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

Simultaneous test for Means: An Unblind Way to the F-test in One-way Analysis of Variance