# Statistical Tests – Normality Check

> Statistical Tests – Normality Check is a paid API for AI agents from stats-tests.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-21).

Screens a numeric sample for normality using skewness, excess kurtosis, Jarque-Bera test with p-value, and the 68-95-99.7 rule check.

## Facts

- Endpoint: GET https://stats-tests.x402tookit.com/normality-check?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-21
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/statistical-tests-normality-check-3f2ad65b
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_iow1yXxDrTnptVWk2-lBf

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability statistical-tests-normality-check-3f2ad65b
```

Example prompt: Can you run a normality check on these values and tell me the skewness, excess kurtosis, Jarque-Bera statistic, p-value, and whether the data passes the 68-95-99.7 rule? The sample is: 12.3, 14.1, 13.8, 15.0, 12.9, 14.7, 13.2, 16.1, 11.8, 14.5, 13.9, 15.3, 12.6, 14.0, 13.5

## When to prefer this

Choose this endpoint when you need a quick, comprehensive normality screen combining moment-based metrics (skewness, kurtosis), an omnibus test (Jarque-Bera), and an empirical rule check in a single call. Ideal as a pre-flight check before parametric tests (t-test, ANOVA, regression) that assume normality. Prefer this over manual calculation or generic statistics libraries when you need a structured, verdict-ready JSON response with p-values. For very large samples or formal hypothesis testing workflows, complement with the sibling endpoints for specific tests.

## Known failure modes

- Fewer than 8 or more than 500 values provided — returns error or degraded result
- Non-numeric values in the sample — parsing failure
- Missing required 'values' query parameter — validation error
- Degenerate input (all identical values) — undefined skewness/kurtosis

## How this service works

Normality screen for a sample: skewness, excess kurtosis, Jarque-Bera test with p-value, and the 68-95-99.7 rule check.

## Output

Returns a JSON object containing: sample size (n), mean, standard deviation, skewness, excess kurtosis, Jarque-Bera statistic, p-value, significance flag at 5%, percentages of values within 1/2/3 standard deviations, a human-readable verdict and summary, list of reasons supporting the verdict, any checks not performed, and optional degraded/disclaimer flags.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "values"
     ],
     "properties": {
      "values": {
       "type": "string",
       "description": "Sample values (8 to 500)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "n": {
       "type": [
        "null",
        "number"
       ]
      },
      "sd": {
       "type": [
        "null",
        "number"
       ]
      },
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "mean": {
       "type": [
        "null",
        "number"
       ]
      },
      "pValue": {
       "type": [
        "null",
        "number"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "skewness": {
       "type": [
        "null",
        "number"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "jarqueBera": {
       "type": [
        "null",
        "number"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "within1SdPct": {
       "type": [
        "null",
        "number"
       ]
      },
      "within2SdPct": {
       "type": [
        "null",
        "number"
       ]
      },
      "within3SdPct": {
       "type": [
        "null",
        "number"
       ]
      },
      "excessKurtosis": {
       "type": [
        "null",
        "number"
    
… (truncated)
```

## More

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