Centering is a problem in multilevel analysis that needs to be addressed. Multilevel analysis gives researchers a choice between centering within context and grand mean centering, both statistically sound ways to improve estimation of the parameters in the model. Researchers of the most widely used software package for the analysis of hierarchically nested data, HLM, commonly center within context. The practice of centering around the group mean, while not adding the mean back into the model deletes information from the data, may lead to overestimation of the macro level variables in the model. Centering around the group mean is fitting another model. Reasons to center or not to center are discussed, based on examples from data from the National Education Longitudinal Study of 1988. Comparison of data from public and private schools about mathematics achievement shows that different conclusions are reached depending on the data management scheme. Although research on school effects is not yet free of methodological and conceptual problems, existing models have the potential to expand knowledge when used correctly. (Contains 6 tables and 17 references.) (SLD)