Abstract:
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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 (www.timss.org) 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.
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