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The Essentials of Biostatistics for Physicians, Nurses, and Clinicians,
First Edition. Michael R. Chernick.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.

CHAPTER 8

Contingency Tables

Contingency tables are cross - tabulations of one categorical variable

versus another. They are used to test hypotheses about association

between the variables or differences among proportions. We will see

that the chi - square test is an approximate test for association when the

data set is large enough. Large enough means that each cell in the table

is fi lled with a reasonable number of counts (5 as a minimum is a good

rule of thumb).

On the other hand, Fisher ’ s exact test and its generalizations achieve

the exact signifi cance level, but require an added assumption that the

row sums and the column sums are fi xed at their observed levels when

comparing the existing table with other possible arrangement that occur

under the null hypothesis of no association (sometimes referred to as

independence).

The simplest table is the 2 × 2, where each variable can have only

two categories. However, in general, we have the R × C table where R

is the number of categories for the row variable, and C is the number

of categories for the column.

8.1 2 × 2 TABLES AND CHI - SQUARE

For an example of a 2 × 2 table, consider the case: Let us consider

whether or not there is a difference in the preference for western