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Standard Errors and Confidence Interval Estimators for Expected Selection Response
Author(s) -
Bridges W. C.,
Knapp S. J.,
Cornelius P. L.
Publication year - 1991
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci1991.0011183x003100020002x
Subject(s) - confidence interval , statistics , estimator , selection (genetic algorithm) , mathematics , standard error , interval (graph theory) , credible interval , coverage probability , heritability , standard deviation , tolerance interval , biology , combinatorics , computer science , artificial intelligence , genetics
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 R 1 ) 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 R 2 ) ranged from 0.880 to 0.940 and 0.934 to 0.980 for stated coverages of 0.90 and 0.95, respectively. Both R 1 and R 2 are valid interval estimators for R if the usual assumptions of the analysis of variance are met.