The effect of interaction and rounding error in two-way ANOVA: example of impact on testing for normality

Abstract

A key issue in various applications of analysis of variance (ANOVA) is testing for the interaction and the interpretation of resulting ANOVA tables. In this note it is demonstrated that for a two-way ANOVA, whether interactions are incorporated or not may have a dramatic influence when considering the usual statistical tests for normality of residuals. The effect of numerical rounding is also discussed.

Keywords:

• analysis of variance
• rounding error
• Shapiro–Wilk test
• factorial experiment
• interaction