Consistency of estimates of variance components.

THE ESTIMATION OF VARIANCE COMPONENTS has important applications in genetic research, and geneticists were among the first to use analysis of variance extensively for that purpose. Early examples of component estimation in genetics are contained in papers by Lush et al. (1934), Bywaters (1937), and Stonaker and Lush (1942). Numerous later papers could also be cited. The earlier component estimates in the genetic literature were not accompanied by measures of reliability or confidence limits of any sort. The first attempt to place confidence limits were made by Knapp and Nordskog (1946) in connection with estimation of the ratio of genetic to total variance in beef cattle. Research on the genetics of quantitative characters of economic plants now in progress at the North Carolina Experiment Station relies heavily on variance component estimation. In designing our experiments, prediction of the sampling variance of component estimates has been predicated on normal distribution theory. Whether this is satisfactory depends on conformity of observed distributions of component estimates with assumptions of normality and homogeneity of variances throughout the experimental material. A preliminary investigation of the problem has been made using data collected for estimation of genetic variance components in corn.