174 PART 4 Comparing Groups

dichotomous variables has two rows and two columns. Because a 2 × 2 cross-tab

table has four cells, it’s commonly called a fourfold table. Another name you may

see for this table is a contingency table.

Chapter  12 includes a discussion of fourfold tables, and all that is included in

Chapter 12 applies not only to fourfold tables but also to larger cross-tab tables.

But because the fourfold table plays a pivotal role in public health with regard to

certain calculations used commonly in epidemiology and biostatistics, it warrants

a chapter all its own — this one! In this chapter, we describe several common

research scenarios in which fourfold tables are used, which are: comparing pro-

portions, testing for association, evaluating exposure and outcome associations,

quantifying the performance of diagnostic tests, assessing the effectiveness of

therapies, and measuring inter-rater and intra-rater reliability. In each scenario,

we describe how to calculate several common measures called indices (singular:

index), along with their confidence intervals. We also describe ways of sampling

called sampling strategies (see Chapter 6 for more on sampling).

Focusing on the Fundamentals

of Fourfold Tables

In contemplating statistical testing in a fourfold table, consider the process. As

described in Chapter 12, you first formulate a null hypothesis (H0) about the four-

fold table, set the significance level (such as α = 0.05), calculate a test statistic,

find the corresponding p value, and interpret the result. With a fourfold table, one

obvious test to use is the chi-square test (if necessary assumptions are met). The

chi-square test evaluates whether membership in a particular row is statistically

significantly associated with membership in a particular column. The p value on

the chi-square test is the probability that random fluctuations alone, in the

absence of any real effect in the population, could have produced an observed

effect at least as large as what you saw in your sample. If the p value is less than

α (which is 0.05 in your scenario), the effect is said to be statistically significant, and

the null is rejected. Assessing significance using a chi-square test is the most

common approach to testing a cross-tab of any size, including a fourfold table.

But fourfold tables can serve as the basis for developing other metrics besides chi-

square tests that can be useful in other ways, which are discussed in this chapter.

In the rest of this chapter, we describe many useful calculations that you can

derive from the cell counts in a fourfold table. The statistical software that cross-

tabulates your raw data can provide these indices depending upon the commands

it has available (see Chapter 4 for a review of statistical software). Thankfully (and

uncharacteristically), unlike in most chapters in this book, the formulas for many

indices derived from fourfold tables are simple enough to do manually with a