Statistical Analysis with Missing Data., 3rd Edition

2Missing Data in Experiments

2.1 Introduction

An important problem, historically, occurs with missing outcome data in controlled experiments. This was arguably the first missing data problem to be systematically treated in a principled way, and its treatment anticipated modern missing data methods, particularly the expectation–maximization (EM) algorithm (Dempster et al. 1977) discussed in Chapter 8.

Controlled experiments are generally carefully designed to allow revealing statistical analyses to be made using straightforward computations. In particular, corresponding to a standard classical experimental design, there is a standard least squares analysis, which yields estimates of parameters, standard errors for contrasts of parameters, and the analysis of variance (ANOVA) table. The estimates, standard errors, and ANOVA table corresponding to most designed experiments are easily computed because of balance in the designs. For example with two factors being studied, the analysis is particularly simple when the same number of units is assigned to each combination of factor levels. Textbooks on experimental design catalog many examples of specialized analyses (Box et al. 1985; Cochran and Cox 1957; Davies 1960; Kempthorne 1952; Winer 1962; Wu and Hamada 2009).

Because the levels of the design factors in an experiment are fixed by the experimenter, missing values, if they occur, do so in the outcome variable, Y, rather than in the design factors, X. Consequently, we restrict ...