One-way ANOVA API

Run a one-way analysis of variance across >=2 groups, computing between/within sums of squares, mean squares, the F statistic F=MSB/MSW, an upper-tail F p-value, eta-squared effect size, and a decision. Auditable: returns the full ANOVA table. Answers 'do these groups have different means','one-way ANOVA F and p','is the group effect significant'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-anova-one-way

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticsanovaf-testvariancegroupseta-squaredinference

API URLhttps://x402.hexl.dev/v1/calc/stat-anova-one-way

Integration docs

Example request

{
  "groups": [
    [
      1,
      2,
      3
    ],
    [
      4,
      5,
      6
    ],
    [
      7,
      8,
      9
    ]
  ]
}

Example response

{
  "f": 27,
  "dfBetween": 2,
  "dfWithin": 6,
  "pValue": 0.001,
  "alpha": 0.05,
  "ssBetween": 54,
  "ssWithin": 6,
  "msBetween": 27,
  "msWithin": 1,
  "etaSquared": 0.9,
  "groups": 3,
  "totalN": 9,
  "rejectNull": true,
  "rating": "significant",
  "interpretation": "F(2,6)=27, p=0.001; at least one group mean differs at alpha=0.05."
}

Input schema

{
  "type": "object",
  "required": [
    "groups"
  ],
  "properties": {
    "groups": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "description": ">=2 numeric arrays",
      "examples": [
        [
          [
            1,
            2,
            3
          ],
          [
            4,
            5,
            6
          ],
          [
            7,
            8,
            9
          ]
        ]
      ]
    },
    "alpha": {
      "type": "number",
      "default": 0.05
    }
  }
}

Output schema

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