Step 3 · Choosing the appropriate test statistic
Our example is about the distribution of non-metric variables (rare/frequent internet use; men/women) in one sample.
| Sample | Applied to | Scale level | Test statistics / Comments |
|---|
| One sample | Distributions | Non-metric | Kolmogorov-Smirnov and χ² test for goodness of fit; runs test for randomness; binomial test for dichotomous variables |
| Means | Metric | t-test (variance unknown); z-test (variance known) |
| Proportions | Metric | z-test |
| Two independent samples | Distributions | Non-metric | Kolmogorov-Smirnov test for agreement of distributions between two samples |
| Means | Metric | Two-sample t-test; F-test for equality of variances |
| Proportions | Metric, Non-metric | z-test; χ² test |
| Ranks / Medians | Non-metric | Mann-Whitney U-test (more sensitive than the median test) |
| Paired samples | Means | Metric | Paired-difference t-test |
| Proportions | Non-metric | McNemar test for binary variables; χ² test |
| Ranks / Medians | Non-metric | Wilcoxon signed-rank test (more sensitive than the sign test) |
