Premium
Comparisons of Some Chi‐Squared Goodness‐of‐Fit Test Statistics in Sparse One‐Way Multinomials
Author(s) -
Lawal H. Bayo
Publication year - 1993
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710350508
Subject(s) - mathematics , statistics , goodness of fit , test statistic , pearson's chi squared test , statistic , null hypothesis , chi square test , f test , likelihood ratio test , statistical hypothesis testing , test (biology) , null distribution , paleontology , biology
The behavior of Pearson's X 2 test, the likelihood ratio test Y 2 and the two of its derivatives, G 2 and G k 2 , the Freeman‐Tukey test (FT) and the Cressie and Read test Statistic I (2/3) are examined in this study. Estimated attained α levels based on 1000 simulated samples when the approximating distribution is χ k ‐1 2 , are computed for these tests for the various values of k, n and seven null hypotheses. Results from estimated power computations indicate that none of the test statistics has a clear advantage over any others, and that the choice of which test to use must therefore rest mainly on the performances with regards to the attained α levels when the χ 2 approximation is invoked. In this respect, the log‐normal approximation proposed by Lawal and Upton (1980) is strongly recommended. This is closely followed by the I (2/3).