The Relation between Covariance and Individual Curvature Analyses of Experiments with Background Trends

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Abstract
When the two variates in covariance analysis are the means of groups of observations subject to trends which differ for different experimental units, an alternative analysis, in terms of individual regressions, is available. This latter has been used to examine the dependence of the covariance regression coefficient, and the residual variance, on the individual regression parameters. Applied to the continuous trial used in dairy cattle experiments the analysis shows that, beyond the usual procedure of minimizing differences between yield levels, it is important for precise experimentation to minimize differences between individual rates of lactation decline. The analysis further shows how the precision of such experiments may be expected to fall off for longer experiments as differences between individual slopes introduce more variation than is compensated for by the reduction of the within animal contribution.

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