www.socscistatistics.com/tests/fisher/default2.aspx). Only the major statistical

software packages (like SAS, SPSS, and R, described in Chapter 4) offer the Fisher Exact test for

tables larger than

because the calculations are so intense. For this reason, the Fisher Exact

test is only practical for small cell counts.

The calculations can become numerically unstable for large cell counts, even in a

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 participants were patients who chose which

treatment they were using. In this section, 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 significant. 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 randomly 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 explicit criteria for what constitutes morning

sickness). Then you’ll tabulate the results in a 2 × 2 cross-tab. The table will look similar to Figure

12-1, but instead will say “supplement” and “placebo” as the label on the two rows, and “did” and

“did not” experience morning sickness as the headings on the two columns. And you’ll test for a

significant effect with a chi-square or Fisher Exact test. So, your sample size calculation question is:

How many subjects must you enroll to have at least an 80 percent chance of getting

on the

test if the supplement truly can reduce the incidence from 80 percent to 60 percent?