CHAPTER 12 Comparing Proportions and Analyzing Cross-Tabulations 171

»

» ^{The calculations can become numerically unstable for large cell counts, even}

in a 2

2 table. The equations involve the factorials of the cell counts and

marginal totals, and these can get very large — even for modest sample

sizes — often exceeding the largest number that a computer program can

handle. Many programs and web pages that offer the Fisher Exact test for

fourfold tables fail with data from more than 100 subjects.»

» ^{Another issue is — like the chi-square test — the Fisher Exact test is not for}

detecting gradual trends across ordinal categories.

Calculating Power and Sample Size for

Chi-Square and Fisher Exact Tests

Note: The basic ideas of power and sample-size calculations are described in

Chapter 3, and you should review that information before going further here.

Earlier in the section “Examining Two Variables with the Pearson Chi-Square

Test,” we used an example of an observational study design in which study par-

ticipants were patients who chose which treatment they were using. In this sec-

tion, we use an example from a clinical trial study design in which study

participants are assigned to a treatment group. The point is that the tests in this

section work on all types of study designs.

Let’s calculate sample size together. Suppose that you’re planning a study to test

whether giving a certain dietary supplement to a pregnant woman reduces her

chances of developing morning sickness during the first trimester of pregnancy,

which is the first three months. This condition normally occurs in 80 percent of

pregnant women, and if the supplement can reduce that incidence rate to only

60 percent, it would be considered a large enough reduction to be clinically sig-

nificant. So, you plan to enroll a group of pregnant women who are early in their

first trimester and randomize them to receive either the dietary supplement or a

placebo that looks, smells, and tastes exactly like the supplement. You will ran-

domly assign each participant to the either the supplement group or the placebo

group in a process called randomization. The participants will not be told which

group they are in, which is called blinding. (There is nothing unethical about this

situation because all participants will agree before participating in the study that

they would be willing to take the product associated with each randomized group,

regardless of the one to which they are randomized.)

You’ll have them take the product during their first trimester, and you’ll survey

them to record whether they experience morning sickness during that time (using