Compare 3 or more groups

Do the centers of two groups differ?
Parametric Approach: Two-sample t-test. Tests differences in means. Assumes normal distribution in both groups. See chap. 5.
Nonparametric Approach. Rank-sum (also called Mann-Whitney) test. Tests differences in medians. No distributional assumption required. See chap. 5.

Do paired data differ?
Parametric Approach: Paired t-test. Tests whether the mean difference is zero. Assumes differences follow a normal distribution. See chapter 6.
Nonparametric Approach. Sign or signed-rank test. Tests whether the median difference is zero. No assumption of a normal distribution required. See chapter 6.

Do the centers of three or more groups differ?
Parametric Approach: Analysis of variance. Tests differences between means. Assumes residuals follow a normal distribution. See chapter 7.
Nonparametric Approach. Kruskal-Wallis test. Tests differences between medians. Does not require data follow a normal distribution. See chapter 7.

Chapter references are to the course textbook Statistical Methods in Water Resources.