  After rejecting the null hypothesis in the analysis of variance, the next
step is to make the pairwise comparisons to find out differences in means. The
purpose of this paper is threefold. The foremost aim is to suggest expression
for calculating decision limit that enables us to collect the test and pairwise
comparisons in one step. This expression is proposed as the ratio of between
square for each treatment and within sum of squares for all treatments. The
second aim is to obtain the exact sampling distribution of the proposed ratio
under the null hypothesis. The exact sampling distribution is derived as the
beta distribution of the second type. The third aim is to use beta distribution
and adjusted p values to create decision limit. Therefore, reject the null
hypothesis of equal means if any adjusted point falls outsides the decision
limit. Simulation study is conducted to compute Type one error. The results
show that the proposed method controls the type one error near nominal values
using Benjamini-Hochberg adjusted p-values. Two applications are given to show
the benefits of the proposed method.

Methodology