# Statistical Tests

Chi-square, ANOVA, Mann-Whitney, Fisher exact, binomial and paired t-tests, multiple-comparison corrections, effect sizes, power and normality.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://stats-tests.x402tookit.com/openapi.json
- x402 manifest: https://stats-tests.x402tookit.com/.well-known/x402
- Catalog (free): https://stats-tests.x402tookit.com/catalog
- Health (free): https://stats-tests.x402tookit.com/health
- Uptime (free): https://stats-tests.x402tookit.com/uptime

## Endpoints (10)

### GET /anova-oneway — $0.02
One-way ANOVA across 2 to 12 groups: F statistic, degrees of freedom, p-value, eta squared and omega squared, with group means.
Params: groups: string
Example: https://stats-tests.x402tookit.com/anova-oneway?groups=6%2C8%2C4%2C5%2C3%2C4%3B8%2C12%2C9%2C11%2C6%2C8%3B13%2C9%2C11%2C8%2C7%2C12

### GET /binomial-test — $0.02
Exact binomial test of k successes in n trials vs a hypothesised probability, with p-values and the Clopper-Pearson CI.
Params: successes: integer, trials: integer, p0?: number, confidence?: number
Example: https://stats-tests.x402tookit.com/binomial-test?successes=8&trials=10&p0=0.5

### GET /chi-square-test — $0.02
Chi-square goodness of fit (observed vs expected counts) or independence test on a table, with p-value and effect size.
Params: observed?: string, expected?: string, table?: string
Example: https://stats-tests.x402tookit.com/chi-square-test?observed=5%2C8%2C9%2C8%2C10%2C20

### GET /effect-size-2x2 — $0.02
Odds ratio, relative risk, risk difference and number needed to treat from a 2x2 table, each with a confidence interval.
Params: exposedEvents: integer, exposedNoEvents: integer, unexposedEvents: integer, unexposedNoEvents: integer, confidence?: number
Example: https://stats-tests.x402tookit.com/effect-size-2x2?exposedEvents=20&exposedNoEvents=80&unexposedEvents=10&unexposedNoEvents=90

### GET /fisher-exact — $0.02
Fisher's exact test for a 2x2 table: two-sided and one-sided p-values from the hypergeometric distribution, plus odds ratio.
Params: a: integer, b: integer, c: integer, d: integer
Example: https://stats-tests.x402tookit.com/fisher-exact?a=3&b=1&c=1&d=3

### GET /mann-whitney — $0.02
Mann-Whitney U test for two independent samples: U, exact p for small samples without ties or normal approximation, effect size.
Params: a: string, b: string
Example: https://stats-tests.x402tookit.com/mann-whitney?a=1%2C2%2C3%2C4%2C5&b=6%2C7%2C8%2C9%2C10

### GET /multiple-comparisons — $0.02
Adjust p-values for multiple testing (Bonferroni, Sidak, Holm, Benjamini-Hochberg) and see which tests survive.
Params: pvalues: string, alpha?: number
Example: https://stats-tests.x402tookit.com/multiple-comparisons?pvalues=0.01%2C0.04%2C0.03%2C0.005

### GET /normality-check — $0.02
Normality screen for a sample: skewness, excess kurtosis, Jarque-Bera test with p-value, and the 68-95-99.7 rule check.
Params: values: string
Example: https://stats-tests.x402tookit.com/normality-check?values=4.1%2C5.2%2C4.8%2C5.0%2C5.5%2C4.9%2C5.1%2C6.0%2C4.7%2C5.3%2C4.4%2C5.6

### GET /paired-t-test — $0.02
Paired t-test on before and after data: mean change, t, degrees of freedom, p-value, confidence interval and Cohen dz.
Params: before: string, after: string, alpha?: number
Example: https://stats-tests.x402tookit.com/paired-t-test?before=10%2C12%2C14%2C16%2C18&after=11%2C14%2C17%2C20%2C23

### GET /power-t-test — $0.02
Sample size for a two-sample, one-sample or paired t-test from effect size, alpha and power; or the power for a given size.
Params: effectSize: number, design?: string, alpha?: number, power?: number, nPerGroup?: integer
Example: https://stats-tests.x402tookit.com/power-t-test?effectSize=0.5&design=two-sample&alpha=0.05&power=0.8

## Terms

All results are computed locally with standard algorithms, provided as is. Statistical tests rest on assumptions (independent observations, adequate sample size, roughly normal data for parametric tests) that this service cannot verify, and a small p-value does not show cause, size or importance of an effect. Not professional statistical, medical or financial advice. Inputs travel in the query string, so keep data lists short and never send personal data.