Chi-Square Test Calculator

Run chi-square goodness-of-fit or independence tests from observed counts or contingency tables

Example Results

1 examples

Run a goodness-of-fit test

Compare observed category counts with equal expected counts

{
  "result": {
    "chiSquare": 2,
    "degreesOfFreedom": 4,
    "pValue": 0.7358,
    "rejectNull": false
  }
}
View input parameters
{ "testType": "goodness-of-fit", "observedCounts": "18, 22, 20, 16, 24", "expectedCounts": "20, 20, 20, 20, 20", "contingencyTable": "30, 20\n15, 35", "alpha": 0.05, "decimalPlaces": 4 }

Key Facts

Category
Math, Date & Finance
Input Types
select, textarea, number
Output Type
json
Sample Coverage
4
API Ready
Yes

Overview

The Chi-Square Test Calculator is a statistical utility designed to perform goodness-of-fit and independence tests. By inputting observed counts, expected counts, or a contingency table, users can quickly calculate the chi-square statistic, degrees of freedom, and p-value to determine whether to reject the null hypothesis at a specified significance level.

When to Use

  • •When comparing observed categorical data against expected distributions to check for goodness of fit.
  • •When analyzing a contingency table to determine if two categorical variables are independent.
  • •When conducting hypothesis testing for academic research, market analysis, or survey data requiring a chi-square statistic.

How It Works

  • •Select the test type: Goodness of Fit or Independence.
  • •Enter your data as comma-separated observed and expected counts, or input a multi-row contingency table.
  • •Adjust the alpha level (significance level) and preferred decimal places for the output.
  • •The calculator computes the chi-square value, degrees of freedom, and p-value, indicating whether the null hypothesis should be rejected.

Use Cases

Evaluating whether customer preferences across different product categories match historical sales distributions.
Testing if there is a significant relationship between demographic groups and voting preferences in survey data.
Checking if the outcomes of a random event, like rolling a die, follow a uniform expected distribution.

Examples

1. Testing a Fair Die

Statistics Student
Background
A student rolls a six-sided die 120 times and records the frequency of each face to see if the die is fair.
Problem
Needs to compare the observed frequencies against the expected frequency of 20 for each face.
How to Use
Select 'Goodness of Fit', enter the observed counts, enter '20, 20, 20, 20, 20, 20' for expected counts, and set alpha to 0.05.
Example Config
Test Type: goodness-of-fit
Observed Counts: 18, 22, 20, 16, 24, 20
Expected Counts: 20, 20, 20, 20, 20, 20
Outcome
The tool calculates the chi-square statistic and p-value, showing whether the die's behavior significantly deviates from a fair distribution.

2. Analyzing Survey Demographics

Market Researcher
Background
A researcher surveys men and women on whether they prefer brand A or brand B.
Problem
Wants to determine if brand preference is independent of gender.
How to Use
Select 'Independence' and input the 2x2 survey results into the Contingency Table field.
Example Config
Test Type: independence
Contingency Table:
30, 20
15, 35
Outcome
The calculator outputs the degrees of freedom and p-value, indicating if there is a statistically significant relationship between gender and brand preference.

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FAQ

What is the difference between goodness-of-fit and independence tests?

A goodness-of-fit test compares one categorical variable to an expected distribution, while an independence test evaluates whether two categorical variables are related using a contingency table.

How do I format the contingency table?

Enter one row per line with comma-separated values. For example, type '30, 20' on the first line and '15, 35' on the second line for a 2x2 table.

What does the alpha value mean?

Alpha represents the significance level, typically set to 0.05. It is the probability threshold used to determine whether to reject the null hypothesis.

What outputs does the calculator provide?

The tool outputs the chi-square statistic, degrees of freedom, p-value, and a boolean result indicating whether to reject the null hypothesis.

Can I change the precision of the results?

Yes, you can adjust the decimal places setting to round the calculated chi-square and p-value to your preferred precision, up to 10 decimal places.

API Documentation

Request Endpoint

POST /en/api/tools/chi-square-test-calculator

Request Parameters

Parameter Name Type Required Description
testType select No -
observedCounts textarea No -
expectedCounts textarea No -
contingencyTable textarea No -
alpha number No -
decimalPlaces number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-chi-square-test-calculator": {
      "name": "chi-square-test-calculator",
      "description": "Run chi-square goodness-of-fit or independence tests from observed counts or contingency tables",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=chi-square-test-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]