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Activity Number: 300 - Innovations in and Applications of Imputation
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
Sponsor: Government Statistics Section
Abstract #302904 Presentation
Title: An Empirical Study of Correlation Coefficient Aggregation in Multiple Imputation
Author(s): Jianjun Wang* and Xin Ma
Companies: and University of Kentucky
Keywords: Multiple Imputation; Fisher's Z Transformation; Correlation Analyses; Math and Science Achievements; Large-scale Data Analysis

When Multiple Imputation (MI) is implemented to treat missing data in a correlational study, “SPSS uses a ‘naively pooled’ Pearson correlation coefficient [r] which is the simple average of the corresponding parameter in each of the imputed data sets” (SPSS PMR 58061,227,000). Nonetheless, for a nonzero population correlation coefficient (rho), the distribution of the sample correlation coefficient r is skewed. To normalize the distribution of r, SAS (2010) “combines sample correlation coefficients computed from a set of imputed data sets by using Fisher’s z transformation” (p. 4508). In this study, both SPSS and SAS approaches are taken to compare the impact of result pooling between r average and Fisher’s z transformation. The MI data were adopted from an NSF-funded project ( to compute Pearson correlation coefficients prior to the result pooling. Similar findings are obtained from the nationally-representative sample of 10,221 students in the latest phase of a trend study that lasted for more than two decades.

Authors who are presenting talks have a * after their name.

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