  Current pooling rules for multiply imputed data assume infinite populations.
In some situations this assumption is not feasible as every unit in the
population has been observed, potentially leading to over-covered population
estimates. We simplify the existing pooling rules for situations where the
sampling variance is not of interest. We compare these rules to the
conventional pooling rules and demonstrate their use in a situation where there
is no sampling variance. Using the standard pooling rules in situations where
sampling variance should not be considered, leads to overestimation of the
variance of the estimates of interest, especially when the amount of
missingness is not very large. As a result, populations estimates are
over-covered, which may lead to a loss of statistical power. We conclude that
the theory of multiple imputation can be extended to the situation where the
sample happens to be the population. The simplified pooling rules can be easily
implemented to obtain valid inference in cases where we have observed
essentially all units and in simulation studies addressing the missingness
mechanism only.
