Critical value & p-value lookup API

Acts as a programmatic statistical table: computes critical values or p-values for the normal, Student t, chi-square and F distributions given alpha/confidence, tail and degrees of freedom. Answers 'What is the t/F/chi-square critical value at this alpha and df?', 'What is the p-value for this test statistic?'.

Price$0.06per request

MethodPOST

Route/v1/stats/distribution-critical-value

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticscritical-valuep-valuet-distributionchi-squaref-distributionquantilelookup

API URLhttps://x402.hexl.dev/v1/stats/distribution-critical-value

Integration docs

Example request

{
  "distribution": "t",
  "mode": "critical",
  "alpha": 0.05,
  "df": 10
}

Example response

{
  "distribution": "t",
  "mode": "critical",
  "alpha": 0.05,
  "tail": "two",
  "criticalValue": 2.228139,
  "df": 10,
  "df1": null,
  "df2": null,
  "interpretation": "t critical value at alpha=0.05 (two) = 2.2281."
}

Input schema

{
  "type": "object",
  "required": [
    "distribution"
  ],
  "properties": {
    "distribution": {
      "type": "string",
      "enum": [
        "normal",
        "t",
        "chi-square",
        "f"
      ]
    },
    "mode": {
      "type": "string",
      "enum": [
        "critical",
        "pvalue"
      ]
    },
    "alpha": {
      "type": "number",
      "examples": [
        0.05
      ]
    },
    "confidence": {
      "type": "number"
    },
    "tail": {
      "type": "string",
      "enum": [
        "two",
        "left",
        "right",
        "upper"
      ]
    },
    "df": {
      "type": "number",
      "examples": [
        10
      ]
    },
    "df1": {
      "type": "number"
    },
    "df2": {
      "type": "number"
    },
    "statistic": {
      "type": "number"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}