How to use this calculator
- Enter the number of independently reviewed items.
- Enter how many met the stated criterion.
- Select the confidence level.
- Calculate and compare both bounds with your decision threshold.
#3166 · AI & Technology Tool
Analytics Team Confidence Interval Calculator
Turn an analytics team review sample into a plausible range for the team’s acceptance rate. This is useful when a manager has checked a subset of dashboards, queries, models, or analysis tickets and wants to quantify sampling uncertainty. The Wilson interval stays within 0% and 100% and is more reliable than adding and subtracting a basic standard error. Keep the review criterion consistent across every sampled item.
Calculator
Sample evidenceFormula
Wilson interval = adjusted center ± adjusted margin
The observed proportion is x ÷ n. The adjustment uses the selected confidence z-score and keeps both limits within 0% and 100%.
What the result means
The main result is the observed rate. The lower and upper bounds describe sampling uncertainty under the stated confidence level; they do not include bias from how items were selected or judged.
Use one consistent acceptance rule and a representative sample. A narrow interval cannot correct a biased review process.
Example calculation
With 108 accepted items out of 120 at 95% confidence, the observed acceptance rate is 90.00% and the Wilson interval is approximately 83.34% to 94.20%.
Tips for better results
- Define the validation rule before sampling.
- Sample across relevant sources and time periods.
- Avoid counting duplicate or dependent items as independent.
- Use the lower bound for conservative threshold checks.
- Increase the sample size when the interval is too wide.
Frequently asked questions
Why does this calculator use the Wilson interval?
Wilson intervals remain bounded between 0% and 100% and generally perform better than a basic normal interval for small samples or rates near the extremes.
Can I enter a 100% pass rate?
Yes. The interval will still show uncertainty below 100%, reflecting that a finite sample cannot prove every future item will pass.
Should the sampled items be independent?
Ideally, yes. Repeated or clustered items can make the interval look more precise than the underlying evidence supports.
What happens if I choose 99% instead of 95% confidence?
The interval becomes wider because a higher confidence level requires more coverage of plausible underlying rates.
Can I compare the lower bound with an internal threshold?
Yes, if the threshold and review rule were defined in advance. The lower bound is a conservative value for that comparison, not a guarantee.
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Interval inputs
| Variable | Meaning |
|---|---|
| n | Items reviewed |
| x | Items meeting criterion |
| p | x ÷ n |
| z | Confidence z-score |