A Statistical Hypothesis Testing Method for the Rank Ordering of the Priorities of the Alternatives in the Analytic Hierarchy Process

In analytic hierarchy process (AHP), a ratio scale (π₁,π₂,...,π_t) for the priorities of the alternatives {T₁,T₂,...,T_t} is used for a decision problem in which π_i/π_j is used to quantify the ratio of the priority of T_i to that of T_j. In a group decision-making setup, the subjective estimates of π_i/π_j are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples.