Confidence interval estimators for heritability for several mating and experiment designs

Confidence interval estimators have not been described for several heritability (H) estimators relevant to recurrent family selection. Previously described H interval estimators do not apply to onefactor mating designs in split-plot in time experiment designs in one or more locations, one-factor mating designs for several experiment designs in two or more locations and years, and two-factor mating designs for several experiment designs in two or more locations or years. Our objective was to derive H interval estimators for these cases. H reduced to a function of constants and a single expected mean square ratio in every case; H=1-E(M')/E(M″) where E(M') is a linear function of expected mean squares and E(M″) is a single expected mean square. It was shown that F'=[M″/E(M″)]/[M'/E(M')] has an approximate F-distribution with df″ and df' degrees of freedom, respectively, where M' and M″ are mean squares corresponding to E(M') and E(M″), respectively. H is a function of F', therefore, we used F' to define an approximate (1-α) interval estimator for H.