Proportion Test Calculator

In short A two-proportion z-test asks whether two rates could plausibly come from the same underlying proportion. The figures loaded above — 120 of 1,000 against 90 of 1,000 — give z = 2.1883, p = 0.0287 and a difference of three percentage points, so the gap is larger than sampling noise comfortably explains. The standard error uses the POOLED proportion, because the null hypothesis being tested says the two rates are equal; the confidence interval for the difference uses the unpooled version, because there you are estimating a gap rather than testing whether it is zero. That asymmetry is deliberate and is why a borderline test and its interval can occasionally disagree. Squaring z gives 4.7887, which is exactly the chi-square statistic for the same 2×2 table — the two tests are algebraically identical, so a chi-square on a 2×2 IS a two-proportion z-test. Two warnings that matter more than the arithmetic. Report the ABSOLUTE difference rather than the relative one: a move from 1% to 2% is a 100% lift and one percentage point, and only one of those figures tells you what you gained. And checking an A/B test repeatedly, stopping the moment p drops below 0.05, inflates the false-positive rate well past 20% — fix the sample size in advance.