Testing for ordered alternatives with increased precision in one of the samples

Abstract

Chase (1974) found a moderately good approximation for the chi-bar-squared, χ 2 ⁠ , and E -bar-squared, E ¯ 2 ⁠ , distributions for an important special case of comparing ordered dose levels with a zero control where there are more observations on the control. We sharpen his results and extend them to include the case in which the increased precision is on an intermediate sample. This provides new information concerning the behaviour of the χ 2 and E ¯ 2 distributions when the precisions are unequal.