Friedman Test: How to Run It Online and Report It in APA7
The Friedman test compares three or more related measurements using ranks within each participant. It is the non-parametric alternative to one-way repeated-measures ANOVA.
What is Friedman Test?
The Friedman test compares three or more related measurements using ranks within each participant. It is the non-parametric alternative to one-way repeated-measures ANOVA.
When to use it
Use it for the same participants measured under three or more conditions or at three or more times when the outcome is ordinal or not normally distributed.
Example question: Did pain ratings differ across three time points?
Preparing your data
Wide format: one row per participant and one numeric column per condition or time point.
Example dataset (simulated; first rows of 20): id, time1, time2, time3 (0 to 10 pain ratings for the same participants); wide format.
| id | time1 | time2 | time3 |
|---|---|---|---|
| 1 | 6 | 7 | 3 |
| 2 | 3 | 3 | 5 |
| 3 | 5 | 4 | 3 |
| 4 | 6 | 3 | 5 |
| 5 | 6 | 7 | 5 |
| 6 | 6 | 5 | 4 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Friedman Test tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select all the columns that contain the repeated measurements.
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- The same participants are measured in all conditions; participants with missing values are dropped.
- The outcome is at least ordinal.
- Participants are independent of each other.
- The ranks within each participant can be compared across conditions.
Key numbers to look at
- χ2F statistic with df = conditions − 1 and p.
- Mean ranks per condition.
- Kendall's W as effect size.
- Post hoc pairwise comparisons with a multiple-comparison correction.
Effect size
Kendall's W ranges from 0 (no agreement) to 1 (complete agreement); about .1 small, .3 moderate, .5 large.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Friedman Test in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Using it for independent groups (use Kruskal–Wallis).
- Running pairwise follow-up tests without adjusting the p-values.
- Forgetting to report how many participants had complete data.
Related analyses and alternatives
- One-way ANOVA with repeated measures: If the data are roughly normal.
- Wilcoxon Test: Two related measurements, or post hoc comparisons.
- Kruskal-Wallis Test: Independent groups.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What do the mean ranks mean?
Each participant's scores are ranked across the conditions; the mean rank shows which condition tends to get higher scores.
How is Friedman different from Kruskal–Wallis?
Friedman is for related (repeated) measurements. Kruskal–Wallis is for independent groups.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.