The Analysis of Variance and Derivation of Standard Errors for Incomplete Data

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Abstract
A previous paper (Bio-metrics 14(2): 257-286) dealt with the estimation of missing values. A standard analysis of the completed data yields the correct estimates of treatment effects and of error. However, other sums of squares in the standard analysis, in particular the treatment sum of squares, are incorrect. The present paper gives simple correction formulae by means of which the standard analysis may be adjusted to give the correct analysis (or analyses). The corresponding formulae are given for an analysis of covariance. The paper also provides a formula by means of which the variance and covariances of treatment comparisons may be adjusted for the effect of missing values. The theoretical derivations in the paper include the singular cases, such as omission of whole blocks or treatments. A detailed numerical example is given, and the use of the missing value theory as a tool for expanding the range of available experimental designs is illustrated in the derivation of an analysis for balanced incomplete block designs with several missing blocks.

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