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.
