13. Comparing several means (one-way ANOVA)

This chapter delves into the foundational principles and applications of one-way ANOVA (Analysis of Variance), a pivotal statistical tool introduced by Sir Ronald Fisher in the early 20th century. Despite its name suggesting a focus on variances, ANOVA primarily investigates differences in means across multiple groups. Through the use of a clinical trial example involving three drugs—placebo, Anxifree, and Joyzepam—the chapter illustrates the mechanics of one-way ANOVA, highlighting its ability to discern whether observed differences in outcomes, such as mood improvements, are statistically significant. Readers are guided through the calculations underpinning the F-statistic, including between-group and within-group variability, and how these components inform hypothesis testing. The chapter also explores the practicalities of conducting ANOVA using jamovi, ensuring accessibility for researchers and students.

Building on the core functionality of one-way ANOVA, the chapter addresses essential topics like effect size computation, post hoc testing for multiple comparisons, and adjustments for violations of assumptions. Key assumptions such as homogeneity of variance, normality, and independence are discussed alongside diagnostic methods and remedies, such as the Welch ANOVA and non-parametric alternatives like the Kruskal-Wallis test. For designs involving repeated measures, the chapter introduces the Friedman test. Emphasis is placed on the practical interpretation of results, including effect sizes and adjusted p-values, fostering a comprehensive understanding of ANOVA's capabilities and limitations in real-world research contexts.