In the context of human genetics, sampling is often nonrandom in that pedigrees are frequently selected by virtue of their having at least one affected individual. For quantitative traits, it may be that the proband is selected because of a phenotypic value above some predetermined cut-point; this will also be true for diseases defined by a cut-point above which individuals are said to be affected (e.g. diabetes, hypertension, and obesity). Relatively little attention has been given to the implications of these forms of nonrandom sampling. In this paper, we show that the biases introduced by such sampling are sufficient to lead to erroneous model specification and biased parameter estimates in path analysis. Existing methodologies used to correct for such sampling (e.g., elimination of proband or regression techniques) also result in similar bias in estimation and model fitting. Thus, it is possible to make inferences which do not reflect underlying biology, but are artifacts of the sampling design. As a consequence, method-of-moment estimators are developed for means, variances, and correlations under such sampling. Simulation results are used to demonstrate the superiority of this method over alternate strategies.