Two Sample Proportions Interval Calculator

Formula Used

The standard Wald confidence interval for the difference between two independent sample proportions is calculated using the following statistical formula:

$(\hat{p}_1 - \hat{p}_2) \pm Z_{\alpha/2} \times \sqrt{\frac{\hat{p}_1(1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2(1 - \hat{p}_2)}{n_2}}$

Where $\hat{p}_1 = x_1 / n_1$ and $\hat{p}_2 = x_2 / n_2$ represent the sample proportions, and $Z_{\alpha/2}$ is the critical value corresponding to your chosen confidence level.

How to Use This Calculator

1. Enter the number of successes ($x_1$) and total sample size ($n_1$) for your first independent group.
2. Input the successes ($x_2$) and sample size ($n_2$) for your second comparison group.
3. Select your preferred confidence level, estimation technique, and tail options from the parameter columns.
4. Click the Calculate Interval button to generate instant statistical results and bounds.