When researchers use designs that call for multiple groups, the most commonly…

Concept

A statistical test must match the number and relationship of the groups being compared.

Tests based on a single standardized mean difference handle one or two groups, whereas analysis of variance uses a ratio of explained to unexplained variation to assess several group means together.

Application

The design contains multiple groups. Analysis of variance therefore compares between-group variation with within-group variation through an F statistic; the relevant test is the F-test.

Contrast

• Z-test — typically standardizes one mean or a difference between two means under large-sample or known-variance conditions.

• t-test for difference of means — compares two independent group means.

• paired t-test — compares two related measurements through their pairwise differences.

• F-test — uses a variance ratio and supplies the test statistic for analysis of variance.

Cross-check

Counting the groups gives the same selection rule: two-group mean comparisons lead to t- or Z-based procedures, while a several-group mean comparison leads to ANOVA and its F statistic.

Hence the required test is the F-test.