Binomial Test

{
  "asOf": "2026-10-11T08:55:55.001Z",
  "clopperPearson": {
    "level": 0.95,
    "lower": 0.44390454,
    "upper": 0.97478927
  },
  "degraded": false,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "hypothesisedProbability": 0.5,
  "notChecked": [
    "independence of trials and a constant success probability",
    "choice of one-sided versus two-sided test (decide before looking)",
    "…1 more"
  ],
  "pValueGreater": 0.0546875,
  "pValueLess": 0.98925781,
  "pValueTwoSided": 0.109375,
  "reasons": [
    "Exact binomial probabilities: valid for any sample size.",
    "One-sided: P(X >= 8) = 0.05469, P(X <= 8) = 0.9893."
  ],
  "sampleProportion": 0.8,
  "significantAt5pct": false,
  "source": "computed locally",
  "successes": 8,
  "summary": "8 of 10 (80%) vs p0 = 0.5: two-sided exact p = 0.1094; 95% Clopper-Pearson CI 0.4439 to 0.9748.",
  "trials": 10,
  "verdict": "NOT_SIGNIFICANT"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://stats-tests.x402tookit.com/binomial-test?p0=0.5&successes=8&trials=10'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://stats-tests.x402tookit.com/binomial-test?p0=0.5&successes=8&trials=10' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fstats-tests.x402tookit.com%2Fbinomial-test
const res = await pay("https://stats-tests.x402tookit.com/binomial-test?p0=0.5&successes=8&trials=10");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://stats-tests.x402tookit.com/binomial-test?p0=0.5&successes=8&trials=10")
    print(res.status_code, res.text)