Analyze A/B outcomes with precise proportion testing tools. See pooled estimates, confidence intervals, and decisions. Built for analysts comparing rates across real datasets today.
| Group | Successes | Sample Size | Sample Proportion |
|---|---|---|---|
| Landing Page A | 45 | 120 | 0.3750 |
| Landing Page B | 62 | 118 | 0.5254 |
For the null hypothesis that both population proportions are equal, first compute the sample proportions:
p1 = x1 / n1 and p2 = x2 / n2
Next compute the pooled proportion:
p̂ = (x1 + x2) / (n1 + n2)
Then calculate the pooled standard error:
SE = √[ p̂(1 - p̂)(1/n1 + 1/n2) ]
The z statistic is:
z = (p1 - p2) / SE
The two sided p-value is 2 × (1 - Φ(|z|)). One sided p-values use the relevant tail area. The confidence interval for the observed difference uses the unpooled standard error.
A two sample z test for proportions helps compare success rates from two groups. It is widely used in A/B testing, product analytics, medicine, quality control, and survey research. The calculator estimates whether an observed gap is likely due to random sampling. It also reports confidence intervals, pooled values, and a clear decision. This makes it useful for fast evidence based comparisons.
Use this method when each sample is independent and observations are binary. A record must be either a success or a non success. Sample sizes should be large enough for normal approximation rules. That means expected successes and failures should usually exceed five in both groups. When counts are very small, exact methods may be safer. This page also shows adequacy checks so the result is easier to trust.
The calculator converts raw counts into sample proportions, then builds the pooled standard error under the null hypothesis that both population proportions are equal. It computes the z statistic, p value, confidence interval, critical value, and a final reject or fail to reject decision. It also reports the observed difference, relative risk, and odds ratio. These extra outputs help analysts interpret both statistical significance and practical direction.
Start with the p value and compare it with alpha. A small p value suggests the groups differ beyond ordinary random variation. Next, inspect the confidence interval. If it excludes zero, the difference is supported by the interval estimate as well. Then review the direction of the effect. Positive differences favor sample one, while negative differences favor sample two. Use business context before making decisions. Statistical significance alone does not measure impact size, cost, risk, or implementation value.
Teams often compare conversion rates, click through rates, churn flags, defect rates, response rates, and model acceptance rates. The same framework supports experiments, cohort analysis, and campaign measurement. Because the inputs are simple counts, it fits dashboards and reviews. Still, sampling design matters. Bias, tracking errors, and populations can distort conclusions even when the z test looks significant.
It compares two independent population proportions using sample data. Common examples include conversion rates, defect rates, response rates, and pass rates across two groups.
Use it when outcomes are binary, samples are independent, and expected successes and failures are large enough for the normal approximation to be reasonable.
The pooled estimate is used under the null hypothesis that both population proportions are equal. It provides the standard error for the z test statistic.
Alpha is the significance threshold for the hypothesis test. Confidence level equals 1 minus alpha, expressed as a percentage for the interval estimate.
A small p-value suggests the observed difference is unlikely under the null hypothesis. That gives evidence that the two population proportions are different in the chosen direction.
The warning appears when an expected cell count falls below five. In that case, the z approximation may be weak, and exact methods may be better.
It estimates a plausible range for the true difference in population proportions. If the interval excludes zero, the samples support a nonzero difference.
Yes. It is useful for comparing two conversion rates in experiments, provided assignment is independent and the sample counts are large enough.
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.