CI: difference of two means API

Builds a Welch or pooled t confidence interval for the difference between two independent means from summary stats, returning the interval, df, t-critical and margin of error. Answers 'What is the 95% CI for the gap between two group means?', 'Does the mean difference exclude zero?'.

Price$0.06per request

MethodPOST

Route/v1/stats/ci-diff-means

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticsconfidence-intervaldifference-of-meanswelchtwo-sampleinferencemargin-of-errort-distribution

API URLhttps://x402.hexl.dev/v1/stats/ci-diff-means

Integration docs

Example request

{
  "mean1": 10,
  "sd1": 2,
  "n1": 30,
  "mean2": 8,
  "sd2": 2.5,
  "n2": 30
}

Example response

{
  "difference": 2,
  "confidence": 0.95,
  "method": "Welch",
  "df": 55.3337,
  "tCritical": 2.0038,
  "standardError": 0.584523,
  "marginOfError": 1.171251,
  "lower": 0.828749,
  "upper": 3.171251,
  "rating": "excludes zero (significant)",
  "interpretation": "95% CI for (mean1 - mean2): [0.8287, 3.1713]."
}

Input schema

{
  "type": "object",
  "required": [
    "mean1",
    "sd1",
    "n1",
    "mean2",
    "sd2",
    "n2"
  ],
  "properties": {
    "mean1": {
      "type": "number",
      "examples": [
        10
      ]
    },
    "sd1": {
      "type": "number",
      "examples": [
        2
      ]
    },
    "n1": {
      "type": "integer",
      "examples": [
        30
      ]
    },
    "mean2": {
      "type": "number",
      "examples": [
        8
      ]
    },
    "sd2": {
      "type": "number",
      "examples": [
        2.5
      ]
    },
    "n2": {
      "type": "integer",
      "examples": [
        30
      ]
    },
    "confidence": {
      "type": "number",
      "examples": [
        0.95
      ]
    },
    "equalVariance": {
      "type": "boolean"
    }
  }
}

Output schema

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