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Exact Binomial Test with Clopper-Pearson CI
x402
Exact Binomial Test with Clopper-Pearson CI is a paid API for AI agents from stats-tests.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-21).
Performs an exact binomial test for k successes in n trials against a hypothesised probability, returning two-sided and one-sided p-values plus the Clopper-Pearson confidence interval.
Price / call$0.02
Success—
StatusUnknown
How this service works
Exact binomial test of k successes in n trials vs a hypothesised probability, with p-values and the Clopper-Pearson CI.
Output
Returns the sample proportion, two-sided p-value, one-sided p-values (less and greater), Clopper-Pearson confidence interval (lower, upper, level), a significance verdict, a plain-language summary, the echo of inputs (trials, successes, hypothesised probability), and an asOf timestamp.
Example use cases
A/B conversion rate significance test
“I ran an A/B test and got 312 conversions out of 1,050 visitors in the treatment group. Can you do an exact binomial test against a baseline conversion rate of 0.25 and tell me if it's statistically significant at the 5% level, with a 95% confidence interval?”
Coin or dice fairness check
“I flipped a coin 200 times and got 118 heads. Run an exact binomial test to see if the coin is significantly biased away from a 50% probability, and give me the two-sided p-value and 95% Clopper-Pearson interval.”
Manufacturing defect rate audit
“Our quality audit found 9 defective units in a batch of 150. Test whether this is significantly higher than our accepted defect probability of 0.04, using a one-sided p-value and a 99% confidence interval.”
Technical details
Endpoint
GEThttps://stats-tests.x402tookit.com/binomial-test?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need an exact (not approximate) binomial test — particularly for small sample sizes where the normal approximation is unreliable, or when you need the Clopper-Pearson interval (the gold-standard conservative exact CI for a proportion). Prefer it over z-proportion tests when n*p or n*(1-p) is small, or when regulatory/scientific rigor demands an exact method.
Side effects
- Missing required parameters (successes or trials) returns a validation error
- successes greater than trials returns an invalid input error
- p0 outside [0,1] is rejected
- confidence outside [0.8, 0.999] is rejected
- non-integer successes or trials may be rejected
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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