Calculator Input
Enter successes and sample sizes for two independent groups. The computed result appears above this form after submission.
Example Data Table
| Example | Successes | Sample Size | Observed Proportion |
|---|---|---|---|
| Treatment | 84 | 150 | 0.5600 |
| Control | 63 | 145 | 0.4345 |
| With a 95% Wald interval, the estimated difference is about 0.1255, and the interval is approximately 0.0123 to 0.2388. | |||
Formula Used
1) Observed Proportions
p1 = x1 / n1 and p2 = x2 / n2
2) Difference in Proportions
d = p1 - p2
3) Wald Standard Error
SE = √[ p1(1 - p1) / n1 + p2(1 - p2) / n2 ]
4) Wald Confidence Interval
d ± z* × SE
5) Agresti-Caffo Adjustment
p1* = (x1 + 1) / (n1 + 2) and p2* = (x2 + 1) / (n2 + 2)
d* = p1* - p2*, then use d* ± z* × SE* with the adjusted proportions and adjusted sample sizes.
Use this calculator for two independent samples. The interval assumes binomial outcomes and random sampling. Agresti-Caffo is often more stable for smaller samples.
How to Use This Calculator
- Enter labels for both groups.
- Type the number of successes for each group.
- Enter each group’s total sample size.
- Choose a confidence level, such as 95%.
- Select Wald or Agresti-Caffo as the interval method.
- Pick how many decimal places you want shown.
- Click Calculate Interval.
- Review the result section above the form, the chart, and the export buttons.
Frequently Asked Questions
1) What does this calculator measure?
It estimates the confidence interval for the difference between two independent proportions. The result shows a plausible range for Group A minus Group B based on sample data.
2) What does it mean if the interval includes zero?
If zero falls inside the interval, the observed gap is not clearly separated from random sampling variation at the selected confidence level.
3) When should I use Wald versus Agresti-Caffo?
Wald is simple and common. Agresti-Caffo is often preferred when samples are smaller or observed proportions are near 0 or 1 because it tends to be more stable.
4) Can the two groups have different sample sizes?
Yes. The groups do not need equal sample sizes. The formulas directly account for each sample’s own size and proportion.
5) What counts as a success?
A success is the outcome of interest in each group, such as a conversion, pass, defect, response, or treatment outcome. Both groups should use the same definition.
6) Can I use percentages instead of counts?
This tool expects counts, not percentages. Convert your data into successes and total sample sizes before calculating the interval.
7) What assumptions matter most?
The samples should be independent, observations should be binary, and the data should reasonably reflect random sampling or random assignment.
8) Is this the same as a hypothesis test?
Not exactly. A confidence interval estimates a range for the difference. A hypothesis test focuses on whether evidence rejects a specific null value, usually zero.