One‐way Analysis of Variance

Abstract

This chapter introduces the use of analysis of variance (ANOVA) for hypothesis testing of more than two sample means with normal distributions. ANOVA is a family of hypothesis testing methods for dealing with data obtained from different experimental designs. The variation of observations within groups played an important role in identifying the differences between means when hypothesis testing was performed to compare multiple population means. A more common way to interpret ANOVA is that it partitions the variation into different components, that is, the essence of ANOVA is the partitioning of variances. The chapter introduces three assumptions of ANOVA: independence, normality, and homogeneity of variances, and ways to verify the assumptions of normality and homogeneity of variances. Bartlett's and Levene's tests are widely used to test for the homogeneity of variances of multiple samples. The chapter focuses on three common transformations: square-root transformation, logarithmic transformation, and arcsine transformation.