# The 2 × 2 tabulation

In previous articles, I gave examples of categorical data and explained the categories of these data: binary, ordinal, and nominal.

I will deal mainly with binary data in which the outcome takes only 2 values, such as yes/no or 0/1. Some examples of binary data include tooth loss (yes/no), bracket loss (yes/no), and reaching an event such as successful completion of therapy vs no successful completion.

Binary data are often presented in a 2-way tabulation (2 × 2 table) or a cross-tabulation that displays the relationship between 2 binary variables.

We say that there is an association between 2 binary variables if the distribution of 1 variable varies across the levels of the other variable.

## Example

Research question: In a clinical trial, 2 types of wires (A and B) were used for 6 months in 2 patient groups. This time, we will not measure residual crowding between the 2 wires (a continuous outcome), but we will use a binary outcome: reaching complete alignment (success) or not reaching complete alignment (failure). We will tabulate the frequencies of successes and failures for each wire and make some calculations.

In 2 × 2 tables, the most frequently applied measures of effect are the risk ratio (RR) and the odds ratio (OR) (see previous articles for more details and a review). The Table presents our data and the calculations of the risks per wire, as well as the RR and OR, which show the relationships between alignment status and wire type.

Table