Statistical comparisons of multiple classifiers

This paper discusses the issue of comparing multiple classifiers, applied to the same test dataset of a classification problem. Assume that the output is 0 if a classifier correctly classifies a test feature point and the output is 1 otherwise. Then all the outputs from a given classifier constitute a sample of 0 and 1, and all the samples are correlated. From these dependent samples, we use Cochran's Q statistic, as an overall test statistic, to detect whether or not the error rates of the classifiers are significantly different. When, the null hypothesis that the error rates are equal is rejected, a thorough analysis of the nature of the error rates, such as the ranking of the error rates, is undertaken. For this purpose, we employ the Scheffe and Bonferroni multiple comparison procedures, based on dependent samples. We also use examples to demonstrate how to make these statistical comparisons.