We propose improvements to existing degrees of freedom used for significance testing of multivariate hypotheses in small samples when missing data are handled using multiple imputation. The improvements are for 1) tests based on unrestricted fractions of missing information and 2) tests based on equal fractions of missing information with M(p−1) ≤ 4, where M is the number of imputations and p is the number of tested parameters. Using the mi command available as of Stata 11, we demonstrate via simulation that using these adjustments can result in a more sensible degrees of freedom (and hence closer-to-nominal rejection rates) than existing degrees of freedom.


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