ABSTRACT
This chapter considers tests for association, effect measures, and confidence intervals for the 2×2 $ 2\times 2 $ table of unpaired data. Inverse sampling, also called negative binomial sampling, is a useful technique in studies of rare events. If conventional sampling is used, that is if the group sizes are determined ahead of the actual sampling, we run the risk of observing zero events in one or both groups. Consider the null hypothesis of no association between the variables defining the rows and columns. Karl Pearson introduced the chi-squared statistic in 1900 as the sum of the squared relative differences between observed and expected frequencies. The difference between probabilities is an important effect measure in many applications, such as randomized controlled trials and cohort studies, where have sampling under the row margins fixed model or the total sum fixed model.
