A typical structural equation model is intended to reproduce the means, variances, and correlations or covariances among a set of variables based on parameter estimates of a highly restricted model. It is not widely appreciated that the sample statistics being modeled can be quite sensitive to outliers and influential observations, leading to bias in model parameter estimates. A classic public epidemiological data set on the relation between cigarette purchases and rates of 4 types of cancer among states in the United States is studied with case-weighting methods that reduce the influence of a few cases on the overall results. The results support and extend the original conclusions; the standardized effect of smoking on a factor underlying deaths from bladder and lung cancer is 0.79. (Contains 5 figures.)