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Apply Mann-Whitney, Kruskal-Wallis, and other nonparametric methods
Passed 22 of 23 test cases with the skill, and 19 of 23 without it.
3 fixed19 passed either way1 still failing0 broke
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One of 3 test cases the skill fixed. Same model, same prompt, with and without the skill.
Write a standard APA-style reporting sentence for a Wilcoxon signed-rank test where the median difference was 4.5, the test statistic W was 12.0, p was .003, and effect size r was .58.
| Checked | Without skill | With skill |
|---|---|---|
| The test statistic is designated using the letter W. | Passed | Passed |
| The median difference is formatted as Mdn_diff = 4.5. | Missed | Passed |
The instructions your model reads when the skill loads.
A skill for selecting and applying nonparametric statistical tests when data violate parametric assumptions. Covers rank-based tests for group comparisons, correlation, and paired data, with implementation examples and guidance on reporting.
Use nonparametric tests when:
- Data are ordinal (Likert scales, rankings)
- Distribution is clearly non-normal (heavy skew, outliers)
- Sample size is very small (n < 15-20 per group)
- Homogeneity of variance is violated
- You are analyzing ranks or medians rather than means
Use parametric tests when:
- Data are approximately normal (or n > 30 by CLT)
- Variance is homogeneous across groups
- You need greater statistical power
- The parametric assumptions are reasonably met
| Parametric Test | Nonparametric Alternative | Use Case |
|---|---|---|
| Independent t-test | Mann-Whitney U | Compare 2 independent groups |
| Paired t-test | Wilcoxon signed-rank | Compare 2 related samples |
| One-way ANOVA | Kruskal-Wallis H | Compare 3+ independent groups |
| Repeated measures ANOVA | Friedman test | Compare 3+ related samples |
| Pearson correlation | Spearman rank correlation | Measure association |
| Chi-square test | Fisher's exact test | Compare proportions (small n) |
from scipy import stats
test cases passed, vs 19 / 23 without
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