How do I assess an association between two variables?

There are more than 10 commonly used statistics for demonstrating an association between two variables. But have no fear! Choosing the correct one is not difficult. You choose the bivariate statistic based on: (1) the type of risk factor and outcome variable you have; and (2) whether the data are unpaired or paired (repeated observations or matched data). Bivariate statistics for unpaired data are shown in Table 5.1. Bivariate statistics for repeated observations and matched data are shown in Tables 5.22 and 5.28 and discussed in Sections 5.10 and 5.11.

How do I assess an association between two dichotomous variables (comparison of proportions)?

The most commonly used tests for the association between two dichotomous variables with unpaired data are the chi-squared test and Fisher's exact test.

It is easiest to follow these tests if you think of them in terms of a two-by-two contingency table (also referred to as a cross tabulation table) as shown in Table 5.2. (It is called a two-by-two table because it has two rows and two columns.)

In a two-by-two table, each subject will fall into one of the four cells – labeled a, b, c, d – depending on that subject's values on the risk factor and the outcome. The column totals (a + c and b + d) and the row totals (a + b and c + d) are referred to as marginal totals.