Toolkit
Which Test Do I Use?
Answer two or three questions about your data and goal; the chooser names the procedure, its conditions, the chapter that teaches it and a Python one-liner.
All procedures at a glance
| Goal | Data | Procedure | Chapter |
|---|---|---|---|
| Estimate a mean | σ unknown, normal or large n | one-mean t-interval | 06 |
| Estimate a proportion | ≥ 5 successes and failures | one-proportion z-interval (plus-four if small) | 06 |
| Estimate an SD | normal population | χ²-interval (else bootstrap) | 06, 12 |
| Estimate anything else | any | bootstrap interval | 12 |
| Test one mean | normal or large n / symmetric | t-test (z if σ known) / Wilcoxon signed-rank | 07 |
| Test one proportion | n p₀ and n(1 − p₀) ≥ 5 | one-proportion z-test (or exact binomial) | 07 |
| Test one SD | normal population | χ²-test | 06 |
| Compare two means, independent | normal or large / skewed same shape | Welch t (pooled if equal SDs) / Mann–Whitney | 08 |
| Compare two means, paired | differences normal / symmetric | paired t / paired Wilcoxon | 08 |
| Compare two SDs | both normal / otherwise | F-test / Levene | 08 |
| Compare two proportions | ≥ 5 successes and failures each | two-proportions z | 08 |
| Compare 3+ means | normal, rule of 2 / otherwise | one-way ANOVA + Tukey / Kruskal–Wallis | 11 |
| One categorical distribution | expected counts OK | χ² goodness of fit | 09 |
| Two categorical variables | one population / several | χ² independence / χ² homogeneity | 09 |
| Two quantitative variables | linear, residuals OK | regression & correlation inference | 10 |
| Many predictors / binary outcome | — | multiple / logistic regression | 12 |
| Many tests at once | — | Bonferroni / Benjamini–Hochberg | 12 |
Before any procedure
Plot the data. Check how it was collected (random? independent? time series?). Look for outliers. No decision tree can replace those three minutes.