2 x 2 Tables

The simplest form of crosstabulation is the 2 by 2 table where two variables are "crossed," and each variable has only two distinct values.

For example, suppose we conduct a simple study in which males and females are asked to choose one of two different brands of soda pop (brand A and brand B); the data file can be arranged like this:

Gender Soda
case 1 Male A
case 2 Female B
case 3 Female B
case 4 Female A
case 5 Male B
... ... ...

The resulting crosstabulation could look as follows:

Soda: A Soda: B
Gender: Male 20 (40%) 30 (60%) 50 (50%)
Gender: Female 30 (60%) 20 (40%) 50 (50%)
50 (50%) 50 (50%) 100 (100%)

Each cell represents a unique combination of values of the two crosstabulated variables (row variable Gender and column variable Soda), and the numbers in each cell tell us how many observations fall into each combination of values. In general, this table shows us that more females than males chose the soda pop brand A, and that more males than females chose soda B. Thus, gender and preference for a particular brand of soda may be related (later we will see how this relationship can be measured).