## 31.11 Summary

To test a hypothesis about a population odds ratio, based on the value of the sample odds ratio, initially assume the value of the population odds ratio in the null hypothesis (usually one) to be true. Then, expected counts (Step 2) can be computed. Since the sample odds ratio varies from sample to sample, under certain statistical validity conditions a quantity closely-related to the sample odds ratio varies with an approximate normal distribution. This distribution describes what values of the sample odds ratio could be expected in the sample if the value of the populations odds ratio in the null hypothesis was true. The test statistic is a $$\chi^2$$ statistic, which compares the expected and observed counts. (The value of $$\sqrt{\chi^2/\text{df}}$$ is like a $$z$$-score, where ‘df’ is the ‘degrees of freedom’ reported by software, and so an approximate $$P$$-value can be estimated using the 68–95–99.7 rule.) Software reports the $$P$$-value to assess whether the data are consistent (Step 4) with the assumption.