Start from your design, not from the test you have heard of.
Two independent groups, numeric outcome → independent-samples t-test. Assumptions violated, or n small → Mann–Whitney U.
Same units measured twice → paired t-test. Non-normal differences → Wilcoxon signed-rank.
Three or more independent groups → one-way ANOVA, followed by a post-hoc test only if the ANOVA is significant. Non-normal → Kruskal–Wallis.
Two categorical variables → chi-square test of independence. Any expected count below 5 → Fisher's exact test.
Two numeric variables → Pearson correlation if the relationship looks linear and the data are roughly normal; Spearman otherwise.
Three rules that matter more than the choice itself:
- Decide the test before you see the data.
- Always report the effect size and a confidence interval, not just p. "Significant" without a magnitude tells the reader nothing about whether it matters.
- n = 3 per group almost never supports a strong claim. Say so honestly rather than hoping nobody notices.