One-Way Analysis of Variance
DOI link for One-Way Analysis of Variance
One-Way Analysis of Variance book
This chapter introduces the analysis of variance (ANOVA) statistic with a focus on one-way ANOVA. First, the conditions for conducting a one-way ANOVA are presented, followed by an explanation of the benefits of one-way ANOVA over multiple independent t tests. Here, the idea of controlling for Type I error rate is discussed. Next, an in-depth examination of one-way ANOVA is presented, including a discussion of the partitioning of variance into between-group and within-group components. Through a discussion of these two components of variance, the idea of between-group variation being divided by random error variance (i.e., MSb/MSe) is presented, and links to other inferential statistics that use that same general formula are made. The process for calculating the various sums-of-squared deviations, mean-squared deviation, variance, and F value is presented next, followed by the process of hypothesis testing to determine whether the differences between sample means are statistically significant. The meaning and procedure of post-hoc tests are then described, with a focus on Tukey HSD tests. After a discussion of a common measure of effect size in ANOVA, eta squared, examples of one-way ANOVA's using both step-by-step calculations and output from Statistical Package for the Social Sciences are presented.