CI for the Difference of Two Proportions
Computes the confidence interval for the difference between two proportions, using the Wald method. It's the companion to the two-proportion z-test and the basis of any A/B test reading: beyond saying whether the difference is significant, it shows the plausible range for its real size. If the interval doesn't contain zero, there's a significant difference. For example: variant A converted 45 of 100 and B, 30 of 100 — what's the interval for the difference? Enter the successes and the total of each group and the confidence level.
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CI for the Difference of Two Proportions
Computes the confidence interval for the difference between two proportions, using the Wald method. It's the companion to the two-proportion z-test and the basis of any A/B test reading: beyond saying whether the difference is significant, it shows the plausible range for its real size. If the interval doesn't contain zero, there's a significant difference. For example: variant A converted 45 of 100 and B, 30 of 100 — what's the interval for the difference? Enter the successes and the total of each group and the confidence level.
The size of the difference between A and B
Every A/B test ends with the same question: is the version that converted more actually better, and by how much? The two-proportion test says whether the difference is significant, but it's the confidence interval that shows what really matters for the business decision: the plausible range for the size of that difference.
The calculation, by the Wald method, centers the interval on the observed difference between the two proportions and extends a margin on each side. That margin combines the uncertainty of each proportion, through their summed standard errors, multiplied by the normal critical value corresponding to the confidence level. The larger the samples, the narrower and more informative the interval.
Enter the successes and the total of each group and the confidence level. The tool returns the point difference and the interval bounds. The reading is direct: if the interval doesn't contain zero, the difference is significant; if it does, the two groups may well have the same rate, and any observed advantage could be just sampling noise.
Related Tools
CI for Difference of Two Means (t)
Computes the confidence interval for the difference between the means of two independent groups, using the t distribution with pooled variances. It's the natural companion to the two-sample t-test: instead of only saying whether the difference is significant, it shows the plausible range for the real size of that difference. If the interval doesn't contain zero, there's a significant difference at the chosen level. Enter the two samples of values and the confidence level.
Two-Proportion z-Test
Computes the two-proportion z-test statistic, which compares the success rates of two independent groups — the backbone of any A/B test. For example: variant A converted 45 of 100 and B converted 30 of 100; is the difference real or noise? The statistic uses the pooled proportion of the two groups to estimate the standard error under the hypothesis that the proportions are equal. Enter the successes and the total of each of the two groups.
CI for the Ratio of Two Variances
Computes the confidence interval for the ratio between the variances of two normal populations, σ₁²/σ₂². Instead of just testing whether the variances differ, it gives a plausible range for how many times one is larger than the other. If the interval contains the number 1, there's no evidence the spreads are different. The calculation uses the F distribution, and because it's asymmetric, the bounds come from F quantiles with the degrees of freedom swapped. Enter the two samples and the confidence level.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.