Abstract

Paired comparison or animal dominance data are often displayed in a directed, asymmetric, graph. Under the “chance” hypothesis the two possible directions of each arc are equally likely. If the observed graph is complete, Kendall's test compares the number of circular triads in the observed graph with the distribution of this number under chance. Unobserved (missing) arcs complicate this test. Some modifications of Kendall's test, involving imputed values for the missing arcs, have been proposed in the literature. This paper examines optimal imputed values with respect to two criteria, and how these values may be used to modify the tests. Each approach is also illustrated with four example complete graphs and a simple missing data mechanism, and three real data sets are analyzed.

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