METHOD GUIDE
Friedman Test in SPSS
Complete Cases, Kendall's W and Adjusted Pairwise Tests
The test ranks each participant's scores across the conditions, so anyone missing one measurement drops out. SPSS gives the omnibus result, while the effect size and the follow-up comparisons need deliberate steps.
IN SHORT
What the Test Compares and What Drops Out
A Friedman test compares three or more related measurements, such as one outcome under several conditions or occasions, by ranking each participant’s values and comparing the mean ranks across conditions. It fits an ordinal or continuous outcome and does not rely on the sphericity condition of its parametric counterpart. To run the Friedman test in SPSS, open Analyze, Nonparametric Tests, Related Samples (Legacy Dialogs, K Related Samples in the older layout), select the condition variables, choose Friedman’s two-way analysis of variance by ranks, and request all pairwise comparisons. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
Ranking within each participant raises questions that the output alone cannot settle. If the mean at each condition is the quantity of interest, a parametric comparison across the same conditions takes the place of the ranks.
Friedman Test
The rank-based comparison of related measurements carried out within your study design, with the handling of missing occasions, the effect size and the pairwise follow-up agreed for your data.
Repeated Measures ANOVA
The parametric comparison of means across the same occasions or conditions, for a continuous outcome when the mean is the quantity of interest and sphericity is handled.
BEFORE YOU RUN IT
Design Questions Before Ranking the Conditions
The ranking is done within each participant, so four design questions are answered first, and the one about missing values often changes the sample more than any other.
Same Participants Throughout Every participant contributes a value to every condition, or matched sets of equal size do. Independent groups need another rank test, and unbalanced designs need a model that allows missing cells.
Complete Cases Only A participant missing one occasion drops out of the test entirely. Count how many do, report it, and consider whether a mixed model that uses every available value fits the question better.
Conditions in Order For measurements over time, list the occasions in their true order. The test itself ignores that order, so a question about a trend across occasions needs an analysis built for trends.
A Scale That Ranks Sensibly Ranks within a participant need values that compare sensibly across conditions. Coarse ratings produce many ties within participants, and the text should say how many cases were affected.
IN SPSS
How to Run the Friedman Test in SPSS
The outline is for IBM SPSS. The Related Samples dialog adds pairwise comparisons to the omnibus test, and Kendall's coefficient of concordance is a separate test option, with labels that vary by version.
- Confirm the design: the same participants measured under three or more conditions, one column per condition.
- Count the participants with a missing value in any column, since they are excluded.
- Open Analyze, Nonparametric Tests, Related Samples (Legacy Dialogs, K Related Samples in the older layout), and select the condition variables.
- Choose Friedman’s two-way analysis of variance by ranks, and add Kendall’s coefficient of concordance for an effect size.
- In the Related Samples dialog, set multiple comparisons to all pairwise.
- Read the omnibus summary and the mean ranks, then the adjusted pairwise table.
READING THE OUTPUT
What the Friedman Tables Show and What They Leave Out
The mean ranks describe the conditions, Friedman pairwise comparisons in SPSS localize the difference, and neither estimates how large the change was, which is where the effect size comes in.
| Output element | What it tells you | What to check |
|---|---|---|
| Ranks (legacy dialog) | The mean rank of each condition across participants | That conditions are listed in their true order and mean ranks are not described as medians |
| Test Statistics (legacy dialog) | N, the chi-square statistic, its degrees of freedom and the asymptotic significance | That N is the number of complete cases, not the number of participants recruited |
| Related-Samples Friedman’s Two-Way Analysis of Variance by Ranks Summary | Total N, the test statistic, degrees of freedom and asymptotic significance | That the Total N is compared with the planned sample and the dropped cases are explained |
| Kendall’s W (Test Statistics) | The agreement among participants’ rankings, from 0 to 1 | That it is described as consistency of ranks, with the sample size beside it |
| Pairwise Comparisons | Each pair of conditions with the standardized statistic, Sig. and Adj. Sig. | That the adjusted column is reported and the adjustment named, since the number of pairs rises with every added condition |
| Descriptive Statistics (optional) | The mean, median and quartiles of each condition | That medians are reported per condition, as ranks alone give no scale for the outcome |
| Exact or Monte Carlo significance (Exact option) | A p-value without the chi-square approximation | That it is requested for few participants and the version used is stated |
REPORTING
Reporting the Omnibus Result With Kendall's W
Placeholders only: each blank is filled from your output, and the sentence is a frame and not a finding.
Write the core as χ²(df) = ___, N = ___, p = ___, giving N as the number of complete cases, and add Kendall’s W = ___ as the effect size, described as the agreement among participants in how they ranked the conditions. Name the pairwise method and the family of comparisons it adjusts over, then report the adjusted significance for the pairs that answer the research question, with the direction in words. Kendall’s W in SPSS comes without an interval, so any interval is taken from a bootstrap or another program. Give the median and interquartile range of each condition, state how many participants were excluded for a missing value, and say whether the order of conditions was randomized or fixed.
COMMON MISTAKES
What Reviewers Question in a Friedman Analysis
Six issues recur, and three of them concern participants and conditions that are lost or misread before any statistic is computed.
Dropped Participants Unreported Cases with a missing value in any condition leave the test without notice. The Total N is smaller than the sample, and the text reports the difference and its likely cause.
Omnibus Taken as the Answer A significant result says that not all conditions are alike. Which ones differ comes from adjusted pairwise comparisons, which are planned and reported with their adjustment.
Mean Ranks as Scores Mean ranks lie between 1 and the number of conditions and carry no measurement scale. The change in the outcome is described with medians and quartiles per condition.
Pairwise Without Adjustment Four conditions give six pairs and six give fifteen. Unadjusted pairwise significance values overstate the evidence, so the adjusted column and its method are reported.
Independent Groups Entered Columns that hold different participants are not related measurements. The test treats each row as one participant, so a rank test for independent groups is the match for that design.
Time Trend Left Untested The omnibus test ignores the order of occasions, so a steady rise or fall is not tested by it. A question about a trend calls for an analysis planned for trends in advance.
Already run this analysis? Independent Statistical Review checks how missing occasions were handled, the pairwise adjustment and the effect size before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About the Friedman Output
Why N falls below the sample, how Kendall's W relates to the test and whether presentation order matters are the questions this output raises, along with a review of the handling of missing occasions.
Why is the N in my Friedman output smaller than my sample?
SPSS uses only participants with a value in every condition, so anyone missing one measurement is excluded. Report both numbers and consider why the values are missing. If the loss is substantial or related to the outcome, the result describes a selected subgroup, and a mixed model that uses all available values may answer the question better.
How do I read Kendall's W next to the Friedman test?
Kendall’s W is the Friedman statistic rescaled to run from 0 to 1, and it measures how consistently participants ranked the conditions. A value near 0 means little agreement and a value of 1 means identical rankings. It works as an effect size for the omnibus result and is read with the number of conditions and participants, since fixed benchmarks are only rough guides.
Does the order in which conditions were presented matter for the test?
The test ignores order, so a fixed order confounds the condition with practice, fatigue or time. Counterbalancing or randomizing the order in the design is the remedy, and the analysis cannot repair its absence. Say in the methods which order was used and how it was handled.
Can a statistician check how I handled missing occasions and pairwise tests?
Yes. An in-house PhD-level statistician can review the complete-case count, the pairwise adjustment and the effect size in your output, or carry out the analysis on your data from the start. For the tables and the write-up alone, Results Reporting & Interpretation covers that stage. The interpretation and conclusions remain yours.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
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
How Many Participants
Did Your Friedman Test Keep?
Send the conditions, the number of participants with every measurement and any output you have. Missing occasions, the pairwise adjustment and the effect size are worked through with you at the assessment.
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