Analysis of Variance

This chapter explains the tests of analysis of variance (ANOVA): one-way, two-way and higher orders. Using our employment dataset, we explain one-way analysis of variance, where there is one dependent variable (of our interest) whose means we want to compare across the group (called the factor). We discuss these assumptions required to be met for undertaking one-way ANOVA (which are valid for higher order ANOVAs too). We then undertake one-way ANOVA and find that the mean of at least one of the groups (factors) differs from the rest. We, therefore, explain the procedure to undertake Post Hoc analysis for groupwise comparison of means. We explain the process to estimate the effect sizes of the pairs for which the difference in mean is statistically significant. Next, we discuss two-way ANOVA and the terminology associated with its factors; there are two factors in two-way ANOVA. Continuing with our example of employment, we explain the procedure of undertaking two-way ANOVA using two approaches; the second approach helps examine the interaction effect between the factors. We end the chapter by explaining the procedure to undertake higher order ANOVAs. The chapter also has an appendix on effect size calculations, when variance is equal.