16 Comparing means among more than two groups

Tutorial learning objectives

  • Learn how to analyze a numeric response variable in relation to a single categorical explanatory variable that has more than two groups. In other words, we will learn how to compare the means of more than 2 groups.
  • Learn how to implement all the steps of an Analysis of Variance (ANOVA), which is often the most suitable method for testing the null hypothesis of no difference between the means of more than two groups (i.e. \(\mu_1 = \mu_2 = \mu_3 = \mu_i..\))

It might seem strange that a test designed to compare means among groups is called “Analysis of Variance”. The reason lies in how the test actually works, as described in Chapter 15 of the text.

  • Here we learn fixed-effects ANOVA (also called Model-1 ANOVA), in which the different categories of the explanatory variable are predetermined, of direct interest, and repeatable. These methods therefore typically apply to experimental studies.
  • When the groups are sampled at random from a larger population of groups, as in most observational studies, one should typically use a random-effects ANOVA (also called Model-2 ANOVA). Consult the following webpage for tutorials on how to conduct various types of ANOVA.
  • In this tutorial we’re learning about a One-way ANOVA, in which there is only one explanatory (categorical) variable
  • Learn the assumptions of ANOVA
  • Learn appropriate tables and graphs to accompany ANOVA
  • Learn how to conduct a post-hoc comparison among all pairs of group means: the Tukey-Kramer post-hoc test