I am always forgetting when to use which statistical test, so I wrote them down here in case it helps anyone else. I am certainly not an expert so be sure to double check for your own purposes!
Start here if your outcomes are categorical...
This means that your data is not continuous and have no inherent order. For example: red, green, blue. If your data looks more like "scale of 1 to 10" or "rarely vs. sometimes vs. often," it is probably continuous or ordinal (see next section).
If your observations are independent...
For example, in a between-subjects study.
and your sample size is small...
Fisher's exact test.
and your sample size is moderate or large...
chi-squared test.
or the groups are paired (within-subjects)...
and the categories are binary...
McNemar's test.
or there are more than 3 categories...
Stuart-Maxwell test or Bowker's test of symmetry.
or here if your outcomes are continuous or ordinal.
Continuous = full numerical range, like time or percentile. Ordinal = ordered but discrete, like 5-point Likert scales or poor/fair/excellent ratings. Some ordinal data may be numerical, like the number of stars for a product review. This does not mean that ordinal data can be averaged because the distance between two points may not be consistent.
If you are comparing 2 groups...
and the groups are independent (between-subjects)...
and you can assume the distributions are normal (parametric)...
t-test.
and the distributions are unknown or skewed (nonparametric)...
Mann-Whitney U test.
or the groups are paired (within-subjects)...
and you can assume the distributions are normal (parametric)...
paired t-test.
and the distributions are unknown or skewed (nonparametric)...
Wilcoxon signed-rank test.
or you are comparing more than 2 groups...
and you can assume the distributions are normal (parametric)...
ANOVA.
and the distributions are unknown or skewed (nonparametric)...
Kruskal-Wallis test.
If you have many more groups or categories, you should probably look into regressions. Please email me if you see any errors or have any suggestions.