Multiple Means and Variance Ratios: ANOVA

This chapter presents four separate scenarios of a survey with random samples of 30 Democrats, 30 Republicans, and 30 Independents in the community. It explores how far apart the sample means are, and how high the sample variances are. Variance ratios and the F-distribution can be used in an ingenious way to broadly analyze sample mean differences. The analysis of variance (ANOVA) does not reveal which specific groups are different from which, just whether at least two groups' samples may represent populations with different population means. ANOVA needs to assume that all samples come from populations with the same population variance. If all the groups' samples in a given scenario come from populations with the same population mean and population variance, then all the groups' sample means will be members of a common sample mean distribution. Finally, the chapter illustrates where each of the four scenarios maps onto the F distribution.