A Monte Carlo study of the robustness of the standard deviation of the sample correlation coefficient to the assumption of normality.
Brooks, Camilla Anita
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From the case studies presented, one could conclude that for large values of n the standard deviation of r, the usual estimator of the correlation coefficient, and its transform z are only negligibly affected by variation in skewness or variation in kurtosis, the effect being slightly greater for variation in kurtosis. When the variations are in both skewness and kurtosis, the standard deviation of r and of Z are more affected by non-normality, a few significantly so. In small samples (n=10, n=5) the standard deviations of r and,z are quite visibly larger for variations in skewness and variations in kurtosis. The effect is greater for the simultaneous variation of the two. However, all of the values fall within a 95% confidence interval. It would appear then that the increase in the standard deviation of rand z is due more to the natural rise of the standard deviation in small samples rather than to non-normality. Viewing the studies made in totality we may in final conclusion state that the effect of non-normality on the standard deviation of r for samples of any size is not significant enough for concern; i.e., from this Monte Carlo study we will state that the standard deviation of the sample correlation coefficient is robust to the assumption of normality.
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