The role of education in the process of socioeconomic attainment is a topic of long standing interest to sociologists and economists. Recently there has been growing interest not only in estimating the average causal effect of education on outcomes such as earnings, but also in estimating how causal effects might vary over individuals or groups. In this paper we point out one of the under-appreciated hazards of seeking to estimate heterogeneous causal effects: conventional selection bias (that is, selection on baseline differences) can easily be mistaken for heterogeneity of causal effects. This might lead us to find heterogeneous effects when the true effect is homogenous, or to wrongly estimate not only the magnitude but also the sign of heterogeneous effects. We apply a test for the robustness of heterogeneous causal effects in the face of varying degrees and patterns of selection bias, and we illustrate our arguments and our method using National Longitudinal Survey of Youth 1979 (NLSY79) data.