Comparisons of Some Chi‐squared Tests for the Test of Independence in Sparse Two‐Way Contingency Tables

Abstract

Abstract We consider in this paper, the behaviour of a class of the CRESSIE READ (1984) power divergence test statistics indexed by parameter λ ‐ I (λ), with the modified X 2 test statistics (LU) proposed by LAWAL and UPTON (1984), for sparse contingency tables ranging from the 3×3 to the 10×10. We present a sample of our results here. The results indicate that the LU test out‐performs either the Cressie‐Read suggested test I (2/3) or the Pearson's test ‐ I (1). Our results further show that the modification to the likelihood ratio test [ Y 2 = I '(0)] proposed by WILLIAMS (1976) performs like the parent Y 2 test, very poorly compared with either the I (2/3), X 2 or the LU test statistics. Power results also indicate that the powers of the LU test are in all cases considered in this study slightly higher than those of X 2 and I (2/3) tests. The LU test is therefore strongly recommended for use with sparse two‐way contingency tables because in all of the cases considered, none of the other test statistics consistently out‐performs the LU test with respect to attained α level or power.