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Welch T-Test (Two-Sample & One-Sample)
x402
Welch T-Test (Two-Sample & One-Sample) is a paid API for AI agents from math-stats.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).
Performs a Welch two-sample or one-sample t-test, returning t statistic, degrees of freedom, p-value, confidence interval, and Cohen's d effect size.
Price / call$0.02
Success—
StatusUnknown
How this service works
Welch two-sample or one-sample t-test: t statistic, degrees of freedom, p-value, confidence interval and Cohen's d.
Output
Returns a JSON object with: t statistic, degrees of freedom, two-sided p-value, confidence interval (lower, upper, level), Cohen's d effect size, means of each sample, sample sizes, difference between means, standard error, a boolean 'significant' flag, a human-readable summary and verdict, and the alpha level used.
Example use cases
Clinical trial group comparison
“I have measurements from a treatment group (14.2, 15.8, 13.9, 16.1, 15.0) and a control group (12.1, 11.8, 13.0, 12.5, 11.9). Run a Welch t-test at alpha 0.05 and tell me whether the difference is statistically significant and how large the effect is.”
Manufacturing quality check
“Our process is supposed to produce parts with a mean length of 50mm. I measured 10 parts: 50.2, 49.8, 51.1, 50.5, 49.6, 50.9, 50.3, 49.7, 51.0, 50.4. Run a one-sample t-test against mu=50 and tell me if we're significantly off target.”
Academic score comparison between cohorts
“Compare these two student cohorts' exam scores: Cohort A got 78,82,75,88,91,70 and Cohort B got 85,89,92,88,95,87. Use alpha 0.01 and give me the p-value, degrees of freedom, and whether the difference is significant.”
Technical details
Endpoint
GEThttps://math-stats.x402tookit.com/t-test?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a rigorous parametric significance test comparing two independent groups (Welch t-test handles unequal variances) or testing a sample against a known population mean. It is more appropriate than a z-test when population variance is unknown or sample sizes are small, and better than a proportion z-test (see sibling endpoint) when the outcome variable is continuous. Prefer the correlation endpoint for measuring linear association rather than mean differences.
Side effects
- Missing required sample A values returns an error
- Sample with fewer than 2 values causes invalid degrees of freedom
- Non-numeric values in sample strings cause parsing errors
- Alpha outside 0.001–0.2 range rejected
- Providing both b and mu simultaneously may cause ambiguous test specification
- Very small samples may produce unreliable p-values flagged via degraded or reasons fields
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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