A Comparison of the <i>X</i> ² , −2 Log <i>R</i> , and Multinomial Probability Criteria for Significance Tests When Expected Frequencies are Small

Abstract

Abstract The exact multinomial, and exact and χ2 probabilities for χ2 and −2 log R have been compared. The −2 log R χ 2 probabilities are on average closer to the multinomial than are the corresponding χ2 probabilities. The differences between the exact and χ2 probabilities are usually smaller for χ2 than for −2 log R. A pattern was observed among the five types of significance levels, and an explanation was proposed.