Reporting a Friedman Test in SPSS
Chi-Square, Kendall's W and Pair Results
Reporting a Friedman test in SPSS rests on a chi-square statistic with df, N and p, then a medians table, Kendall's W as the effect size and pairwise results whose adjustment is named. Each part has a printed source, and the N counts complete cases only.
IN SHORT
What Goes Into a Friedman Write-Up
A Friedman report states whether the ranks of a within-person outcome differ across three or more occasions or conditions. It gives the chi-square statistic with its df, N and p, an effect size, a median for each occasion and pairwise results with their adjustment named. For reporting a Friedman test in SPSS, the values come from Analyze, Nonparametric Tests, Related Samples (or Legacy Dialogs, K Related Samples), where Kendall’s W is offered as a separate choice in the same dialogs. Labels depend on the release. Within OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, the in-house PhD-level statisticians are the ones who match each figure in a Friedman write-up to the saved output.
In This Guide
ANALYSIS SUPPORT
Analysis Support for This Method
Whether ranks or a model of the means suits repeated measurements shapes the whole write-up. Both routes are set out below, one for ranks within each participant and one for means across occasions.
Friedman Test
The rank-based analysis of one outcome measured on several occasions, carried out for your data, with pairwise follow-ups and wording that fit the output.
Repeated Measures ANOVA
The analysis of means across occasions in the same participants, where the outcome and the model assumptions can be defended.
BEFORE YOU REPORT IT
Four Facts the Paragraph Is Built On
The facts below are read from the output before drafting, because they set how the statistic, the effect size and the pairs are worded.
N Is Complete Cases The test uses only participants with a value on every occasion. The N in the output counts them, and it can sit well below the number of rows in the data file.
Name of the Statistic SPSS prints a chi-square statistic with df equal to the number of occasions minus one. It is written as a chi-square, not as an F or an H.
Effect Size Is a Separate Test The Friedman table carries no effect size. Kendall's W is a separate test option ticked in the same dialog, it prints its own table, and it runs from 0 to 1.
Source of the Pairs Pairwise rows are printed in the newer layout. Where they are absent, the pairs come from a separate analysis, and the paper names the method and its adjustment.
IN SPSS
Taking Each Figure From the Friedman Output
The checks and the run itself are in Friedman Test in SPSS: Checks and Reporting, and the values below are collected from the output that IBM SPSS produced.
Take Chi-Square, df, N and p
From the test summary, or the Test Statistics table in the legacy layout, take the Test Statistic (Chi-Square), Degrees of Freedom, the N and the Asymptotic Significance.
Check: The df equals the number of occasions minus one, and N counts participants with every occasion present, which may be fewer than the rows in the file.
Take Kendall's W From Its Table
Tick Kendall’s W among the test options of the same dialog, and take the coefficient from the table it prints.
Watch: Take W from the output of the same dialog, with the number of occasions beside it. A W from a different variable list or missing-value setting would not match the chi-square.
Take Medians for Each Occasion
Run descriptive statistics for each occasion and take the median with the first and third quartiles.
Tip: Depending on the missing-data setting, descriptives can use more cases than the test did. If so, note it beneath the table or restrict the run to the complete cases.
Collect the Pair Results
From Pairwise Comparisons, take for each pair the test statistic, the standard error and the adjusted significance, labeled Adj. Sig. in the newer output.
Watch: The legacy output prints no pairwise rows for this test. Pairs from a separate analysis are described as such, with their own method and adjustment, and not as part of the Friedman output.
Name the Adjustment Method
Find the adjustment method in the note under the pairwise table and write its name into the paragraph.
Check: Once the adjustment is named, call every pairwise p-value adjusted. A paragraph that mixes adjusted and unadjusted values under one label cannot be traced to the output.
Write Up the Test, W and the Pairs
Write the chi-square sentence, then the pairwise sentence, fill the medians table and compare each part with the output.
Check: Compare the words used for each pair with its Adj. Sig. row. A pair described as different must carry an adjusted value that meets the threshold set for the study.
READING THE OUTPUT
Where Each Figure From the Friedman Output Is Placed
The rows follow the paragraph, from the statistic through the effect size and the descriptive run to the pairwise results.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| N | Test summary, or Test Statistics table | The N in the sentence, which counts complete cases only and may sit below the rows in the file |
| Test Statistic (Chi-Square) | Test summary or Test Statistics table | The chi-square, written with its df and N together, as χ²(df, N) |
| Degrees of Freedom | Same place | The df inside the parentheses, equal to the number of occasions minus one |
| Asymptotic Sig. (Asymp. Sig. in legacy tables) | Same place | The p-value, with a printed .000 given as p < .001 and no claim of a zero probability |
| Kendall’s W | Its own table, when ticked in the same dialog | The effect size, labeled and stated with the number of occasions it is based on |
| Mean Rank | Ranks table | The ordering of the occasions; mean ranks are not medians and do not go in a column of medians |
| Sample 1-Sample 2 and Adj. Sig. | Pairwise Comparisons | Each pair by its occasion labels, with the adjusted p and the method named once |
| Median and quartiles | A separate descriptive run | The medians table, one row per occasion, with the quartiles written as two values |
REPORTING
The Chi-Square Sentence, a Medians Table and Worded Pairs
The paragraph moves from the omnibus statistic to the pairs, and the medians table gives the reader the level at each occasion.
Reporting Friedman test results in APA style gives the statistic as χ²(df, N) with its p-value, followed by W. A Friedman results table lists the median and quartiles for every occasion, with a note carrying the test. The pairs are worded with their adjustment in the same paragraph. The frame is for three occasions.
A Friedman test showed that [outcome] [differed / did not differ] across the three occasions, χ²(___, N = ___) = ___, p = ___, Kendall’s W = ___. Medians were ___ at [Time 1], ___ at [Time 2] and ___ at [Time 3]. Pairwise comparisons with a [adjustment method] adjustment showed that [Time 1] differed from [Time 3] (adjusted p = ___) but not from [Time 2] (adjusted p = ___). Medians and quartiles for each occasion are in Table 1, and the N counts participants with all three occasions.
| Table 1. Distribution of [Outcome] at Each Occasion, With Friedman Test Results | ||||
|---|---|---|---|---|
| Occasion | n | Mdn | IQR (Q1 to Q3) | Mean rank |
| [Time 1] | ___ | ___ | ___ to ___ | ___ |
| [Time 2] | ___ | ___ | ___ to ___ | ___ |
| [Time 3] | ___ | ___ | ___ to ___ | ___ |
| Note. χ²(___, N = ___) = ___, p = ___, Kendall’s W = ___. Pairwise p-values carry the [method] adjustment. N counts participants with every occasion present. | ||||
Kendall’s W is a coefficient of concordance, read as the extent to which participants ranked the occasions in the same order, from 0 for no agreement to 1 for complete agreement. It is derived from the same ranks as the chi-square. No single threshold separates small from large, so the paper gives W with the number of occasions and reads it against comparable studies. SPSS prints no interval for W, which is then described as a point estimate. Because W is bounded by 0 and 1 and tied to the ranks, it is not comparable with a standardized mean difference.
COMMON MISTAKES
Friedman Paragraphs a Reviewer Would Send Back
Checking the sentence against the three printed outputs, the test, W and the pairs, turns up each of these.
W Left Out A chi-square and p without an effect size say that ranks differ but not by how much. Kendall's W is printed in its own table and is added to the sentence.
Asymptotic p Unnamed The printed p is asymptotic, an approximation that can be rough with few participants. The paragraph names the type, and says so where an exact p was obtained.
Pairs Without a Method Pairwise results with no adjustment named cannot be reproduced. The method is taken from the output note and written once in the paragraph.
Rows Reported as N Giving the number of rows in the file as N overstates the data behind the test. The N printed with the statistic counts complete cases.
Statistic Mislabeled Calling the Friedman statistic an F, an H or Cochran's Q mixes up three different tests. It is a chi-square with df equal to the occasions minus one.
Occasion Order Lost A medians table sorted by value or alphabet hides the trend over time. Rows follow the order of the occasions, as the text does.
Does every pair in the paragraph have a printed row behind it? Independent Statistical Review checks that, then the statistic, W and the medians table.
FREQUENTLY ASKED QUESTIONS
Equal Medians, Wilcoxon Follow-Ups and the Size of W
Equal medians beside a significant result look like a contradiction and are not one; signed-rank follow-ups and the reading of W come after that.
How do I word a significant result when the medians are equal?
Describe it through the ranks: participants tended to rank one occasion above another, and the medians are given as description only. The test compares rank distributions within persons, so equal medians do not contradict a significant result. Name the occasion that tended to receive higher ranks from the mean ranks, and avoid writing that the medians differed.
Can I use Wilcoxon tests in place of the pairwise rows?
Yes, if the method is named and the p-values are adjusted for the number of pairs. Signed-rank tests on each pair are a common follow-up, and the paper says so. They are described as a separate analysis after the Friedman test, with the adjustment named, and not as part of its output.
How large must Kendall's W be to count as large?
No single threshold applies, so read W against the number of occasions and the field’s literature. A W of 1 means every participant ranked the occasions identically, and 0 means no agreement. State the value, say that it is a point estimate, and avoid labels such as large without a reference.
Does a Friedman write-up review include the pairwise wording?
Pairwise sentences are part of it. An in-house PhD-level statistician at OnlineSPSS goes through the chi-square, W, the medians table and each pairwise sentence against the saved tables. The work falls under Results Reporting & Interpretation, and what the trend means for your question is for you to judge.
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What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
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NEXT STEP
Do N, df and W Line Up
With the Output?
N, df and W each have a printed source, and pairs taken from a separate signed-rank analysis need one too, named apart from the Friedman output.
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