Rubin multiple-imputation pooling
Combine complete-data estimates and SEs using within- and between-imputation variance.
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Use 2–100 proper imputations of the same estimand, each with positive SE. Transform bounded or ratio measures to an appropriate approximately normal analysis scale before pooling.
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Pooled estimate
- 2
- Within variance
- 0.26268
- Between variance
- 0.025
- Total variance
- 0.29268
- Pooled SE
- 0.54099908
- Rubin df
- 380.71814
- 95% lower
- 0.93627975
- 95% upper
- 3.0637203
How to interpret the output
Total variance is mean(SE²)+(1+1/m)×sample variance(estimates). The interval uses the original large-complete-data Rubin degrees of freedom; it is not the Barnard–Rubin small-sample adjustment. Imputation model validity, missingness assumptions and Monte Carlo stability remain essential.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.