A statistical model that uses an iterative maximum likelihood estimation procedure is proposed for measuring and testing the association between polymorphic genetic markers and quantitative traits in human pedigrees, after adjusting for covariates such as age and sex. The model allows the quantitative trait to have a familial correlation structure among the individuals in the sample and to follow one of a broad class of skewed or kurtotic underlying distributions. The use of the model is illustrated, and the results are compared to those using models that assume normality without any transformation and do not incorporate familial correlations.