How to Combine the Results after the Multiple Imputation
The overall estimate of Q is simply the average of the M estimates from M multiple imputed datasets.
The overall variance of 
is
is
Where the average variance of M within-imputed datasets (
) is 
and the variance between-imputed dataset is 
The overall degree of freedom (df) is
) is 
and the variance between-imputed dataset is 
The overall degree of freedom (df) is
Where the df of imputed datasets is 
and the df of observed data is
If the df of the complete data (dfcompleted) are large [Notes: for complex sampling design, dfcomplete = # of PSU - # of Strata], the overall degree of freedom is
and the df of observed data is 
If the df of the complete data (dfcompleted) are large [Notes: for complex sampling design, dfcomplete = # of PSU - # of Strata], the overall degree of freedom is
Then, the confidence intervals can be
The estimated percent rate of missing information for Q is
Notes: Usually M = 5 or 10 is enough, but the M is better to be great than the percent rate of missing information.
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