2018•Unpublished venueRequires access

Two‐Way Analysis of Variance

K. Paul Nesselroade Jr., Laurence G. Grimm

Abstract

The two-way analysis of variance (ANOVA) is an analytical procedure that allows us to investigate both main effects and interactions. Viewing diagrams and graphs of data from factorial designs allow us to speculate about the presence of main effects and interactions. There are three separate null hypotheses when conducting a two-way ANOVA, each requiring a separate F ratio to test them. The two-way ANOVA yields three different F ratios: one for Factor A, Factor B, and an interaction. This chapter presents both definitional and computational formulas for the two-way ANOVA. The assumptions for the two-way ANOVA are the same as those for the one-way ANOVA. The F tests in the two-way ANOVA allow us to test the null hypothesis for each independent variable as well as the interaction. Multiple comparisons are conducted to help interpret why a null hypothesis is being rejected.

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Key concepts: Analysis of variance, Mixed-design analysis of variance, Null (SQL), One-way analysis of variance, Main effect, Statistics, Null hypothesis, Variance (accounting)