The Analysis of Covariance with Incomplete Data

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Abstract
If a set of data y, with corresponding concomitant data x1,X2,..Xp, is incomplete in relation to a given experimental design, both the data y and the concomitant data X1,X2,...,Xp should be completed with estimated missing values, each set of missing values being determined in the usual way. The (p+1) sets of equations will have the same matrix of coefficients, so that inversion of this one matrix is sufficient to determine all sets of missing values. In the analysis of sums of squares and products for the completed data, the residual line is correct, but the treatments line needs adjustment for a correct test of significance. The necessary adjustment formulae are given. The variance of a treatment comparison (unadjusted) is determined in the usual way (adjustment being made for the missing values), and the additional variance for covariant adjustment of the comparison is given by the standard formula for complete data. Detailed numerical illustration is given.

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