Test differences between two proportions using flexible inputs. See pooled errors, confidence intervals, and decisions. Download neat summaries for classwork, reviews, and client documentation.
| Scenario | Successes | Trials | Observed Rate |
|---|---|---|---|
| Landing Page A | 84 | 200 | 0.4200 |
| Landing Page B | 63 | 210 | 0.3000 |
This sample compares two conversion rates from a simple A/B test. Enter these values into the form to review the z statistic, p value, and confidence interval.
Sample proportion for Group A: p1 = x1 / n1
Sample proportion for Group B: p2 = x2 / n2
Pooled proportion: p = (x1 + x2) / (n1 + n2)
Pooled standard error: SE = sqrt[ p(1 - p)(1/n1 + 1/n2) ]
Z statistic: z = (p1 - p2) / SE
Two-tailed p value: p = 2 × [1 - Φ(|z|)]
Left-tailed p value: p = Φ(z)
Right-tailed p value: p = 1 - Φ(z)
Confidence interval for p1 - p2: (p1 - p2) ± z* × sqrt[ p1(1-p1)/n1 + p2(1-p2)/n2 ]
If continuity correction is enabled, the calculator reduces the absolute difference by 0.5 × (1/n1 + 1/n2) before computing the z statistic.
A two proportion p value calculator compares two observed rates. It checks whether the gap between them is likely due to random sampling. This method is common in A/B testing, surveys, clinical screening, and conversion analysis. You enter successes and total trials for both groups. The tool then estimates each sample proportion. Next, it builds the pooled standard error. Then it computes a z statistic and the related p value. A smaller p value suggests stronger evidence of a real difference.
The p value helps you judge statistical significance. It does not measure business value by itself. It measures how surprising your result would be if both true proportions were equal. That makes it useful for experiments and decision reviews. This calculator also shows the confidence interval for the difference in proportions. That interval adds practical context. It shows the likely range for the true gap. You can also inspect Cohen’s h to judge effect size.
The two proportion z test works best with adequate sample size. Each group should have enough expected successes and failures. This page checks that condition and shows a note. If expected counts are too small, the normal approximation may be weaker. In that case, results need extra care. Many analysts still use this tool as a fast screening step. It is especially helpful for marketing tests, product trials, quality checks, and classroom statistics problems.
This calculator combines several outputs in one place. You can test left-tailed, right-tailed, or two-tailed hypotheses. You can change alpha, confidence level, and decimal precision. You can also apply continuity correction when needed. The result block appears above the form for quick reading. The export buttons help with homework, reports, and audit trails. Because the page also includes formulas, example data, and FAQs, it supports both quick answers and deeper understanding.
It tests whether two sample proportions differ significantly. It uses a two proportion z test and reports the z statistic, p value, and confidence interval.
Use a two-tailed test when you only care whether the proportions are different. It checks for either a positive or negative gap.
Use a one-tailed test when your research question has one clear direction. For example, you only want to test whether Group A outperforms Group B.
The pooled proportion combines successes from both groups. It is used in the standard error for the null hypothesis that both true proportions are equal.
It shows a plausible range for the true difference between the two population proportions. If the interval excludes zero, that supports a meaningful difference.
Continuity correction makes the z test more conservative. Some instructors or analysts prefer it when working with discrete counts and moderate sample sizes.
Yes. It works well for conversion rates, response rates, defect rates, and pass rates, as long as your data can be written as successes out of total trials.
The normal approximation may be less reliable. Treat the result carefully and consider an exact method or a larger sample when precision matters.
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.