CI: difference of proportions API

Computes a Wald confidence interval for the difference between two independent proportions, returning the interval, z, standard error and margin of error. Answers 'What is the CI for the difference between two rates?', 'Is the lift between two proportions significant?'.

Price$0.04per request

MethodPOST

Route/v1/stats/ci-diff-proportions

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticsconfidence-intervaldifference-of-proportionswaldtwo-sampleinferenceconversionab-test

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

Integration docs

Example request

{
  "successes1": 120,
  "n1": 200,
  "successes2": 90,
  "n2": 200
}

Example response

{
  "proportion1": 0.6,
  "proportion2": 0.45,
  "difference": 0.15,
  "confidence": 0.95,
  "z": 1.96,
  "standardError": 0.049371,
  "marginOfError": 0.096765,
  "lower": 0.053235,
  "upper": 0.246765,
  "method": "Wald",
  "rating": "excludes zero (significant)",
  "interpretation": "95% CI for (p1 - p2): [0.0532, 0.2468]."
}

Input schema

{
  "type": "object",
  "required": [
    "successes1",
    "n1",
    "successes2",
    "n2"
  ],
  "properties": {
    "successes1": {
      "type": "integer",
      "examples": [
        120
      ]
    },
    "n1": {
      "type": "integer",
      "examples": [
        200
      ]
    },
    "successes2": {
      "type": "integer",
      "examples": [
        90
      ]
    },
    "n2": {
      "type": "integer",
      "examples": [
        200
      ]
    },
    "confidence": {
      "type": "number",
      "examples": [
        0.95
      ]
    }
  }
}

Output schema

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