2010 Volume 6 Issue 1 Pages 63-74
When one calculates the correlation between entrance examination score and GPA score, in most cases the estimated correlation coefficient is smaller than expected; this problem is commonly known as selection bias. To estimate the true correlation coefficient under selection, maximum likelihood and Bayesian estimation procedures have been proposed in former studies. In this paper, we evaluated the behavior of both type of point estimates under small sample conditions by numerical simulation study in which sample size, true correlation coefficient and the proportion of the missing data are manipulated. The results can be summarized as follows: (1) Estimations are satisfactory when sample size is large (2) In terms of the closeness between the average estimates and the true values, Bayesian estimation performed better (3) In terms of the mean squared error, maximum likelihood estimation performed better. The R codes used in this study are shown in Appendix.
