Non-Parametric Tests in SPSS: 3 Common Tests Step by Step

Q: Are non-parametric tests less powerful than parametric tests?

When the assumptions of the parametric test hold, it has slightly more power. When they do not, the non-parametric test is both more accurate and more honest. With large samples the loss is small: for normally distributed data Mann-Whitney retains about 95% of the power of the t-test.

Q: Should I still report means alongside a non-parametric test?

Means can appear in the general descriptive table, but the non-parametric result itself is reported with medians and mean ranks, because the test compares ranks, not means. Mixing the two in one sentence confuses the reader about what was tested.

Q: How do I run pairwise comparisons after Kruskal-Wallis in an older SPSS version?

Run a Mann-Whitney test for each pair of groups and divide .05 by the number of comparisons (three groups give three comparisons and an alpha of .0167). Treat a pair as significant only below that threshold, and state the correction explicitly in the text.

Q: What is the non-parametric alternative to multiple regression?

There is no single direct equivalent among non-parametric tests. Options are ordinal regression if the outcome is ordinal, multiple regression with bootstrapped confidence intervals if only the residuals are non-normal, or a transformation of the outcome. Discuss the choice with your supervisor and document it.

Q: Do examiners accept chi-square for large tables such as 4 × 5?

Yes, provided the expected-count condition is met; otherwise merge categories. For large tables, add the adjusted standardized residuals to identify the cells driving the association; values beyond ±1.96 mark the cells that differ from independence.

By the Mastermind PhD team · Last updated: 3 November 2026 · Editorial policy

The normality test failed, your data are ranks, or your sample has twenty cases: which test do you use now? Non-parametric tests are the answer, and they are not a weaker “plan B”. They are tools designed for data that do not meet the assumptions of the t-test, ANOVA and Pearson’s r, and examiners accept them readily when the choice is justified and the result is reported properly. This guide explains when to use them, which non-parametric test replaces which parametric one, and then takes the three most common tests in theses one by one: the SPSS steps, how to read the output, the effect size, and the APA sentence.

This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.

What are non-parametric tests? Non-parametric tests do not assume that the data follow a particular distribution such as the normal distribution, and they do not work with means and variances. They work with the ranks of the values or with frequencies. They are used with ordinal data, with continuous data that depart markedly from normality, with small samples and with influential outliers, and their results are interpreted in terms of medians and mean ranks rather than arithmetic means.

Table of Contents

When should you use non-parametric tests instead of parametric ones?

Four situations justify non-parametric tests, and documenting one of them in the results chapter is enough:

The dependent variable is ordinal by nature: a rank, a grade band from poor to excellent, or a single Likert item.
A marked departure from normality that the other remedies did not resolve, especially with groups smaller than about 30.
Genuine outliers that cannot be excluded or justified and that change the mean substantially.
A small sample that does not allow you to rely on the robustness of the parametric test.

What does not justify the choice: running both tests and keeping the one closer to your hypothesis, or using non-parametric tests “to be safe” without checking the assumptions at all.

Which test replaces which? The map

Question	Parametric test	Non-parametric alternative	What to report
Difference between two independent groups	Independent samples t-test	Mann-Whitney U	Medians, mean ranks, U, z, p, r
Difference between three or more independent groups	One-way ANOVA	Kruskal-Wallis H	Medians, H, df, p, η²H, then pairwise comparisons
Difference between two measurements of the same people	Paired samples t-test	Wilcoxon signed-rank	Medians, z, p, r
Difference between three or more repeated measurements	Repeated measures ANOVA	Friedman	χ²F, df, p, Kendall’s W
Relationship between two variables	Pearson’s r	Spearman’s rho or Kendall’s tau	rs, N, p
Relationship between two nominal variables	None	Chi-square test of independence	χ², df, N, p, Cramér’s V

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Mann-Whitney U: the alternative to the independent samples t-test

Steps. Analyze, then Nonparametric Tests, then Legacy Dialogs, then 2 Independent Samples. Move the dependent variable to Test Variable List and the grouping variable to Grouping Variable, define the two codes, and make sure Mann-Whitney U is ticked. The newer route (Nonparametric Tests, then Independent Samples) gives the same test with a standardized statistic and a cleaner summary table. The test dialog does not print medians; obtain them from Explore or Compare Means with the grouping variable.

Reading the output. The Ranks table gives n, mean rank and sum of ranks for each group; the group with the higher mean rank scores higher on the variable. The Test Statistics table gives U, Wilcoxon W, z and the p value (Asymp. Sig. for larger samples, Exact Sig. when it appears for small samples).

Effect size. r = z ÷ √N, where N is the total number of cases in both groups; .10 small, .30 medium, .50 large (Cohen, 1988; Tomczak & Tomczak, 2014).

APA sentence. “A Mann-Whitney U test indicated that anxiety scores were significantly lower among principals (Mdn = 2.80, n = 22) than among teachers (Mdn = 3.40, n = 158), U = 1,081, z = −2.87, p = .004, r = .21, a small-to-medium effect.” Make clear that you are comparing ranks and medians, not means.

non-parametric tests: what this guide covers - When should you use non-parametric tests instead of parametric ones?، Which test replaces which? The ma — What this guide covers – the Mastermind PhD team

Kruskal-Wallis H: the alternative to one-way ANOVA

Steps. Analyze, then Nonparametric Tests, then Legacy Dialogs, then K Independent Samples. Move the dependent and grouping variables, click Define Range and enter the lowest and highest group codes, and tick Kruskal-Wallis H.

Reading the output. The Ranks table gives the mean rank of each group. The Test Statistics table gives H (labeled Chi-Square), df (number of groups minus one) and the p value.

Pairwise comparisons. A significant H says only that at least one group differs. To find which, use the newer route: Analyze, then Nonparametric Tests, then Independent Samples; under Settings choose Kruskal-Wallis with Multiple comparisons set to All pairwise. SPSS produces a Pairwise Comparisons table with Bonferroni-adjusted significance (Adj. Sig.). The manual alternative is a Mann-Whitney test for each pair with alpha divided by the number of comparisons.

Effect size. η²H = (H − k + 1) ÷ (n − k), where k is the number of groups and n the sample size (Tomczak & Tomczak, 2014); .01 small, .06 medium, .14 large.

APA sentence. “A Kruskal-Wallis test showed a significant difference in job satisfaction across qualification levels, H(2) = 9.84, p = .007, η²H = .03. Bonferroni-adjusted pairwise comparisons indicated that the only significant difference was between teachers with a master’s degree (mean rank = 178.2) and diploma holders (mean rank = 124.6), p = .005.”

Wilcoxon signed-rank test: the alternative to the paired samples t-test

Steps. Analyze, then Nonparametric Tests, then Legacy Dialogs, then 2 Related Samples. Move the two measurements (pre-test and post-test) as a pair and tick Wilcoxon.

Reading the output. The Ranks table gives the number of negative ranks (post-test lower than pre-test), positive ranks (post-test higher) and ties; the direction of change is read from which type is more numerous and has the higher mean rank. The Test Statistics table gives z and the p value. SPSS bases z on the smaller rank sum, so z is usually negative; its sign does not by itself indicate the direction of change.

Effect size. r = z ÷ √N. Some authors use the number of pairs as N and others the total number of observations; state which you used.

Worked example and APA sentence. Forty-seven students completed an attitude-to-reading scale before and after a program. The Ranks table shows 38 positive ranks, 6 negative ranks and 3 ties; medians rose from 3.20 to 4.10. Test Statistics: z = −4.12, p < .001. Effect size: r = 4.12 ÷ √47 = .60. The sentence: “A Wilcoxon signed-rank test showed that attitude-to-reading scores were significantly higher after the program (Mdn = 4.10) than before it (Mdn = 3.20), z = −4.12, p < .001, r = .60, a large effect; 38 of 47 students improved, 6 declined and 3 were unchanged.”

Where do Friedman and chi-square fit among non-parametric tests?

The Friedman test extends Wilcoxon to three or more repeated measurements (pre-test, post-test, follow-up): Analyze, then Nonparametric Tests, then Legacy Dialogs, then K Related Samples. Report χ²F, df, p and Kendall’s W as the effect size, followed by pairwise Wilcoxon tests with a Bonferroni correction.

The chi-square test of independence is not a replacement for a parametric test but the primary test for two nominal variables (sector and type of participation). Run it from Analyze, then Descriptive Statistics, then Crosstabs, with Chi-square and Phi and Cramer’s V under Statistics and Observed and Expected under Cells. The main condition is that at least 80% of the cells have an expected count of 5 or more and none has an expected count below 1 (McHugh, 2013); otherwise merge categories or use Fisher’s exact test for a 2 × 2 table. Report it as “χ²(2, N = 300) = 11.6, p = .003, Cramér’s V = .20″, together with the percentages that show the direction of the association.

Which mistakes do examiners mark most often?

Reporting means with Mann-Whitney or Kruskal-Wallis instead of medians and mean ranks.
Running Kruskal-Wallis without adjusted pairwise comparisons after a significant result.
Omitting the effect size “because the test is non-parametric”.
Running chi-square on percentages or means instead of raw counts, or with small expected counts and no remedy.
Describing a negative z in Wilcoxon as “a decrease” without reading the Ranks table.
Justifying the choice with a general claim (“non-parametric tests are more accurate”) instead of the results of the assumption checks.
Running parametric and non-parametric tests on the same data and reporting whichever was significant.

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Frequently asked questions

Are non-parametric tests less powerful than parametric tests?