Assessment of three way interaction in 2 × J × K tables

Abstract

The power of a test for no three way interaction in 2 × J × K tables, performed by partitioning the K strata into two groups was investigated by simulation. Mantel-Haenszel estimation techniques were used to calculate the test statistic. The power was compared with that of Pearson's X 2 and the likelihood ratio G 2. The partition test had substantially greater power than either X 2 or G 2 in cases most favorable to the partition test and somewhat greater power for cases moderately favorable to it. The greater power can be explained by the smaller degrees of freedom for the partition test ( J − 1 vs ( J − 1)( K − 1) for X 2 and G 2). The results also suggest that the distribution of the test statistic more closely follows a non-central chi square distribution in non-null cases for the partition test. If an appropriate partitioning of the strata can be made, the partitioning test would be preferable to the widely used X 2 and G 2 tests.