Multivariate Analysis Exact Size and Power Properties of Five Tests forMultinomial Proportions

In this article, exact properties of the chi-square test, likelihood ratio test (LRT), Hoel’s test (1938), Nass ’ test (1959), and an exact test, for testing the multinomial proportions, are investigated numerically. Numerical studies show that the size behavior of the chi-square test for the multinomial distribution with three or more cells is erratic only when the probabilities are at the boundaries. Otherwise the chi-square test performs very satisfactorily. Hoel’s test offers a little improvement over the 2-test. The 2-test is, in general, superior to the LRT, and inferior to the exact test with respect to size properties. The exact test exhibits very good size properties. Nass ’ test offers improvement over the 2-test. Power studies indicate that the tests are equally powerful provided the sizes of the tests are close to each other for a given parameter configuration. Some recommendations regarding the choice of a test for practical applications are given, and the tests are illustrated using a biological example