Stepwise multiple tests for successive comparison of treatment effects

P.N. Somerville and Wei Liu


Suppose k treatments under comparison are ordered.  Of interest are the difference m2 -m1, m3 -m2, ... ,mk-mk-1.  Lee and Spurrier (1995) proposed one-sided and two-sided confidence interval procedures for making  the successive comparisons between treatments.  In this paper one-sided and two-sided step-up and step-down tests are developed for the family of hypotheses Hi0 : mi+1 -mi = 0, i = 1,... ,k-1.  These stepwise tests are more powerful than the simultaneous confidence intervals in terms of rejection of hypotheses.  The critical constants required for applying these multiple test are provided, and the tests are illustrated with a numerical example.