Paired T Test

{
  "asOf": "2026-10-11T08:55:56.841Z",
  "cohensDz": 1.8973666,
  "confidenceInterval": {
    "level": 0.95,
    "lower": 1.036756839,
    "upper": 4.963243161
  },
  "degraded": false,
  "degreesOfFreedom": 4,
  "differences": [
    1,
    2
  ],
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "meanAfter": 17,
  "meanBefore": 14,
  "meanDifference": 3,
  "notChecked": [
    "that the pairs are truly matched (same subject measured twice)",
    "normality of the differences for small samples",
    "…2 more"
  ],
  "pValueTwoSided": 0.0132356,
  "pairs": 5,
  "reasons": [
    "Tests whether the mean of the paired differences is zero. Effect size dz: about 0.2 small, 0.5 medium, 0.8 large.",
    "Small sample: normality of the differences matters."
  ],
  "sdDifferences": 1.58113883,
  "significant": true,
  "source": "computed locally",
  "standardError": 0.7071067812,
  "summary": "Mean change 3 (after minus before), t(4) = 4.2426, two-sided p = 0.01324 -> significant at alpha 0.05; 95% CI 1.03676 to 4.96324; Cohen's dz 1.897.",
  "tStatistic": 4.242640687,
  "verdict": "SIGNIFICANT"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://stats-tests.x402tookit.com/paired-t-test?after=11%2C14%2C17%2C20%2C23&before=10%2C12%2C14%2C16%2C18'

# 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/paired-t-test?after=11%2C14%2C17%2C20%2C23&before=10%2C12%2C14%2C16%2C18' \
  | 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%2Fpaired-t-test
const res = await pay("https://stats-tests.x402tookit.com/paired-t-test?after=11%2C14%2C17%2C20%2C23&before=10%2C12%2C14%2C16%2C18");
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/paired-t-test?after=11%2C14%2C17%2C20%2C23&before=10%2C12%2C14%2C16%2C18")
    print(res.status_code, res.text)