Simulated intraclass correlation coefficients and their ztransforms

Abstract

We examined three issues: (1) properties of the intraclass correlation coefficient (r ₁); (2) normality of its z transform; and (3) Fisher's formula for the variance of z. To do this we simulated 1,000 samples of r ₁ and of z for several values of p, both for equal and for unequal family sizes. Those samples permitted us to evaluate some of Fisher's remarks on the bias, variance, and normally of r ₁ Furthermore, they showed us that all simulated z transforms were normally distributed with variances that agreed with the values calculated from a modification of Fisher's formula. Those last two results affirm the applicability of the z transform and of Fisher's modified formula to studies in human genetics involving unequal family sizes.

Keywords:

• Interclass correlation coefficient
• Fisher's z transform
• Simulated intraclass correlation coefficients
• Simulated z transforms