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MASH : Maths and Stats Help

Friedman's ANOVA


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




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.