Comparison of Several Treatments With a Control Using Multiple Contrasts.

A problem frequently encountered in the practice of statistics is the comparison of several treatments with a control or standard. We consider an experimental situation where prior knowledge indicates that all of the treatments are at least as effective as the control and the problem is to determine if any are significantly better than the control. A number of statistical procedures have been proposed for this situation, of which the best known is Dunnett's (1955) multiple comparison procedure. Dunnett's test rejects equality of the treatments and the control for a large value of the maximum contrast of the data vector with several vectors that are located "symmetrically" within the alternative region. We study a large class of such tests, which includes Dunnett's test as a particular case. One of these tests, which is based on the maximum contrast of the data vector with several orthogonal vectors, is very easy to implement and has an uncomplicated, good, and fairly uniform power function over the entire alternative region. In fact, a small Monte Carlo power study suggests that this orthogonal contrast test is approximately "maximin" within this class of tests. Moreover, the simplicity of the power function of the orthogonal contrast test enables the experimenter to determine sample sizes for designed experiments with specific power characteristics. Such sample size determinations can be difficult, if not impossible, using other procedures. Abelson and Tukey (1963) suggested tests for a large class of restricted problems that are based on contrasts of the data vector with a single vector that is "centrally" located within the alternative region. These single contrast tests have the advantage that their distributions under the null hypotheses (a t distribution) and under the alternative (a... [ABSTRACT FROM AUTHOR]