A novel variation of the Haplotype Relative Risk (HRR) of Rubinstein et al. [Hum Immunol 1981;3:384] is proposed, in order to glean increased information about linkage disequilibrium or allelic associations by analyzing haplotype-based data rather than genotypic data. It is shown that statistical tests based on our design give much higher power than those based on the original HRR approach. Several additional nonparametric tests based on the same data are analyzed, and power is computed for each of them. Further, parametric likelihood methods are applied to testing linkage equilibrium, and estimating δ, the coefficient of linkage disequilibrium, from the same data.