170 PART 4 Comparing Groups

Those exclamation points indicate calculating the factorials of the cell counts (see

Chapter 2). For the example in Figure 12-1, the observed table has a probability of

Pr

(60!)(40!)(43!)(57!)

(33!)(27!)(10!)(30!)(100!)

00196

0.

Other possible tables with the same marginal totals as the observed table have

their own Pr values, which may be larger than, smaller than, or equal to the Pr

value of the observed table. The Pr values for all possible tables with a specified set

of marginal totals always add up to exactly 1.

The Fisher Exact test p value is obtained by adding up the Pr values for all tables

that are at least as different from the H0 as your observed table. For a fourfold

table that means adding up all the Pr values that are less than (or equal to) the Pr

value for your observed table.

For the example in Figure 12-1, the p value comes out to 0.00385, which means

that there’s only 1 chance in 260 (because 1 0 00385

260

/ .

) that random fluctua-

tions could have produced such an apparent effect in your sample.

Noting the pros and cons of

the Fisher Exact test

The big advantages of the Fisher Exact test are as follows:»

» ^{It gives the exact p value.»}

» ^{It is exact for all tables, with large or small (or even zero) cell counts.}

Why do people still use the chi-square test, which is approximate and doesn’t

work for tables with small cell counts? Well, there are several problems with the

Fisher Exact test:»

» ^{The Fisher calculations are a lot more complicated, especially for tables larger}

than 2

2. Many statistical software packages either don’t offer the Fisher Exact

test or offer it only for fourfold tables. Even if they offer it, you may execute

the test and find that it fails to finish the test, and you have to break into the

program to stop the procedure. Also, some interactive web pages perform the

Fisher Exact test for fourfold tables (including 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 2

2 because the calculations are so intense. For this reason,

the Fisher Exact test is only practical for small cell counts.