Science & Education

Shapiro-Wilk, Anderson-Darling and Lilliefors Normality Tutor

Run the three workhorse normality tests (Shapiro-Wilk AS R94, Anderson-Darling, Lilliefors) with a Q-Q plot and a Monte-Carlo power comparison.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/shapiro-wilk-anderson-darling-lilliefors-normality-tutor' \
  -H 'Content-Type: application/json' \
  -d '{"data":"0.0987, 0.0533, 0.0293, 0.0246, 0.0200, 0.0194, 0.0191, 0.0180, 0.0172, 0.0132, 0.0102, 0.0084, 0.0077, 0.0058, 0.0016, 0.0000, -0.0026, -0.0036, -0.0042, -0.0114, -0.0139, -0.0222, -0.0333, -0.0348, -0.0363, -0.0363, -0.0402, -0.0583, -0.1184, -0.1420","alpha":"0.05","showQqPlot":true,"powerAlternative":"exponential","showPowerCurve":true}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/shapiro-wilk-anderson-darling-lilliefors-normality-tutor

Parameters

Name	Type	Required	Description
data	textarea	Yes	—
alpha	select	Yes	—
showQqPlot	checkbox	No	—
powerAlternative	select	No	—
showPowerCurve	checkbox	No	—

Response format

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-shapiro-wilk-anderson-darling-lilliefors-normality-tutor": {
      "name": "shapiro-wilk-anderson-darling-lilliefors-normality-tutor",
      "description": "Run the three workhorse normality tests (Shapiro-Wilk AS R94, Anderson-Darling, Lilliefors) with a Q-Q plot and a Monte-Carlo power comparison.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=shapiro-wilk-anderson-darling-lilliefors-normality-tutor",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "shapiro-wilk-anderson-darling-lilliefors-normality-tutor",
    "arguments": {
  "data": "0.0987, 0.0533, 0.0293, 0.0246, 0.0200, 0.0194, 0.0191, 0.0180, 0.0172, 0.0132, 0.0102, 0.0084, 0.0077, 0.0058, 0.0016, 0.0000, -0.0026, -0.0036, -0.0042, -0.0114, -0.0139, -0.0222, -0.0333, -0.0348, -0.0363, -0.0363, -0.0402, -0.0583, -0.1184, -0.1420",
  "alpha": "0.05",
  "showQqPlot": true,
  "powerAlternative": "exponential",
  "showPowerCurve": true
}
  }
}

curl -X POST 'https://api.elysiatools.com/en/api/tools/shapiro-wilk-anderson-darling-lilliefors-normality-tutor' \ -H 'Content-Type: application/json' \ -d '{"data":"0.0987, 0.0533, 0.0293, 0.0246, 0.0200, 0.0194, 0.0191, 0.0180, 0.0172, 0.0132, 0.0102, 0.0084, 0.0077, 0.0058, 0.0016, 0.0000, -0.0026, -0.0036, -0.0042, -0.0114, -0.0139, -0.0222, -0.0333, -0.0348, -0.0363, -0.0363, -0.0402, -0.0583, -0.1184, -0.1420","alpha":"0.05","showQqPlot":true,"powerAlternative":"exponential","showPowerCurve":true}'

Name

Type

Required

Description

data

textarea

Yes

—

alpha

select

Yes

—

showQqPlot

checkbox

—

powerAlternative

select

—

showPowerCurve

checkbox

—

{ "mcpServers": { "elysiatools-shapiro-wilk-anderson-darling-lilliefors-normality-tutor": { "name": "shapiro-wilk-anderson-darling-lilliefors-normality-tutor", "description": "Run the three workhorse normality tests (Shapiro-Wilk AS R94, Anderson-Darling, Lilliefors) with a Q-Q plot and a Monte-Carlo power comparison.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=shapiro-wilk-anderson-darling-lilliefors-normality-tutor", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "shapiro-wilk-anderson-darling-lilliefors-normality-tutor", "arguments": { "data": "0.0987, 0.0533, 0.0293, 0.0246, 0.0200, 0.0194, 0.0191, 0.0180, 0.0172, 0.0132, 0.0102, 0.0084, 0.0077, 0.0058, 0.0016, 0.0000, -0.0026, -0.0036, -0.0042, -0.0114, -0.0139, -0.0222, -0.0333, -0.0348, -0.0363, -0.0363, -0.0402, -0.0583, -0.1184, -0.1420", "alpha": "0.05", "showQqPlot": true, "powerAlternative": "exponential", "showPowerCurve": true } } }