Abstract: Multiple imputation is becoming a standard tool for handling nonresponse in sample surveys. A difficult problem in the analysis of a multiply-imputed data set concerns how to combine repeated p-values efficiently to create a va lid significance level. Here we propose, justify, and evaluate the validity of a new procedure, which is superior to the current standard. This problem is inherently difficult when the number of multiple imputations is small, as it must be in common practice, as made clear by its close relationship to a multivariate version of the classic Behrens-Fisher problem with small degrees of freedom.
Key words and phrases: Multiple imputation, missing data, noresponse, surveys, Bayesian inference, Behrens-Fisher problem, incomplete data, hypothesis testing.