Education researchers have long been concerned with finding the appropriate method for correlational analysis of hierarchical data. In recent years, the alternative of hierarchical linear modeling (HLM) has come into extensive use. HLM users typically center some or all student-level predictors either at the grand mean or at the school means. This procedure adds stability to the estimation process and leads to intercepts that are more readily interpretable. Centering also has the effect of changing the coefficients that are being estimated, and cannot be regarded as merely a technical device, when, in fact, it changes the research questions that are actually being asked. Some issues in centering are addressed theoretically and empirically. A combined equation for the two levels of modeling is presented, and some algebraic manipulation is used to show how each form of centering can be expected to modify the estimated coefficients. Data from the National Education Longitudinal Study are analyzed to investigate the effect of minority status on a mathematics achievement test score, comparing results based on centering with those based on raw data. Two tables illustrate the analyses. (SLD)