Are values the same in two or more groups?

Do the centers of two groups differ?

Parametric Test: Two-sample t-test. Tests differences in means. Requires that both groups follow a normal distribution.

Permutation Test: Two-sample perm test. Tests differences in means. __Does not require__ that both groups follow a normal distribution.

Nonparametric Test. Rank-sum (also called Mann-Whitney) test. Tests differences in medians. No distributional assumption required.

See Helsel & others (2020) Chapter 5.

Do paired data differ?

Parametric Approach: Paired t-test. Tests whether the mean difference is zero. Requires that differences follow a normal distribution.

Permutation Test: Paired perm test. Tests differences in means. __Does not require__ that differences follow a normal distribution.

Nonparametric Approach. Sign or signed-rank test. Tests whether the median difference is zero. No assumption of a normal distribution required.

See Helsel & others (2020) Chapter 6.

Do the centers of three or more groups differ?

Parametric Approach: Analysis of variance. Tests differences between means. Requires that each group's data follow a normal distribution.

Permutation Test: One-factor or multi-factor perm tests. Tests differences in means. __Does not require__ that each group's data follow a normal distribution.

Nonparametric Approach. Kruskal-Wallis test. Tests differences between medians. Does not require that each group's data follow a normal distribution.

See Helsel & others (2020) Chapter 7.

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Chapter references are to the 2020 Second Edition of Statistical Methods in Water Resources.