CHAPTER 11 Comparing Average Values between Groups 145

Like the t test, the ANOVA also assumes that the value you are comparing follows

a normal distribution, and that the SDs of the groups you are comparing are sim-

ilar. If your data are not normally distributed, you can use the nonparametric

Kruskal-Wallis test instead of the one-way ANOVA, which we demonstrate later in

the section “Running nonparametric tests.”

Adjusting for a confounding variable

when comparing means

Sometimes you are aware the variable you are comparing, such as reduction in

blood pressure, is influenced by not only a treatment approach (such as drug A

compared to drug B), but also by other confounding variables (such as age,

whether the patient has diabetes, whether the patient smokes tobacco, and so on).

These confounders are considered nuisance variables because they have a known

impact on the outcome, and may be more prevalent in some groups than others.

If a large proportion of the group on drug A were over age 65, and only a small

proportion of those on drug B were over age 65, older age would have an influence

on the outcome that would not be attributable to the drug. Such a situation

would  be confounded by age. (See Chapter  20 for a comprehensive review of

confounding.)

When you are comparing means between groups, you are doing a bivariate com-

parison, meaning you are only involving two variables: the group variable and the

outcome. Adjusting for confounding must be done through a multivariate analysis

using regression.

Comparing means from sets

of matched numbers

Often when biostatisticians consider comparing means between two or more

groups, they are thinking of independent samples of data. When dealing with study

participants, independent samples means that the data you are comparing come

from different groups of participants who are not connected to each other statisti-

cally or literally. But in some scenarios, your intention is to compare means from

matched data, meaning some sort of pairing exists in the data. Here are some

common examples of matched data:»

» ^{The values come from the same participants, but at two or more different}

times, such as before and after some kind of treatment, intervention, or event.»

» ^{The values come from a crossover clinical trial, in which the same participant}

receives two or more treatments at two or more consecutive phases of the trial.