Power to detect normal mixtures: Simulation results

Twenty tests for normality were compared for the purpose of detecting mixtures of two normal components with unequal means but equal variance. The purpose of this study was to determine the power of tests specifically designed to detect mixtures, i.e., the likelihood ratio and Engelman-Hartigan tests, relative to other tests for normality. We considered the entire range of mixing proportions {pi}, 0 < {pi} < 1. For mixtures that are nearly symmetric (0.35 < {pi} < 0.65) the Engelman-Hartigan test was the most powerful. When {pi} > 0.85 or {pi} < 0.15, {radical}b{sub 1} was among the best tests. For intermediate mixing proportions, the likelihood ratio test was best. For situations in which the preferred test had power 50% or more, the power of the likelihood ratio test was also above 50% and within 15 percentage points of the preferred test.