A Note on the Rank Analysis of Incomplete Block Designs -- Applications beyond the Scope of Existing Tables

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Abstract
The iteration formula for the Bradley-Terry method of paired comparisons is Pi = [image], where ai is the total number of times treatment i was ranked first (i = l,...,t) and where there are n repetitions. An approximation formula, pi = [image], gives good first estimates for use in the iteration formula. This formula will suffice for most experimental situations. Where the over-estimation is severe, i.e., there Pi sum to much more than unity, an empirically determined correction may be applied. Determine [image], and the p1 are determined by the approximation formula. The improved first estimates are given by pi = p1-ki, which are then used in the iteration formula.