Chapter 11

Comparing Average Values between Groups

IN THIS CHAPTER

Determining which tests should be used in different situations

Preparing your data, running tests, and interpreting the output

Estimating the sample size you need to compare average values

Comparing average values between groups of numbers is part of almost all biostatistical analyses, and

over the years, statisticians have developed dozens of tests for this purpose. These tests include

several different flavors of the Student t test, analyses of variance (ANOVA), and a dizzying collection

of tests named after the men who popularized them, including Welch, Wilcoxon, Mann-Whitney, and

Kruskal-Wallis, to name just a few. The multitude of tests is enough to make your head spin, which

leaves many researchers with the uneasy feeling that they may be using the wrong statistical test on

their data.

In this chapter, we guide you through the menagerie of statistical tests for comparing groups of

numbers. We start by explaining why there are so many tests available, then guide you as to which ones

are right for which situations. Next, we show you how to execute these tests using R software, and how

to interpret the output. We focus on tests that are usually provided by modern statistical programs (like

those discussed in Chapter 4, which also explains how to install and get started with R).

Grasping Why Different Situations Need Different

Tests

You may wonder why there are so many tests for such a simple task as comparing averages. Well,

“comparing averages” doesn’t refer to a specific situation. It’s a broad term that can apply to different

situations where you are trying to compare averages. These situations can differ from each other on the

basis of these and other factors, which are listed here in order of most to least common:

Within or between: You could be testing differences within groups or differences between

groups.

Number of time points: You could be testing differences occurring at one point or over a number

of time points.

Number of groups: You could be testing differences between two groups or between three or

more groups.

Distribution of outcome: Your outcome measurement could follow the normal distribution or

some other distribution (see Chapter 3).

Variation: You could be testing the differences in variation or spread across groups (see Chapter