Adjustment by Covariance and Consequent Tests of Significance in Split-Plot Experiments

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Abstract
When experimental observations are to be adjusted for covariance on a concomitant variable, when there is more than one part of the analysis from which regressions may be computed (for example main-plot and split-plot error terms), and when regression at all levels may be assumed to be equal, one may prefer to use only one estimate for all adjustments. Provided that variation of the concomitant variable is at random with respect to main-treatments, main-plot yields may be adjusted by the split-plot regression and the adjusted yields analyzed as if observed. A composite estimate may be theoretically more efficient but would be more trouble than it is worth. An alternative test of significance which has been proposed is both more troublesome and slightly less justifiable on theoretical grounds. The method is not strictly valid when applied to missing sub-plots but may be used with negligible error.

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