On the Estimation of the Correlation Coefficient from Grouped Data

Abstract

Abstract This article proposes two estimators of the correlation coefficient, ρ, when statisticians will not construct a master file on individuals because of confidentiality issues. The approach depends on grouping the data according to the values of one of the variables. Group means and total variance for both variables are required to calculate the estimators. The complete bivariate sample need never be compiled. The estimators are shown to be asymptotically normal. Asymptotic and Monte Carlo results are examined. For 1,000 observations in 10 groups, these results indicate that the ratio of the mean squared error (MSE) for one of the proposed estimators relative to that for the usual estimator of ρ ranges from .82 to .95 as ρ ranges from .9 to .25. The proposed estimators are more efficient than previous estimators for grouped data.