Designing completely randomized experiments to detect ordered treatment effects: an empirical study

In designing experiments the researcher frequently must decide as to how to allocate fixed resources among k factor levels (Cox (1958)). This study investigates the effects on the power of a test caused by changes in: the sample size (n); the number of factor levels (k); the allocation of fixed total observations (N) among k and n: the shift parameter (ø); the type of parent population sampled; and, the type of ordered location alternative involved. Using Monte Carlo methods the powers of eight test procedures specifically devised to detect ordered treatment effects under completely randomized designs were evaluated along with those of the more general one-way F test. The results are of interest to researchers in all fields of application.