The Friedman test is the non-parametric alternative to the repeated-measures ANOVA: it compares three or more related conditions measured on the same participants, using ranks, when the data are ordinal or non-normal. Because it works on ranks, the APA 7 write-up uses medians and a chi-square statistic. This guide gives you the exact format, a worked example you can copy, and the mistakes reviewers catch.
What you need before you write a single word
An APA 7 write-up of a Friedman test needs these values from your output:
- The median (Mdn) for each condition. Report medians, not means.
- The test statistic, distributed as chi-square.
- The degrees of freedom (df), which is the number of conditions minus 1.
- The exact p value.
- An effect size, usually Kendall's W (the coefficient of concordance), which ranges from 0 to 1.
- Post hoc comparisons (for example Wilcoxon signed-rank tests with a correction) if the test is significant.
The APA 7 format template
Report the omnibus result in running text using this pattern:
A Friedman test showed a significant difference in [dependent variable] across the [k] conditions, X-squared(df) = X.XX, p = .XXX, Kendall's W = .XX.
Formatting rules reviewers actually check:
- Report medians for each condition, not means and standard deviations.
- Put the degrees of freedom (conditions minus 1) in parentheses after the chi-square statistic.
- No leading zero on p or Kendall's W.
- Round the statistic and W to two decimals. If p is below .001, write p < .001.
- If the test is significant, run and report post hoc comparisons.
A worked example
Suppose 20 participants rated the same product under three packaging designs (1 to 7 scale).
- Design A: Mdn = 4
- Design B: Mdn = 6
- Design C: Mdn = 5
- Omnibus result: X-squared(2) = 12.60, p = .002, Kendall's W = .32
Written up in APA 7, that becomes:
A Friedman test showed a significant difference in ratings across the three packaging designs, X-squared(2) = 12.60, p = .002, Kendall's W = .32. Post hoc Wilcoxon signed-rank tests with a Bonferroni correction indicated that Design B (Mdn = 6) was rated significantly higher than Design A (Mdn = 4), p = .003. No other pairwise comparison was significant.
The APA 7 table (optional)
A small medians table keeps the summary out of the prose. APA tables use horizontal rules only:
| Condition | Mdn |
|---|---|
| Design A | 4 |
| Design B | 6 |
| Design C | 5 |
Note. Ratings on a 1 to 7 scale, N = 20. The difference was significant, X-squared(2) = 12.60, p = .002, Kendall's W = .32.
Mistakes reviewers catch
- Reporting means and SDs. The test ranks within participants, so report medians.
- Using it on independent groups. For three or more separate groups use the Kruskal-Wallis test, not the Friedman test.
- Stopping at the omnibus test. A significant Friedman result says the conditions differ somewhere; run post hoc comparisons to say where.
- No effect size. Report Kendall's W, which ranges from 0 (no agreement) to 1 (complete agreement).
- Writing p = .000. Report p < .001.
When to use it instead of a repeated-measures ANOVA
Use the Friedman test when the dependent variable is ordinal, or continuous but badly non-normal, across three or more related conditions from the same participants. If the ANOVA assumptions hold, repeated-measures ANOVA is more powerful. For two related conditions, use the Wilcoxon signed-rank test.
Let KyroStat do the write-up for you
Formatting a rank-based repeated-measures test, with medians, the chi-square statistic, Kendall's W, and post hoc comparisons, is where errors creep in. KyroStat runs the Friedman test on your data, reports the medians, runs the post hoc comparisons, and hands you the finished APA 7 sentences and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
Should I report means or medians for a Friedman test? Medians. The test works on ranks within participants, so medians describe the conditions appropriately.
What effect size goes with a Friedman test? Kendall's W, the coefficient of concordance, which ranges from 0 to 1.
What is the difference between the Friedman and Kruskal-Wallis tests? Friedman is for related conditions (the same participants measured several times). Kruskal-Wallis is for independent groups of different participants.
My p value shows as .000. What do I write? Report p < .001. A p value is never exactly zero.