For a (k × k) square contingency table with ordered categories, let X(Y) denote the row (column) number. The conditional symmetry model is given by P(X = i, Y = j|X < Y) = P(X = j, Y = i|X >Y), ∀ i < j. In this paper, we study the likelihood ratio tests of conditional symmetry in a square contingency table against two particular classes of one-sided alternatives. We obtain the maximum likelihood estimates under each alternative. The asymptotic null distributions of the likelihood ratio statistics are shown to have chi-bar square type distributions. A simulation study is performed by comparing the powers of different tests. The theory developed is illustrated by using the famous eye vision data from Stuart.
