KR-20 / KR-21 reliability API

Computes Kuder-Richardson KR-20 and KR-21 reliability for dichotomous (0/1) test items from a respondents x items matrix, with per-item difficulties and total-score variance. Answers 'How reliable is my right/wrong test?', 'What is KR-20 vs KR-21 for this item set?'.

Price$0.04per request

MethodPOST

Route/v1/stats/kuder-richardson

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

psychometricsreliabilitykr-20kr-21kuder-richardsondichotomoustest-theoryexam

API URLhttps://x402.hexl.dev/v1/stats/kuder-richardson

Integration docs

Example request

{
  "matrix": [
    [
      1,
      1,
      1,
      0
    ],
    [
      1,
      1,
      0,
      0
    ],
    [
      1,
      0,
      1,
      1
    ],
    [
      0,
      1,
      1,
      1
    ],
    [
      1,
      1,
      1,
      1
    ],
    [
      0,
      0,
      1,
      0
    ]
  ]
}

Example response

{
  "kr20": 0.083333,
  "kr21": 0,
  "nItems": 4,
  "nRespondents": 6,
  "itemDifficulties": [
    0.666667,
    0.666667,
    0.833333,
    0.5
  ],
  "sumPQ": 0.833333,
  "meanTotalScore": 2.666667,
  "totalScoreVariance": 0.888889,
  "interpretation": "unacceptable internal consistency (KR-20)"
}

Input schema

{
  "type": "object",
  "required": [
    "matrix"
  ],
  "properties": {
    "matrix": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "description": "respondents x items matrix of 0/1 correct/incorrect",
      "examples": [
        [
          [
            1,
            1,
            1,
            0
          ],
          [
            1,
            1,
            0,
            0
          ]
        ]
      ]
    }
  }
}

Output schema

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