This paper focuses on the methodology of cross group comparisons of regression coefficients commonly used to identify group differences in status attainment. Using the study of race differences in educational attainment as an example, the paper reviews a number of relevant published studies and demonstrates that evidence for such differences is inconsistent across studies, that differences in the regression coefficients are subject to artifactual sources of fluctuation, and that statistical inferences based on such differences are weak. The paper concludes that the study of statistical interactions requires the design of creative studies and data collection strategies that anticipate and compensate for such problems as inadequate data, differential measurement properties, and differences in the sampling frame. (MJL)