I’m reviewing statistics and epidemiology, but I needed a reminder about the difference between probability and odds. I found Rahul Patwari’s video on Odds Ratios and Risk Ratios helpful, and I borrow from his example in the explanation below. (By the way, it’s good practice to check the URL of any link online to see where it leads. To do this for a web browser, search for how to turn on your status bar.) Three short phrases may help you to remember the difference between these two concepts:

The denominator makes the difference.

Probability is a whole other problem.

Odd one’s out.

Probability is a whole other problem. If you have 10 patients taking a drug, and the 6 experience cardiac events related to that drug, then the probability of experiencing a cardiac event when taking the drug is 6/10 (or 0.6), where 6 is the number of events and 10 is the whole number of patients.

Odd one’s out. In that same example, the odds of experiencing a cardiac event when taking the drug are 6/4 (or 3/2), where 6 is the number of events and 4 is the number of cases in which an event might have occurred but did not. I like to think of the latter as “non-events” that are left out after we count all of the events, since we are often more interested in the events rather than we are the “non-events”.

The denominator makes the difference. In the case of probability, the denominator represents the whole group. In the case of odds, the denominator represents those odd events that were left out, in terms of the events we were studying.