The following table indicates suitable statistical methods for a certain aim of an analysis (see first column below) given the type of available data (categorical or numerical).

Categorical, binomial (two possible outcomes)Numerical (from normal distribution, or non-normal as long as n > 20*)Numerical (from non-normal distribution with outliers and n < 20*)
Describe/summarize a groupProportions, contingency tablesMean, standard deviationMedian, interquartile range
Compare one group to a hypothesized value**One-proportion, chi-square
Binomial test
One-sample t-test

Wilcoxon test
Compare two unpaired groupsTwo-proportion or Fisher's test
(chi-square for large samples)
Unpaired (two-sample) t-testMann-Whitney test
Compare two paired (matched) groupsMcNemar's testPaired t-testWilcoxon test
Compare three or more unmatched groupsChi-square testOne-way ANOVAKruskal-Wallis test
Compare three or more matched groupsCochrane QRepeated-measures ANOVAFriedman test
Quantify association between two variablesContingency coefficientsPearson correlationSpearman correlation
Predict value from another measured variableSimple logistic regressionRegression (linear or nonlinear)Nonparametric regression
Predict value from several measured or binomial variablesMultiple logistic regressionMultiple regression (linear or nonlinear)

* To check whether data (can be assumed to) come from a normal distribution,  do a normality test (e.g.,  Anderson-Darling). If your data strongly deviate from normality, consider transforming them, e.g., taking the (natural) logarithm, the square root, or inverse; transformed data may be more normal.

** A hypothesized value can be a standard/reference value from previous literature, a legal limit, a recommended value, etc.