Friedman Test

The Friedman Test is a non-parametric test for comparing the means of three or more (repeated) groups. It can allow you to reject the null hypothesis (n0=n1=n2), however post hoc tests are required to discover which of the means actually differ.

Assumptions
The assumptions of this test are as follows:
 * 1) Data must be at least at the ordinal level.
 * 2) Data must be in a paired format.
 * 3) The distributions of the differences in the dependent variable between the two or more related groups should be approximately normally distributed.
 * 4) Sphericity must be assumed using Mauchly's test.

Parametric Equivalent
The parametric equivalent of this test is the One way Repeated ANOVA.

Example
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In SPSS
Click Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples...

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Writing up
There was a statistically significant difference in perceived effort depending on which type of music was listened to whilst running, χ2(2) = 7.600, p = 0.022. Post-hoc analysis with Wilcoxon signed-rank tests was conducted with a Bonferroni correction applied, resulting in a significance level set at p < 0.017. Median (IQR) perceived effort levels for the no-music, classical and dance music running trial were 7.5 (7 to 8), 7.5 (6.25 to 8) and 6.5 (6 to 7), respectively. There were no significant differences between the no-music and classical music running trials (Z = -0.061, p = 0.952) or between the classical and dance music running trials (Z = -1.811, p = 0.070) despite an overall reduction in perceived effort in the dance vs. classical running trials. However, there was a statistically significant reduction in perceived effort in the dance music vs. no music trial (Z = -2.636, p = 0.008).