# MASH : Maths and Stats Help

### Friedman's ANOVA

#### Introduction

A Friedman's 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 Wilcoxon Test.

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

If your data is parametric you should consider using a One-Way Repeated-Measures ANOVA

#### Test Procedure

1. Click Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples

2. Within the "Tests for Several Related Samples" Window, move your measurements into the "Test Variables" box.

3. Click "Statistics". Within the "Several Related Samples: Statisitcs", select 'Descriptives' and 'Quartiles'.

4. Select Continue à OK

#### Results

SPSS will generate three tables, to correctly report this test we need two, the Descriptive Statistics and the Test Statistics:

##### 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). For non-parametric tests the most appropriate average would be the Median. You can get this out using the descriptive analysis in SPSS.

##### Test Statistics

This table shows the results of the statistics test including the sample size (N), the Chi-Square statistic (Χ2), the degrees of freedom (df), and the p-value/significance (Asymp. Sig.).

## Reporting the Results in APA Formatting

Samples were evaluated across three times (Week 1, Week 2, Week 3) using a Friedman's analysis of variance. Differences across the weeks were significant, χ2(2) = 22.76, p < .001.

In addition, if your ANOVA is significant you must also carry out and report the post-hoc tests, to find which groups are different to each other. A Wilcoxon test could be considered. You also have options for which correction (for multiple test) to use. In the example below we have used Wilcoxon tests with the Bonferroni adjustment:

Post hoc comparisons were conducted using Wilcoxon tests between weeks, with a Bonferroni's adjusted alpha level of .016 (.05 ÷ 3). The difference between Week 1 and 2 (W = 2874, z = -3.03, = .002.) was statistically significant, between Week 1 and 3 (W = 2277.5, z = 2-4.84, p < .001), as well as between Week 2 and 3 (= 3062.5, z = -2.44., = .015).

If you need help running the post-hoc test check our Wilcoxon Test guide.