Comparing Power Behaviours for Some Goodness‐of‐Fit Test Statistics in Sparse Multinomials

Abstract

AbstractThis paper is concerned with the power behaviour of four goodness‐of‐fit test statistics in sparse multinomials with k cells. Most previous work has been concerned only with both Pearson's X2 and the likelihood ratio test statistics. We consider in this study, two additional test statistics, namely, the Cressie‐Read test statistic – I(2/3) and the modified Freeman‐Tukey test (FT) statistic. Because k ≥ 10 in this study, a Monte Carlo procedure based on 1000 simulated samples is used to estimate the powers for the four test statistics. Alternatives on various line segments are employed. Results suggest that none of the test statistics completely dominate the other and that the choice of which test to use depends on the nature of the alternative hypothesis. These results are consistent with those obtained by West and Kempthorne (1972), although, the Pearson's χ2 test statistic may be preferred because of its closer approximation to the χ2 distribution in terms of the attained α levels.