Chapter 8

Analyzing Complex Experiments

In this chapter, you learn how to analyze a variety of different types of experimental data, including changes measured in percentages, measurements drawn from more than two populations, categorical data presented in the form of contingency tables, samples with unequal variances, and multiple endpoints.

# 8.1 CHANGES MEASURED IN PERCENTAGES

In the previous chapter, we learned how we could eliminate one component of variation by using each subject as its own control. But what if we are measuring weight gain or weight loss where the changes, typically, are best expressed as percentages rather than absolute values? A 250-pounder might shed 20 lb without anyone noticing; not so with an anorexic 105-pounder.

The obvious solution is to work not with before–after differences but with before/after ratios.

But what if the original observations are on growth processes—the size of a tumor or the size of a bacterial colony—and vary by several orders of magnitude? H.E. Renis of the Upjohn Company observed the following vaginal virus titres in mice 144 hours after inoculation with Herpes virus type II:

```Saline controls           10,000, 3000, 2600, 2400, 1500.
Treated with antibiotic   9000, 1700, 1100,   360,     1.```

In this experiment, the observed values vary from 1, which may be written as 100, to 10,000, which may be written as 104 or 10 times itself 4 times. With such wide variation, how can we possibly detect a treatment effect?

The trick employed by ...

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