Abstract
Scheffe (1953) method is a multiple comparison procedure to test simultaneously the contrasts to be expressed by linear combinations among some population means. The procedure is used to carry out the simultaneous test based on the observations obtained across all levels. However, when we perform the test in practical applications, there often are many cases in which we wish early decision with few observations. Thus it is worthwhile to develop a multiple comparison procedure to test sequentially the contrasts based on the sequentially obtained observations for early decision. In this study, we will realize Scheffe method to test the difference of effect between two groups by using the contrasts to show the difference between two groups having some levels. Furthermore, we propose a sequential contrast procedure that tests sequentially the difference of effect based on these contrasts for reducing the number of observations. In the procedure, we present an integral formula to determine the critical values and show how to decide the required sample size with guaranteeing the power of the test. In the simulation studies, we compare Scheffe procedure with our sequential contrast procedure in terms of a rate to reject the null hypothesis at each stage for various configurations of population means.
