Compare two pass/fail defect rates and test whether the difference is statistically significant. Enter events and sample sizes for both groups to get z, p-value, and 95% CI.
Enter events and trials for both samples and press Calculate to run the test.
Line A defect rate looks lower than Line B — but is the gap real? Enter the lab to compare the two rates.
Enter the number of defectives and total items inspected for both samples. Choose your significance level and whether you're testing one-sided or two-sided.
The calculator combines both samples to estimate what the shared rate would be if there were no real difference, then measures how far apart your two rates are.
You get a p-value showing whether the difference is real, plus a 95% confidence range for the true difference between the rates.
Use the calculator above to compare two pass/fail rates and test whether the difference is real or due to chance. The 2 proportions z-test is the standard tool whenever you need to decide whether one process, supplier, line, or shift genuinely produces more defectives than another.
The 2 proportions z-test asks: could the difference in two observed defect rates have occurred by chance if the true rates were identical? You provide the number of defectives and total units for each group. The test computes a z-statistic and p-value. A significant result gives you confidence that one group genuinely has a higher defect rate — not just random variation.
This test compares the defect (or success) rate of two groups. It works out each group's rate, then checks how far apart they are relative to the natural sampling wobble you would expect at those sample sizes — expressed as a z-score and turned into a p-value. A p-value below 0.05 means the two rates are genuinely different, so the gap is not just chance. The confidence interval then gives a plausible range for the true size of the difference between the rates.
Line 1: 12 defects from 300 units (4%). Line 2: 7 defects from 300 units (2.3%). Line 2 looks better — but with only 300 units each, could the gap be a sampling fluke?
The 2 Proportions Test gives p = 0.14 — above 0.05. The data doesn't prove a real difference yet. The gap could easily be down to chance at this sample size.
What to do with this: Collect more data before drawing conclusions. Run a power calculation to find out how many units you'd actually need to detect a real 1.7% difference with confidence.
Instead of eyeballing two percentages and guessing, the 2 proportions test gives you a defensible statistical decision. It distinguishes genuine differences in defect rates from random fluctuation, preventing wasted investigation on noise and missed investigation of real problems.
Use this test in the Analyse phase of DMAIC when your output Y is binary (pass/fail, good/defective) and you want to compare two groups: two shifts, two suppliers, two lines, or before vs after a change. If you need to compare more than two groups, use a chi-square test instead.
The 2 proportions test is the proportion-data equivalent of the 2-sample t-test for means. Both are core Analyse-phase tools in DMAIC. A significant result identifies a categorical X (line, shift, supplier) as a likely contributor to the defect Y, directing the Improve phase.
If the test is significant, identify the operational difference between the two groups — different materials, operators, equipment, or methods. Use a fishbone diagram or 5 Whys to drill into the root cause. Implement a targeted fix in the higher-defect group and verify the improvement with another proportions test after the change. Track the rate over time with a P or NP control chart.
Combine the proportions test with control charts, Pareto analysis, and fishbone diagrams for a complete defect-reduction toolkit.
Use the 2 proportions test when you want to compare two pass/fail or defective/non-defective rates. Typical examples include comparing defect rates between two production lines, two suppliers, two shifts, or before and after a process change (when the measurements are independent). If the data comes from the same items measured twice, use a McNemar test instead.
The z-test uses pooled standard error because under the null hypothesis (the two proportions are equal) we assume a common population proportion. The pooled estimate is (x1+x2)/(n1+n2). The confidence interval for the difference uses unpooled standard error instead, because the CI does not assume the proportions are equal — it estimates the true difference and its uncertainty.
The normal approximation works well when both n1×p̂1, n1×(1−p̂1), n2×p̂2, and n2×(1−p̂2) are all at least 5. As a practical rule of thumb, aim for at least 20–30 observations per sample. For detecting a small difference in defect rates (e.g. 1% vs 2%), you typically need hundreds of observations — use a sample size calculator to plan your study.
The 95% confidence interval gives a range of plausible values for the true difference in proportions (p1 − p2). If the interval does not contain zero, the difference is statistically significant at α = 0.05, consistent with the p-value. The width of the interval shows precision: a narrow CI means a precise estimate, a wide CI means high uncertainty — usually because sample sizes are small.
A significant result tells you the rates differ — structured improvement training shows you how to fix the higher one.
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