Which statistical test should I use?
Four things decide it: whether your outcome is numerical or categorical, how many groups you have, whether those groups are the same people measured twice or different people, and whether the assumptions hold. Every test below says what it answers and what it needs.
Categorical
Compare
Independent t-test
Do two separate groups differ on average?
Kruskal-Wallis
Three or more groups, without assuming normality.
Mann-Whitney U
Two groups, without assuming normality.
One-sample t-test
Is this group's mean different from a known value?
One-way ANOVA
Three or more groups.
Paired t-test
Before and after, in the same people.
Welch's t-test
Two groups with unequal spread.
Wilcoxon signed-rank
Before and after, without assuming normality.
Relate
You do not have to choose. Chavery Research Companion asks the four questions in plain language, checks the assumptions against your own data, recommends the test that fits, and names the alternative when an assumption fails. How that works.