Technical note: Covariance adjustment in beef cattle research

In randomized experiments, analysis of covariance is used to increase preci sion of treatment comparisons. However, for factors that are observational (e.g., breed) or for covariates measured after treatments are applied, it m ay not be biologically meaningful to calculate treatment means adjusted to a common value of the covariate. For example, in beef cattle trials, it may not be meaningful to compare hot carcass weights of medium- and large-fram ed breeds adjusted to a common weaning weight because the breeds have natur ally different mean weights at weaning. If done, this would typically resul t in an undesirable downward adjustment of mean carcass weight for the larg e-framed breed and upward adjustment of the mean carcass weight for the sma ll-framed breed. However, it is desirable to evaluate the mean carcass weig ht for two diets, adjusted to a common weaning weight. Because of randomiza tion, the expected weaning weights of animals on the two diets are equal an d hence the only effect of covariance adjustment is to increase precision o f the diet comparison. This paper presents the statistical methodology for estimating covariance adjusted means (termed partially adjusted means) when the levels of some of the factors are compared at a common value of the co variate but the levels of other factors are compared at differing values of the covariate. The methodology is extended to include several covariates, several factors, and arbitrary interactions among covariates, among factors , and between factors and covariates. These methods can be implemented usin g existing statistical software for linear models. Data are presented from an experiment in which hot carcass weight was recorded for beef cattle. Ana lyses of these data illustrate that adjusted means, partially adjusted mean s, and unadjusted means may differ substantially in magnitude, significance , and in the ranking of treatments.