Sequential One-Sample Grouped Signed Rank Tests for Symmetry: Monte Carlo Studies

摘要

Monte Carlo studies of sequential, one-sample, signed rank tests developed earlier by the authors are reported. The basic tests are the ssr-test based on the sums of signed ranks and the csr-test based on the observed configurations of signed ranks in both of which groups of N observations are obtained sequentially with signed ranks obtained within groups. The mcsr-test is also considered and it is a modification of the csr-test in which signed ranks are obtained anew for the totality of observations available at each stage of the sequential process. The alternative hypothesis in each case is stated in the class of Lehmann alternatives. The main Monte Carlo studies are for the ssr-test with alpha = beta =.05, N = 2(1)10, and (k* sub 1) = 2(1)5, (k* sub 1) indexing the alternative hypotheses. Studies are conducted for the L-model and the phi-model respectively involving a Lehmann class of populations and classical normal populations with location changes. The parameter k* associated with (k* sub 1) describes the L-model while mu(k*) for the phi-model is associated with it. Limited studies are made for the csr-test and the mcsr-test for comparisons. (Author)