CHAPTER 11 Comparing Average Values between Groups 143

Comparing the mean of two

groups of numbers

Comparing the mean of two groups of numbers is probably the most common

situation encountered in biostatistics. You may be comparing mean levels of a

protein that is a hypothesized disease biomarker between a group of patients

known to have the disease and a group of healthy controls. Or, you may be com-

paring a measurement of drug efficacy between two groups of patients with the

same condition who are taking two different drugs. Or, you may be comparing

measurements of breast cancer treatment efficacy in women on one health insur-

ance plan compared to those on another health insurance plan.

Such comparisons are generally handled by the famous unpaired or “independent

sample” Student t test (usually just called the t test) that we describe later in the sec-

tion “Surveying Student t tests.” Importantly, the t test is based on two assump-

tions about the distribution of the measurement value being tested in the two

groups:»

» ^{The values must be normally distributed (called the normality assumption).}

For data that are not normally distributed, instead of the t-test, you can use

the nonparametric Wilcoxon Sum-of-Ranks test (also called the Mann-Whitney U

test and the Mann-Whitney test). We demonstrate the Wilcoxon Sum-of-Ranks

test later in this chapter in the section “Running nonparametric tests.”»

» ^{The standard deviation (SD) of the values must be close for both groups}

(called the equal variance assumption). As a reminder, the SD is the square root

of the variance. To remember why accounting for variation is important in

sampling, review Chapter 3. Also, Chapter 9 provides more information about

the importance of SD. If the two groups you are comparing have very different

SDs, you should not use a Student t test, because it may not give reliable

results, especially if you are also comparing groups of different sizes. A rule of

thumb is that one group’s SD divided by another group’s SD should not be

more than 1.5 to quality for a Student t test. If you feel your data do not qualify,

you can use an alternative called the Welch test (also called the Welch t test, or

the unequal-variance t test). As you see later in this chapter under “Surveying

Student t tests,” because the Welch test accounts for both equal and unequal

variance, it is the only one that is included in R statistical software.

Comparing the means of three or

more groups of numbers

Comparing the means of three or more groups of numbers is an obvious extension

of the two-group comparison in the preceding section. For example, you may have