Proportion Test Online: One-Sample and Two-Sample Z Tests
What is a Proportion Test?
A proportion test draws conclusions about a population rate such as defect rate, conversion rate, pass rate or acceptance rate. A one-sample test checks whether a sample proportion equals a target, and a two-sample test compares whether two independent populations have equal proportions. Tests are based on the binomial distribution with a normal approximation (Z test) for large samples, and the tool also outputs the proportion and its confidence interval so you can judge estimation precision.
Which Confidence Interval to Choose
The classic Wald interval is common for large samples but has poor coverage with small samples. The Wilson interval is more stable when the sample is small or the proportion is near 0 or 1, making it the recommended default. The tool outputs the Wilson interval for one proportion and a Wald or Newcombe interval for the difference of two proportions; an interval that excludes zero (or excludes the target for one proportion) indicates a significant difference.
Application Scenarios
Common in quality and operations: testing whether the defect rate exceeds a target such as 0.5%, whether two suppliers have different pass rates, whether conversion improved after a redesign, or whether two shifts differ in defect rate. You only need the number of successes x and total sample size n (x1/n1 and x2/n2 for two groups), making it a fast field check for proportion-type questions, and it pairs with the A/B test calculator for experiment design and evaluation.
Step-by-Step Usage
Log in, choose one-sample or two-sample, enter successes and sample sizes (two groups), set the target proportion and the test direction (one- or two-tailed), and the tool returns the Z value, p-value, proportion estimates, confidence intervals and a conclusion. When the proportion is near 0 or 1 or the sample is too small, it suggests an exact binomial test and recommends the sample size calculator to plan the experiment so you do not get false negatives from an undersized sample.