144 PART 4 Comparing Groups

recorded some biological measurement, like a value indicating level of response to

treatment among three diagnostic groups (such as mild, moderate, and severe

periodontitis). A comparison of the means of three or more groups is handled by

the analysis of variance (ANOVA), which we describe later in this chapter under

“Assessing the ANOVA.” When there is one grouping variable, like severity of per-

iodontitis, you have a one-way ANOVA. If the grouping variable has three levels

(like mild, moderate, and severe periodontitis), it’s called a one-way, three-level

ANOVA.

The null hypothesis of the one-way ANOVA is that all the groups have the same

mean. The alternative hypothesis is that at least one group has a mean that is

statistically significantly different from at least one of the other groups. The

ANOVA produces a single p value, and if that p is less than your chosen criterion

(typically α = 0.05), you conclude that at least one of the means must be statisti-

cally significantly different from at least one of the other means. (For a refresher

on hypothesis testing and p values, see Chapter 3.) But the problem with ANOVA

is that if it is statistically significant, it doesn’t tell you which groups have means

that are statistically significantly different. If you have a statistically significant

ANOVA, you have to follow-up with one or more so-called post-hoc tests (described

later under “Assessing the ANOVA”), which test for differences between the

means of each pair of groups in your ANOVA.

You can also use the ANOVA to compare just two groups. However, this one-way,

two-level ANOVA produces exactly the same p value as the classic unpaired equal-

variance Student t test.

Comparing means in data grouped

on several different variables

The ANOVA is a very flexible method in that it can accommodate comparing means

across several grouping variables at once. As an example, you could use an ANOVA

for comparing treatment response among participants with different levels of the

condition (such as mild, moderate, and severe periodontitis), who come from dif-

ferent clinics (such as Clinic A and Clinic B), and have undergone different treat-

ment approaches (such as using mouthwash or not). An ANOVA involving three

different grouping variables is called a three-way ANOVA (and compares at a more

granular level).

In ANOVA terminology, the term way refers to how many grouping variables are

involved, and the term level refers to the number of different levels within any one

grouping variable.