Analysis of variance: One-way ANOVA

A one-way ANOVA test is a statistical test used to determine the effect of one nominal (categorical) variable on a continuous outcome variable.

  • Are used to evaluate the effect of one independent variable on a dependent variable.

  • Must be: 1 nominal (categorical) independent variable

  • Must be: 1 numeric dependent variable


Understanding One-way ANOVA

  • ANOVA compares variation between groups to variation within groups.

  • If the between-group variation is significantly larger, it suggests at least one group mean differs.

  • The method is called analysis of variance because it evaluates variance to determine differences in group means.

One-Way ANOVA assumptions

  1. Data within groups are normally distributed with equal variances across groups.

  2. Groups are from independent samples.

  3. When there are only a few observations in each group, check whether the standard errors of the model are normally distributed.

When only a few respondents are in each group, we check residuals instead of data normality.

One-Way ANOVA results