T Test

{
  "alpha": 0.05,
  "asOf": "2026-10-11T06:26:07.896Z",
  "cohensD": -0.89656939,
  "confidenceInterval": {
    "level": 0.95,
    "lower": -3.98409626714,
    "upper": -0.349237066192
  },
  "degraded": false,
  "degreesOfFreedom": 24.98852929,
  "difference": -2.16666666667,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "meanA": 20.82,
  "meanB": 22.98666667,
  "nA": 15,
  "nB": 15,
  "notChecked": [
    "the assumptions: independent observations and roughly normal data (or large samples)",
    "practical importance (a tiny effect can be 'significant' with enough data)",
    "…2 more"
  ],
  "pValueTwoSided": 0.021378001,
  "reasons": [
    "Two-sided test. 'Not significant' means the data do not rule out no difference, not that there is none.",
    "Significance is not importance: check the effect size (Cohen's d: about 0.2 small, 0.5 medium, 0.8 large)."
  ],
  "significant": true,
  "source": "computed locally",
  "standardError": 0.882424510014,
  "summary": "Welch two-sample t-test (unequal variances): t = -2.455, df = 24.99, two-sided p = 0.0214 -> significant at alpha 0.05; difference -2.16667 (95% CI -3.9841 to -0.349237).",
  "tStatistic": -2.455356398,
  "test": "Welch two-sample t-test (unequal variances)",
  "verdict": "SIGNIFICANT"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://math-stats.x402tookit.com/t-test?a=27.5%2C21.0%2C19.0%2C23.6%2C17.0%2C17.9%2C16.9%2C20.1%2C21.9%2C22.6%2C23.1%2C19.6%2C19.0%2C21.7%2C21.4&b=27.1%2C22.0%2C20.8%2C23.4%2C23.4%2C23.5%2C25.8%2C22.0%2C24.8%2C20.2%2C21.9%2C22.1%2C22.9%2C20.5%2C24.4'

# 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://math-stats.x402tookit.com/t-test?a=27.5%2C21.0%2C19.0%2C23.6%2C17.0%2C17.9%2C16.9%2C20.1%2C21.9%2C22.6%2C23.1%2C19.6%2C19.0%2C21.7%2C21.4&b=27.1%2C22.0%2C20.8%2C23.4%2C23.4%2C23.5%2C25.8%2C22.0%2C24.8%2C20.2%2C21.9%2C22.1%2C22.9%2C20.5%2C24.4' \
  | 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%2Fmath-stats.x402tookit.com%2Ft-test
const res = await pay("https://math-stats.x402tookit.com/t-test?a=27.5%2C21.0%2C19.0%2C23.6%2C17.0%2C17.9%2C16.9%2C20.1%2C21.9%2C22.6%2C23.1%2C19.6%2C19.0%2C21.7%2C21.4&b=27.1%2C22.0%2C20.8%2C23.4%2C23.4%2C23.5%2C25.8%2C22.0%2C24.8%2C20.2%2C21.9%2C22.1%2C22.9%2C20.5%2C24.4");
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://math-stats.x402tookit.com/t-test?a=27.5%2C21.0%2C19.0%2C23.6%2C17.0%2C17.9%2C16.9%2C20.1%2C21.9%2C22.6%2C23.1%2C19.6%2C19.0%2C21.7%2C21.4&b=27.1%2C22.0%2C20.8%2C23.4%2C23.4%2C23.5%2C25.8%2C22.0%2C24.8%2C20.2%2C21.9%2C22.1%2C22.9%2C20.5%2C24.4")
    print(res.status_code, res.text)