Open AccessTHE ASSESSMENT OF A TREATMENT EFFECT WHEN A COVARIATE IS OBSERVED ON A SUBSET OF THE UNITS: I. SIMPLE ESTIMATORS
Author(s) -
Rubin Donald B.,
Weisberg Sanford
Publication year - 1974
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1974.tb00671.x
Subject(s) - covariate , estimator , covariance , statistics , mathematics , analysis of covariance , simple (philosophy) , correlation , randomized experiment , econometrics , philosophy , geometry , epistemology
Consider a completely randomized experiment with two groups, say treatment and control, and a covariate X that has been observed on a subset of the units. The objective is to estimate τ, the treatment effect on the variable Y which is recorded for all units. Although the average Y difference in the two groups, , is unbiased for τ, it is common to try to use X to increase the precision of the estimate of τ by forming a covariance adjustment, especially if the correlation between X and Y, ρ, is large. If X is not fully observed it is not clear whether to and/or how to form the covariance adjusted estimate. In addition to , we consider two covariance adjusted estimates of τ, which ignores the units without X, and which fills in group means for the missing values. We compare the three estimators' variances and find the conditions under which each estimator is best.