Canadian Journal of Statistics

General scores statistics on ranks in the analysis of unbalanced designs

Journal Article

Abstract

The authors consider the situation of incomplete rankings in which n judges independently rank ki ∈ {2, …, t} objects. They wish to test the null hypothesis that each judge picks the ranking at random from the space of ki! permutations of the integers 1, …, ki. The statistic considered is a generalization of the Friedman test in which the ranks assigned by each judge are replaced by real‐valued functions a(j, ki), 1 ≤ jkit of the ranks. The authors define a measure of pairwise similarity between complete rankings based on such functions, and use averages of such similarities to construct measures of the level of concordance of the judges' rankings. In the complete ranking case, the resulting statistics coincide with those defined by Hájek & Šidák (1967, p. 118), and Sen (1968). These measures of similarity are extended to the situation of incomplete rankings. A statistic is derived in this more general situation and its properties are investigated.

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