Power of Likelihood Ratio Tests for Heterogeneity of Intraclass Correlation and Variance in Balanced Half-Sib Designs

¹ Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, Scotland

Statistical power of likelihood ratio tests was investigated for detection of heterogeneous variances and intraclass correlation in balanced half-sib designs. Powers of likelihood ratio tests were obtained from simulations. For half-sib designs of sires nested within herds, true intraclass correlations and phenotypic variances, and estimates thereof, were repeatedly sampled, and likelihood ratio tests were conducted. The power for detecting heterogeneity of intraclass correlations was low, but the power for detecting heterogeneous phenotypic variances was nearly always 100%. For balanced cross-classified designs, sires had progeny in all herds, and data were simulated by assuming that heterogeneity of between- and within-sire components was the result of a herd-dependent scale effect. Using this model, the power to detect heterogeneous between-sire components was substantially higher than the corresponding power to detect heterogeneous intraclass correlations in the nested design. It seems unlikely that reliable inference about heterogeneity of genetic variances or heritabilities between individual herds from daily cattle field data can be made.

Key Words: statistical power • likelihood ratio test • heterogeneity of variance

Submitted on March 18, 1991
Accepted on December 9, 1991