Confidence Intervals for Variance Ratios Specifying Genetic Heritability

Abstract

Consider the twofold analysis of variance model with equal subclass numbers, vijk = [mu] + ai + bij + cjjk-, where yijk is the observation, [mu] isa fixed constant, and the at, bij, and cijk are independent normal variables whose means are zero and whose variances are [sigma]2a, [sigma]2b, and [sigma]2c respectively. In some fields of endeavor (especially in Genetics) the above model occurs quite frequently, and an estimate of the quantity, [image] is ofttimes desired. In this paper a method is presented for obtaining an approximate confidence interval for h2 which is quite accurate even for very small sample sizes. The method is patterned somewhat after the method used by Satterthwaite to obtain the approximate distribution of linear functions of Chi-square variates.