14. Factorial ANOVA

Chapter 14 explores the extension of ANOVA to factorial designs, allowing for the analysis of data influenced by multiple categorical predictor variables. This chapter builds on previous concepts introduced in simpler ANOVA and regression models, integrating the use of factorial designs to examine interactions between factors. By employing examples such as the effects of gender and school on student reading comprehension, the chapter demonstrates how factorial ANOVA (specifically two-way ANOVA) provides insights into main effects and interactions between factors. It introduces balanced factorial designs and systematically guides the reader through hypothesis formulation, model interpretation, and statistical testing using jamovi. Detailed explanations of sums of squares, degrees of freedom, and how to compute F-statistics further demystify the underlying mechanics of factorial ANOVA.

Subsequent sections delve into practical applications, such as interpreting interaction effects and understanding the implications of significant main effects in the presence of interactions. The chapter also contrasts factorial ANOVA with regression, highlighting their equivalence in linear modeling. It addresses complex scenarios, such as unbalanced designs, by examining different hypothesis testing strategies, including Type I, II, and III sum of squares. Through visual aids, practical examples, and clear step-by-step analyses, this chapter equips readers with the theoretical and practical tools necessary to perform and interpret factorial ANOVA effectively, fostering a deeper understanding of its power and versatility in experimental research.