Multiple comparison procedures for detecting differences in simply ordered means

In the one-way analysis of variance, we study multiple-comparison procedures that detect differences in the treatment means when they are known to be simply ordered (i.e., μ1⩽μ2⩽⋯⩽μk). Several existing procedures as well as four procedures proposed here are compared by Monte-Carlo techniques. In 1990, Hayter developed a one-sided Studentized range procedure (H), and the max-min technique exploited in 2002 by Liu, Lee, and Peng provides an improved Hayter procedure (M). In her 2001 doctoral dissertation, Liu developed a procedure (L) that is based on the differences in the averages of two blocks of means. A procedure (R), which utilizes the restricted maximum-likelihood estimates of the means corrected for their biases and standard deviations, and an analogue to Fisher's LSD (T) are proposed. For T, the usual F test is replaced by an order-restricted test and one-sided t-tests are used. Declaring μi<μj and μl=μl′ with l⩽i