Non-parametic tests

Parametric tests 

Assume normal distributions, equal population variances and an interval/ratio outcome 

Non-parametric (NP) tests 

Useful for ordinal/ranked data and markedly skewed outcomes 

• Do not have parametric test requirements 

Non-parametric (NP) tests - advantages

Handle ranked/categorical data, skewness and outcomes difficult to quantify 

Non-parametric (NP) tests - limitations

May be less powerful, efficient and specific than parametric alternatives 

Choosing the right test 

Mann–Whitney U 

Compares two independent samples using ordinal ranks 

• Useful for strongly skewed data 

• Non-parametric counterpart of the independent-samples t-test 

• Assumptions: independent observations, ordinal measurement, group distributions roughly similar in shape 

• Test Statistics: U, z, two-tailed p 

Wilcoxon Signed-Rank 

Compares paired ordinal measurements, e.g. before versus after 

• Non-parametric counterpart of the paired-samples t-test 

• Assumptions: appropriate paired observations, ordinal DV, roughly symmetric distribution of paired difference scores 

Wilcoxon Signed-Rank - negative ranks

After < before 

Wilcoxon Signed-Rank - positive ranks

After > before 

Wilcoxon Signed-Rank - ties

Unchanged 

Kruskal–Wallis 

Compares ≥3 independent groups with an ordinal outcome or when regular ANOVA assumptions are violated 

• Non-parametric counterpart of one-way between-groups ANOVA 

• Assumptions: independence, ordinal outcome, broadly similar distribution shapes 

• A significant overall result suggests group differences 

• Does not specify which groups differ 

Spearman’s Rank Correlation 

Measures direction and strength of association between two ordinal variables 

• Alternative to Pearson when normality/linearity requirements cannot be met

Spearman’s Rank Correlation - positive

Higher ranks on one variable tend to accompany higher ranks on the other 

Spearman’s Rank Correlation - negative

Higher ranks accompany lower ranks 

NHST Reporting Checklist 

• State purpose + correct test 

• Variables/grouping 

• Sample size 

• Descriptive ranks 

• Test statistic 

• P-value 

• Reject/do not reject H₀ 

• Statistical conclusion 

• Direction where supported 

Null values for measurements