Measure proportion precision using adjusted confidence bounds. Test multiple confidence levels and sample sizes easily. See interval shifts, chart results, and download polished summaries.
This calculator uses the adjusted Wald method for a binomial proportion interval and can also compare it with standard Wald and Wilson results.
| Scenario | Successes | Trials | Confidence | Adjusted Proportion | Lower Bound | Upper Bound |
|---|---|---|---|---|---|---|
| A/B Test | 12 | 20 | 90% | 58.81% | 41.82% | 75.80% |
| Survey | 48 | 120 | 95% | 40.31% | 31.67% | 48.95% |
| Audit | 5 | 18 | 99% | 33.76% | 9.22% | 58.30% |
| QC Batch | 73 | 100 | 95% | 72.15% | 63.53% | 80.77% |
| Pilot | 140 | 200 | 98% | 69.47% | 62.00% | 76.95% |
The adjusted Wald interval is a corrected confidence interval for a binomial proportion. It improves the ordinary Wald interval by adding a small adjustment to the sample.
1. Compute the critical value:
z = z-score for the selected confidence level
2. Adjust the sample size and successes:
ñ = n + z²
x̃ = x + z² / 2
p̃ = x̃ / ñ
3. Compute the margin of error:
ME = z × √( p̃(1 − p̃) / ñ )
4. Build the interval:
Lower = p̃ − ME
Upper = p̃ + ME
Here, x is the number of successes, n is the number of trials, and p̃ is the adjusted estimated proportion.
It is a confidence interval for a binomial proportion that corrects the ordinary Wald method by adding a small adjustment to the sample count and size.
The ordinary Wald interval can perform poorly with small samples or extreme proportions. The adjusted version usually gives more stable and realistic bounds.
It is useful for surveys, conversion rates, defect rates, pass rates, medical screening proportions, and any yes or no outcome summarized as successes out of trials.
A success is the event of interest in a binomial sample, such as a purchase, approval, defect found, positive test, or completed action.
Yes. That is one reason adjusted methods are valuable. They still provide usable interval estimates near the boundaries where ordinary Wald intervals may behave badly.
A higher confidence level uses a larger critical value, which widens the interval. A lower confidence level narrows it and gives less coverage certainty.
Percent display shows values like 62.50%. Decimal display shows the same quantity as 0.6250. Only the formatting changes, not the calculation.
Comparing methods helps you see how the adjusted interval differs from older or alternative approaches, especially when sample sizes are limited or proportions are extreme.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.