Contingency tables, confusion matrices, classifiers and quality of prediction

In many previous articles, we have talked about contingency tables. These have been used to record the number of samples assigned to different groups after a test has been performed. In our examples, we have mainly focussed on assigning to one of two distributions, the null and alternate distributions (or negative and positive). As an example, the null distribution may consist of animals that have not been treated with a chemical (often called controls) or people taken to court that are innocent.