The Analysis of Covariance with Incomplete Data
Graham N. Wilkinson · Biometrics · 1957
In a paper [4] submitted for publication in this journal, the author has presented simplified methods for setting up and solving equations for missing values. The methods apply to those designs and data for which normal theory, with linear model, provides the appropriate analysis, and have been extended to cover covariance analyses. A. T. James, in a personal communication, drew the author's attention to the fact that concomitant measurements corresponding to missing observations are irrelevant to the analysis of existing observations, and could therefore be replaced by hypothetical values more convenient for determining missing values and for the subsequent analysis of covariance on the completed data. Application of this suggestion has greatly simplified the author's results, and as the procedure is so simple, it has been thought worth while to outline it in this advance note. Since deriving these results, the author's attention has been drawn to a paper by Barnard [1] in which the method of fitting values appears to be the same as that proposed here. Barnard's description is very brief, however, being incidental to the main content of the paper (analysis of a crop-weather scheme), and seems to have been overlooked in the literature and textbooks. The present paper gives details of the fitting process, and also of deriving standard errors and exact significance tests.