Situations

Fourfold tables can arise from a number of different scenarios, including the following:

Comparing proportions between two groups (see Chapter 12)

Testing whether two binary variables are associated

Assessing associations between exposures and outcomes

Evaluating diagnostic procedures

Evaluating therapies

Evaluating inter-rater reliability

Note: These scenarios can also give rise to tables larger than

, and fourfold tables can arise in

other scenarios besides these.

Describing the association between two binary variables

Suppose you conduct a cross-sectional study by enrolling a random sample of 60 adults from the local

population as participants in your study with the hypothesis that being obese is associated with having

HTN. For the exposure, suppose you measure their height and weight, and use these values to calculate

their body mass index (BMI). You then use their BMI to classify them as either obese or non-obese.

For the outcome, you also measure their blood pressure in order to categorize them as having HTN or

not having HTN. This is simple random sampling (SRS), as described in the earlier section “Choosing

the Correct Sampling Strategy.” You can summarize your data in a fourfold table (see Figure 13-2).

The table in Figure 13-2 indicates that more than half of the obese participants have HTN and more

than half of the non-obese participants don’t have HTN — so there appears to be a relationship

between being a membership in a particular row and simultaneously being a member of a particular

column. You can show this apparent association is statistically significant in this sample using either a

Yates chi-square or a Fisher Exact test on this table (as we describe in Chapter 12). If you do these

tests, your p values will be

and

, respectively, and at α = 0.05, you will be

comfortable rejecting the null.

© John Wiley & Sons, Inc.

FIGURE 13-2: A fourfold table summarizing obesity and hypertension in a sample of 60 participants.

But when you present the results of this study, just saying that a statistically significant association

exists between obesity status and HTN status isn’t enough. You should also indicate how strong this