What is Rubin's rules used for in multiple imputation?

• A. They adjust p-values to reflect multiple imputations.
• B. They combine results across imputed datasets accounting for within- and between-imputation variability.
• C. They determine the number of imputations needed.
• D. They replace missing data with the mean.

Answer: (B)

Pooling results across multiple imputed datasets uses Rubin's rules to account for the uncertainty introduced by missing data. After creating several complete datasets and estimating the target parameter in each, Rubin's rules combine those estimates into one overall estimate and an appropriate standard error.

The key idea is that total uncertainty comes from two sources: how precise each dataset’s estimate is (within-imputation variability) and how much the estimates vary across the different imputations (between-imputation variability). You compute the average of the within-imputation variances and the variance of the point estimates across imputations. The overall variance is formed as W + (1 + 1/m)B, where W is the average within-imputation variance, B is the between-imputation variance, and m is the number of imputations. This pooled standard error lets you form confidence intervals and conduct hypothesis tests that reflect the missing data uncertainty. Rubin's rules also provide a way to adjust degrees of freedom for these pooled estimates.

These rules aren’t about adjusting p-values on their own, nor about choosing how many imputations to create, nor about replacing missing values with the mean (which is a single imputation method).