Standard error of measurement API

Computes the Standard Error of Measurement (SD * sqrt(1 - reliability)) and a confidence band around an observed test score. Answers 'How much measurement noise is in this score?', 'What is the 95% confidence interval around an observed score?'.

Price$0.04per request

MethodPOST

Route/v1/stats/standard-error-measurement

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

psychometricssemstandard-error-of-measurementreliabilityconfidence-intervaltest-theoryscoringprecision

API URLhttps://x402.hexl.dev/v1/stats/standard-error-measurement

Integration docs

Example request

{
  "sd": 15,
  "reliability": 0.91,
  "observedScore": 110
}

Example response

{
  "sem": 4.5,
  "reliability": 0.91,
  "sd": 15,
  "confidence": 0.95,
  "zCritical": 1.959964,
  "interpretation": "about 1.96 SEM (8.82 score points) at 95% confidence",
  "observedScore": 110,
  "ciLower": 101.180162,
  "ciUpper": 118.819838
}

Input schema

{
  "type": "object",
  "required": [
    "sd",
    "reliability"
  ],
  "properties": {
    "sd": {
      "type": "number",
      "description": "standard deviation of scores",
      "examples": [
        15
      ]
    },
    "reliability": {
      "type": "number",
      "description": "reliability coefficient 0..1",
      "examples": [
        0.91
      ]
    },
    "observedScore": {
      "type": "number",
      "examples": [
        110
      ]
    },
    "confidence": {
      "type": "number",
      "default": 0.95
    }
  }
}

Output schema

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