Estimation of response to selection and utilization of control populations for additional information and accuracy.

Problems associated with testing and estimation of response to selection are examined. An alternative procedure with increased power for testing hypotheses is given. The increased power results from a more precise method of estimating the variance about response. The new method is based on a Satterthwaite approximation which combines variance components estimated more precisely by other sources of variation in the analysis of variance. The expected variance about response and expected mean squares for the analysis of variance, used in the Satterthwaite procedure, are given. When intergeneration environmental trends cannot be ruled out, a control population must be used to estimate response to selection. However, if the experimental and control populations do not respond in the same direction and with the same magnitude to common environmental effects, then the usual method of estimating response by deviating the experimental values from the control will result in biased estimates. An alternative procedure, using the control as a covariate to adjust for environmental trends, gives relatively unbiased estimates of response in this situation. Some bias results from measurement error associated with the control. However, this bias is usually minimal.