STANDARD ERRORS AND CONFIDENCE-INTERVAL ESTIMATORS FOR EXPECTED SELECTION RESPONSE

Expected selection response (R) is widely used in plant breeding to compare populations and selection schemes, but methods have not been described for estimating variances or confidence intervals of R, or, if they have, their validity is uncertain. In this paper, we describe an exact and approximate standard error of R and normal-approximation intervals of R. We used simulation to test the validity of these intervals by comparing realized coverage probabilities to stated coverage probabilities for different experiment sizes, stated coverage probability values, and values of family-mean heritability (H). Coverages of the normal-approximation interval estimated using the exact standard error (interval R1) ranged from 0.874 to 0.922 and 0.932 to 0.966 for stated coverages of 0.90 and 0.95, respectively. Coverages of the normal-approximation interval estimated using the approximate standard error (interval R2) ranged from 0.880 to 0.940 and 0.934 to 0.980 for stated coverages of 0.90 and 0.95, respectively. Both R1 and R2 are valid interval estimators for R if the usual assumptions of the analysis of variance are met.