Calculator Inputs
Enter pooled parameter estimates and their standard errors from each imputed analysis.
Example Data Table
These sample imputations demonstrate how separate model outputs are combined into one pooled result.
| Imputation | Estimate | Standard Error |
|---|---|---|
| 1 | 2.14 | 0.41 |
| 2 | 2.32 | 0.39 |
| 3 | 2.27 | 0.43 |
| 4 | 2.18 | 0.40 |
| 5 | 2.30 | 0.42 |
Formula Used
Q̄ = (Q1 + Q2 + ... + Qm) / m
Ū = (U1 + U2 + ... + Um) / m, where Ui = SEi2
B = Σ(Qi - Q̄)2 / (m - 1)
T = Ū + (1 + 1 / m)B
SEpooled = √T
r = ((1 + 1 / m)B) / Ū, then ν = (m - 1)(1 + 1 / r)2
Q̄ ± tν, 1-α/2 × SEpooled, using the pooled t distribution.
FMI = ((1 + 1 / m)B) / T, and Relative Efficiency = 1 / (1 + FMI / m)
This calculator pools one parameter at a time. For multiple coefficients, repeat the procedure for each coefficient from the imputed analyses.
How to Use This Calculator
- Run the same statistical model on each imputed dataset.
- Copy the estimate and its standard error from every imputation.
- Enter one row per imputation in the table.
- Set the confidence level, null value, and decimal precision.
- Click Pool Estimates to calculate pooled values using Rubin’s rules.
- Review pooled estimate, total variance, confidence interval, p value, and missing information diagnostics.
- Use the CSV or PDF buttons to export your results.
- Use the example button when you want to test the calculator quickly.
Frequently Asked Questions
1. What does this calculator pool?
It pools one parameter estimate across multiple imputed datasets. Each row should contain the estimate and standard error from the same model term in each imputation.
2. Which pooling method is used?
It uses Rubin’s rules. The calculator combines the average estimate, the average within-imputation variance, and the between-imputation variance to produce pooled uncertainty and inference.
3. Why do I need standard errors?
Standard errors are needed to calculate within-imputation variance. Without them, the calculator cannot estimate total pooled variance or construct valid confidence intervals.
4. Can I enter more than five imputations?
Yes. Use the Add Imputation button to insert as many rows as needed. The pooling formulas automatically adjust to the number of completed imputations.
5. What if between-imputation variance is near zero?
That means imputed estimates are very similar. In that case, the pooled result is driven mostly by within-imputation uncertainty, and degrees of freedom become very large.
6. What does fraction missing information mean?
It shows how much uncertainty is added because missing data required imputation. Larger values indicate that missingness contributes more to total uncertainty.
7. Can I use this for regression coefficients?
Yes. It is commonly used for regression coefficients, mean differences, log-odds, hazard ratios on the model scale, and other single-parameter estimates.
8. Does this calculator replace full statistical software?
It helps verify and summarize pooled results, but full statistical software is still important for fitting the imputed models correctly and handling complex survey or multilevel settings.