One-sample t-test API

Run a one-sample Student's t-test t=(x̄−μ0)/(s/√n) with a two-tailed p-value from the t-distribution, returning the statistic, df, p-value and a reject/fail-to-reject decision. Auditable: echoes sample mean, sd, n. Answers 'is this sample mean different from 5','one-sample t-test p-value','do I reject the null at alpha 0.05'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-t-test-one-sample

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticst-testhypothesis-testone-samplep-valuestudent-tinference

API URLhttps://x402.hexl.dev/v1/calc/stat-t-test-one-sample

Integration docs

Example request

{
  "sample": [
    5,
    6,
    7,
    8,
    9
  ],
  "mu": 5
}

Example response

{
  "t": 2.828427,
  "df": 4,
  "pValue": 0.047421,
  "alpha": 0.05,
  "sampleMean": 7,
  "hypothesizedMean": 5,
  "sampleSd": 1.581139,
  "standardError": 0.707107,
  "n": 5,
  "rejectNull": true,
  "rating": "significant",
  "interpretation": "t(4)=2.828, p=0.0474; reject H0 (mean = 5) at alpha=0.05."
}

Input schema

{
  "type": "object",
  "required": [
    "sample",
    "mu"
  ],
  "properties": {
    "sample": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "description": ">=2 observations",
      "examples": [
        [
          5,
          6,
          7,
          8,
          9
        ]
      ]
    },
    "mu": {
      "type": "number",
      "description": "hypothesized mean μ0",
      "examples": [
        5
      ]
    },
    "alpha": {
      "type": "number",
      "default": 0.05,
      "examples": [
        0.05
      ]
    }
  }
}

Output schema

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