Chi-square test (goodness-of-fit / independence) API

Run a chi-square test: goodness-of-fit χ²=Σ(O−E)²/E for a 1-D count vector, or independence on a 2-D contingency table with expected = row·col/total, returning χ², df, an upper-tail p-value and a decision. Auditable: echoes the test type and df. Answers 'is this die fair','chi-square goodness-of-fit','are these two categorical variables independent'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-chi-square

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticschi-squaregoodness-of-fitindependencecontingencycategoricalp-value

API URLhttps://x402.hexl.dev/v1/calc/stat-chi-square

Integration docs

Example request

{
  "observed": [
    22,
    24,
    38,
    30,
    46,
    44
  ],
  "expected": [
    34,
    34,
    34,
    34,
    34,
    34
  ]
}

Example response

{
  "test": "goodness-of-fit",
  "chiSquare": 15.294118,
  "df": 5,
  "pValue": 0.009177,
  "alpha": 0.05,
  "rejectNull": true,
  "rating": "significant",
  "interpretation": "χ²(5)=15.294, p=0.0092; observed differs from expected at alpha=0.05."
}

Input schema

{
  "type": "object",
  "required": [
    "observed"
  ],
  "properties": {
    "observed": {
      "description": "1-D counts (goodness-of-fit) or 2-D table (independence)",
      "examples": [
        [
          22,
          24,
          38,
          30,
          46,
          44
        ]
      ]
    },
    "expected": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "description": "optional expected counts; defaults to uniform",
      "examples": [
        [
          34,
          34,
          34,
          34,
          34,
          34
        ]
      ]
    },
    "alpha": {
      "type": "number",
      "default": 0.05
    }
  }
}

Output schema

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