## 1.14 Odds Ratio

The odds ratio is the ratio of the odds of an event occurring in one group to the odds of the same event occurring in another group (e.g., an alternative hypothesis versus a null hypothesis). For example, if the odds ratio is 2, then the odds of the event occurring in one group is twice the odds of the event occurring in another group. Mathematically, the odds ratio is calculated as follows: \[OR = \frac{p}{1-p}\] where \(p\) is the probability of the event occurring. any odds ratio weaker than 3:1 is not worth mentioning, odds ratios from 3:1 up to 20:1 are positive evidence for the favored hypothesis, odds ratios from 20:1 up to 150:1 are strong evidence, and odds ratios of more than 150:1 are very strong evidence for the favored hypothesis.