Resumen de Bias in Estimation and Hypothesis Testing of Correlation

B. D. Zumbo, Richard H. Williams, Donald W. Zimmerman

• This study examined bias in the sample correlation coefficient, r, and its correction by unbiased estimators. Computer simulations revealed that the expected value of correlation coefficients in samples from a normal population is slightly less than the population correlation, ñ, and that the bias is almost eliminated by an estimator suggested by R.A. Fisher and is more completely eliminated by a related estimator recommended by Olkin and Pratt. Transformation of initial scores to ranks and calculation of the Spearman rank correlation, rS, produces somewhat greater bias. Type I error probabilities of significance tests of zero correlation based on the Student t statistic and exact tests based on critical values of rS obtained from permutations remain fairly close to the significance level for normal and several non-normal distributions. However, significance tests of non-zero values of correlation based on the r to Z transformation are grossly distorted for distributions that violate bivariate normality. Also, significance tests of non-zero values of rS based on the r to Z transformation are distorted even for normal distributions.