Two simple methods for testing hypotheses stated in terms of linear equality constraints on the treatment parameters, in paired comparisons, or their logarithms are developed. The test statistic constructed for each method can be computed more easily than the corresponding likelihood ratio statistic -2 log λ. The asymptotic chi-square distribution of each of the constructed test statistics, together with the corresponding -2 log λ, is demonstrated and its noncentrality parameter is determined under defined local alternatives. Application of developed procedures for testing hypotheses about main effects and interactions, when the treatments are factorial treatment combinations, is outlined.