Wilcoxon signed-rank test API

Runs the Wilcoxon signed-rank test for paired/one-sample data (drops zeros, tie- and continuity-corrected), returning W+, W-, z and p — a non-parametric alternative to the paired t-test. Answers 'Is there a median shift between paired non-normal measurements?', 'What is the Wilcoxon signed-rank statistic and p-value?'.

Price$0.08per request

MethodPOST

Route/v1/stats/wilcoxon-signed-rank

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticswilcoxonsigned-ranknonparametricpairedmedianinferencep-value

API URLhttps://x402.hexl.dev/v1/stats/wilcoxon-signed-rank

Integration docs

Example request

{
  "differences": [
    1,
    -2,
    3,
    4,
    -1,
    5,
    6
  ]
}

Example response

{
  "W": 4.5,
  "Wplus": 23.5,
  "Wminus": 4.5,
  "n": 7,
  "zerosDropped": 0,
  "zApprox": -1.524002,
  "pValue": 0.127508,
  "alpha": 0.05,
  "method": "normal approximation (tie & continuity corrected)",
  "rejectNull": false,
  "rating": "not significant",
  "interpretation": "Wilcoxon signed-rank W=4.5, z≈-1.524, p≈0.1275; no significant shift at alpha=0.05."
}

Input schema

{
  "type": "object",
  "required": [],
  "properties": {
    "before": {
      "type": "array",
      "items": {
        "type": "number"
      }
    },
    "after": {
      "type": "array",
      "items": {
        "type": "number"
      }
    },
    "differences": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "examples": [
        [
          1,
          -2,
          3,
          4,
          -1,
          5,
          6
        ]
      ]
    },
    "alpha": {
      "type": "number",
      "examples": [
        0.05
      ]
    }
  }
}

Output schema

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