Chapter 13

Taking a Closer Look at Fourfold Tables

IN THIS CHAPTER

Beginning with the basics of fourfold tables

Digging into sampling strategies for fourfold tables

Using fourfold tables in different scenarios

In Chapter 12, we show you how to compare proportions between two or more groups with a cross-

tab table. In general, a cross-tab shows the relationship between two categorical variables. Each row

of the table represents one particular category of one of the variables, and each column of the table

represents one particular category of the other variable. The table can have two or more rows and two

or more columns, depending on the number of different categories or levels present in each of the two

variables. (To refresh your memory about categorical variables, read Chapter 8.)

Imagine that you are comparing the performance of three treatments (Drug A, Drug B, and Drug C) in

patients who could have four possible outcomes: improved, stayed the same, got worse, or left the

study due to side effects. In such a case, your treatment variable would have three levels so your

cross-tab would have three rows, and your outcome variable would have four levels so your cross-tab

would have four columns.

But this chapter only focuses on the special case that occurs when both categorical variables in the

table have only two levels. Other words for two-level variables are dichotomous and binary. A few

examples of dichotomous variables are hypertension status (hypertension or no hypertension), obesity

status (obese or not obese), and pregnancy status (pregnant or not pregnant). The cross-tab of two

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 proportions, 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