The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all ...

A statistical test that allows one to determine whether observed quantities of a specific characteristic differed from the expected value purely by chance.

It is shown that certain conditional distributions, obtained by conditioning on a sufficient statistic, can be used to transform a set of random variables into a smaller set of random variables that ...