How to use
- One row per person, one column per condition or time point (at least 3). A header row is optional.
- Read χ² and p. p < 0.05 means at least one condition differs.
- If it is significant, check the pairwise table; pairs with adjusted p < 0.05 differ.
Options explained
- Mean rank
- Each person's values are ranked within their own row, then the ranks are averaged per condition. A higher mean rank means higher values.
- Kendall's W
- χ² ÷ [n(k − 1)], between 0 and 1, used as the effect size. The closer to 1, the more consistently people rank the conditions the same way.
- Pairwise comparisons
- A Wilcoxon signed-rank test for every pair of conditions, with p multiplied by the number of comparisons (Bonferroni); three conditions mean three comparisons.
Worked example
The sample has 10 people rated at T1, T2 and T3:
| Condition | Median | Mean rank |
|---|---|---|
| T1 | 4.5 | 1.15 |
| T2 | 6 | 2.05 |
| T3 | 7 | 2.80 |
χ²(2) = 14.0, p = 0.0009, Kendall’s W = 0.70, so the time points differ. After the Bonferroni adjustment T1 and T3 differ (p = 0.016), while T1 vs T2 (p = 0.056) and T2 vs T3 (p = 0.067) do not.
APA style: χ²(2) = 14.00, p < .001, W = .70.
Frequently asked questions
How is it different from Kruskal–Wallis?
Kruskal–Wallis compares separate groups of people. Friedman compares the same people across conditions, so the rows must be matched.
What about missing values?
A row with any blank is left out entirely.
Does it match SPSS?
χ², df and p match the Friedman test in SPSS (K related samples) and R's friedman.test(). Newer SPSS versions use Dunn's test for pairwise comparisons, so those p-values differ.
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