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Widely used methods for analyzing missing data can be biased in smallsamples. To understand these biases, we evaluate in detail the situation wherea small univariate normal sample, with values missing at random, is analyzedusing either observed-data maximum likelihood (ML) or multiple imputation (MI).We evaluate two types of MI: the usual Bayesian approach, which we callposterior draw (PD) imputation, and a little-used alternative, which we call MLimputation, in which values are imputed conditionally on an ML estimate. Wefind that observed-data ML is more efficient and has lower mean squared errorthan either type of MI. Between the two types of MI, ML imputation is moreefficient than PD imputation, and ML imputation also has less potential forbias in small samples. The bias and efficiency of PD imputation can be improvedby a change of prior.

The Bias and Efficiency of Incomplete-Data Estimators in Small Univariate Normal Samples