Non-Parametric Tests in MerQur: The Full Repertoire of Distribution-Free Hypothesis Testing
DOI:
https://doi.org/10.53463/merqur.20260446Keywords:
non parametric tests, Mann-Whitney, Wilcoxon, Kruskal-Wallis, FriedmanAbstract
Non-parametric (distribution-free) tests are a family of methods used when data do not come from a parametric distribution, when sample sizes are small, when variables are measured on an ordinal scale, or when the influence of outliers needs to be limited. This study introduces in detail the 7 analyses offered under the Non-Parametric Tests category of MerQur: Mann-Whitney U test, Wilcoxon signed-rank test, Kruskal-Wallis H test, Friedman test, binomial test, sign test, and runs test. For each analysis: (i) the hypothesis tested and application context, (ii) comparison with its parametric counterpart, (iii) required assumptions (rankability, symmetry, independence), (iv) form fields and parameter options in MerQur, (v) reported statistics and effect sizes (rank-biserial correlation, ε², Cliff’s δ), and (vi) interpretation guidance for a typical research question. The asymptotic relative efficiency (ARE) of non-parametric tests relative to their parametric counterparts is discussed: under the normal distribution, the ARE of Mann-Whitney U relative to the independent t-test is approximately 0.955; however, under heavy-tailed distributions, non-parametric tests can be more powerful. MerQur’s outputs provide exact p-value options where feasible and include options such as continuity correction (Yates). In conclusion, MerQur’s Non-Parametric Tests category offers Turkish-localised, reliable, and correct inferential tools for situations where parametric assumptions are violated.
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