The odds are it's wrong: Correcting a common mistake in statistics

Abstract Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into relative probabilities. (2) Alternatively, they learn that coefficients tell us whether the variables make the outcome more or less likely, without knowing how to interpret changes in the odds. (3) They may be instructed in how to calculate predicted probabilities, but the additional steps are too complicated for them to follow. Our key aim is to highlight and correct the common mistake of confusing differences in odds with relative risks. Simply reporting the odds ratio is unhelpful, however, so we describe an easy method of estimating probabilities for both binary and continuous variables.