Analysis of variance of a balanced incomplete block design with missing observations

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Virginia Polytechnic Institute


The problem considered in this paper is that of estimating several missing values and analyzing the resulting augmented data in a balanced incomplete block design.

The estimates are obtained by Yates' procedure of minimizing the error sum of squares.

Explicit formulae are obtained for all cases involving not more than two missing values and for several particular configurations of the missing values within the design. A general solution is obtained which involves the inversion of a symmetric n-square matrix, where n is the number of missing values.

An exact analysis of data augmented by missing value estimates is given which eliminates a positive bias in the treatment sum of squares.

It is possible to treat a balanced incomplete block design as a randomized block design with missing values. Estimates of the missing entries and a randomized block analysis can then be obtained according to the methods of Glenn and Kramer. An example of this procedure is given, and the results are compared with the results obtained by the usual balanced incomplete block analysis.

An example is given illustrating the techniques of missing value estimation and subsequent exact analysis for the balanced incomplete block design.