The "Pooled-Within Classes" Coefficient of Correlation (rw) in Partially Segregated Educational Systems

The purpose of this paper is to point out the logical, theoretical and statistical problems associated with the computation of the "pooled-within" correlation coefficient in partially segregated educational systems. It is argued that, since a between-individual-within-classes relationship of Y to X cannot possibly exist in classes which are entirely homogeneous with respect to either X or Y, the question concerning this relationship should be addressed only to the subsample of heterogeneous classes. Consequently, the measurement of this relationship should be restricted to this subsample, thus yielding a new coefficient, rwH, which is different from the usual coefficient, both conceptually and numerically. The remainder of the paper deals with the theoretical and statistical problems associated with the computation of rwH instead of rw, its interpretation as a sample statistic and its functional relationship to rB and rT, the "between groups" and "total" correlation coefficients, respectively.