CHAPTER 13 Taking a Closer Look at Fourfold Tables 175

calculator (or using Microsoft Excel). All you need are the counts or frequencies of

each of the four cells. For these indices, you can also use a web page for calcula-

tion, which is available here: https://statpages.info/ctab2x2.html. This

chapter demonstrates how to calculate these indices in R (a free, open-source

software described in Chapter 4).

Like any other value you calculate from a sample, an index calculated from a four-

fold table is a sample statistic, which is an estimate of the corresponding population

parameter. A good researcher always wants to quote the precision of that estimate.

In Chapter 10, we describe how to calculate the standard error (SE) and confidence

interval (CI) for sample statistics such as means and proportions. Likewise, in this

chapter, we show you how to calculate the SE and CI for the various indices you

can derive from a fourfold table.

Though an index itself may be easy to calculate manually, its SE or CI usually is

not. Approximate formulas are available for some of the more common indices.

These formulas are usually based on the fact that the random sampling fluctua-

tions of an index (or its logarithm) are often nearly normally distributed if the

sample size is large enough. We provide approximate formulas for SEs where

they’re available, and demonstrate how to calculate them in R when possible.

For consistency, all the formulas in this chapter refer to the four cell counts of the

fourfold table, and the row totals, column totals, and grand total, in the same

standard way (see Figure 13-1). This convention is used in many online resources

and textbooks.

Choosing the Correct Sampling Strategy

In this section, we assume you are designing a cross-sectional study (see

Chapter 7 for a review of study design terminology). Using such a design, though

you could not assess cause-and-effect, you could evaluate the association between

an exposure (hypothesized cause) and outcome. For example, you may hypothe-

size that being obese (exposure) causes a patient to develop hypertension

FIGURE 13-1:

These

designations for

cell counts and

totals are used

throughout this

chapter.

© John Wiley & Sons, Inc.