Examples of dichotomous variables
- Heads or Tails.
- Male or Female.
- Rich or Poor.
- Democrat or Republican.
- Pass or Fail.
- Under age 65 or 65 and over.
Binary variables are a sub-type of dichotomous variable; variables assigned either a 0 or a 1 are said to be in a binary state. For example Male (0) and female (1).
Dichotomous variables can be further described as either a discrete dichotomous variable or a continuous dichotomous variable. The idea is very similar to regular discrete variables and continuous variables. When two dichotomous variables are discrete, there’s nothing in between them and when they are continuous, there are possibilities in between.
- “Dead or Alive” is a discrete dichotomous variable. You can be dead. Or you can be alive. But you can’t be both at the same time.
- “Passing or Failing an Exam” is a continuous dichotomous variable. Grades on a test can range from 0 to 100% with every possible percentage in between. You could get 74% and pass. You could get 69% and fail. Or a 69.5% and pass (if your professor rounds up!).
The line between discrete and continuous dichotomous variables is very thin. For example, it could be argued that a person who has been dead for three days is “more” dead than someone who has been declared brain dead and who is on life support.
The importance of dichotomous variable categories with point biserial
Placing dichotomous variables into discrete or continuous categories becomes important when using the Point Biserial correlation coefficient; care should be taken to place dichotomous variables into their “natural category”. For example, Republican or Democrat are naturally discrete — trying to place them into a continuous category (based on the assumption that many people are not 100% for either party) can interfere with correlation.