142 PART 4 Comparing Groups

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 3).

These different factors can occur in any and all combinations, so there are a lot of

potential scenarios. In the following sections, we review situations you may fre-

quently encounter when analyzing biological data, and advise you as to how to

select the most appropriate testing approach given the situation.

Comparing the mean of a group of numbers

to a hypothesized value

Sometimes you have a measurement from the literature (called a historical control)

that provides a hypothesized value of your measurement, and you want to statis-

tically compare the average of a group to this mean. This situation is common

when you are comparing a value that was calculated based on statistical norms

derived based on the population (such as the IQ test, where 100 has been scaled to

be the population mean).

Typically, comparing a group mean to a historical control warrants using the one-

group Student t test that we describe in the later section “Surveying Student t tests.”

For data that are not normally distributed, the Wilcoxon Signed-Ranks (WSR) test

can be used instead, although it is not used often so we do not cover it in this

chapter. (If you need a review on what normally distributed means, see Chapter 3.)