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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 Paired-Samples t-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 > Legagy 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), best practice is to report them all.

Test Statistics

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

Reporting the Results in APA Formatting

Samples were evaluated across three-time points (Week 1, Week 2, Week3). A Friedman's ANOVA indicated there was a significant effect for test score, χ2(2) = 22.76, p<.001

In addition, if your ANOVA is significant you must  also report your post-hoc results:

On average, Week 3 (Mean = 6.48, SD = 1.72) values were higher than Group B (Mean = 6.03, SD = 1.37), but lower than Group C (Mean = 5.57, SD = 1.12).

Post hoc comparisons were conducted by performing three Wilcoxon Tests.

The differences between Week 1 and Week 2 (Z = 3.03, p=.002), Week 2 and Week 3 (Z = 2.44, p=.015), and Week 1 and Week 3, (Z = 4.84, p<.001), were all considered statistically significant.

 

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