Friedman test (rank test for several time points)

In brief

Rank test for three or more measurements of the same people.

What for

The Friedman test is the alternative to repeated-measures analysis of variance when the values are skewed, have outliers or only express an order. Statable offers it in the question "Does something change over several time points?" below the result ("No normal distribution"); the choice belongs before the calculation.

Requirements

• The same people at all time points, one row per person; people with a gap are left out.
• The values can be ordered (numbers or levels). The test does not use groups.

Reading the result

• χ² and p test whether the time points differ in rank; ties within a person are corrected (as in R and PSPP).
• Kendall's W (0 to 1) is the effect size: .1 small, .3 medium, .5 large. It is not the same as Cohen's kappa.
• With p < .05, pairwise comparisons follow: Wilcoxon test for paired values, Holm adjustment over all pairs.

Reporting the result

χ²(3) = 8.97, p = .030, Kendall's W = .15

Add the medians for each time point.

Limits

• The test only compares ranks within each person; time intervals do not count. With normally distributed values, analysis of variance has more power.
• A person with the same value everywhere contributes nothing; if everyone has the same value everywhere, there is no test.

Source

Hollander, M., Wolfe, D. A., & Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley.