for parametric data. To check if your data is parametric, please check out the dedicated guide: Parametric or Not Guide (PDF)

If your data is non-parametric you should consider using Freidman's ANOVA

#### Test Procedure

1. Click Analyze > General Linear Model > Repeated Measures

2. Within the "Repeated-Measures Define Factors" Window, create a name for your repeate-measures factor and specify the number of levels. Click Add. Click Define.

3. Within the "Repeated Measures" Window, select the dependent variables you are analysing and move them into the "Within-Subjects Variables" box.

4. Click "EM Means". Within the "Repeated Measures: Estimated Marginal Means" window select your within-subjects factor and move it to the "Display Means for" window. Select "Compare Main Effects"

5. Click "Options". Within the "Repeated Measures: Options" window select "Descriptive Statistics" and "Estimates of effect size".

6.

7. Click "Continue" then "OK".

#### Results

SPSS will generate multiple tables, to correctly report this test we need three, the Descriptive Statistics,  the Test of Within-Subjects Effects, and the Pairwise Comparisons:

##### Descriptive Statistics

This table shows the descriptive statistics: the sample size of each group (N), the mean of each group (Mean), and the standard deviation of each group (Std. Deviation), best practice is to report them all.

##### Test of Within-Subjects Effects

This table shows the test results including the F-statistic (F), the two degrees of freedom (df), the two-tailed significance or p-value (Sig), and the effect size (Partial Eta-Squared).

##### Pairwise Comparisons

This table shows all possible comparisons between pairs of within-subjects levels. In this example we see 6 pairs for our 3 different levels (Week_1, Week_2, and Week_3), this is because SPSS tests each pair in both directions, i.e. Week_1 against Week_2 and Week_2 against Week_1

## Reporting the Results in APA Formatting

Samples were evaluated at across three-time points( Week 1, Week 2, Week 3). A One-Way repeated measures ANOVA indicated there was a significant effect for test score across the weeks, (2,118) = 23.16, p < .001, η2 = .282.