# Chi-Square Test Calculator

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

> Canonical page: https://elysiatools.com/en/tools/chi-square-test-calculator

- **Category:** Math & Numbers

- **Keywords:** chi-square test, goodness of fit, independence test, contingency table, p value, calculator

## 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.

## Inputs

- **Test Type** (select)
- **Observed Counts** (textarea): e.g. 18, 22, 20, 16, 24
- **Expected Counts** (textarea): e.g. 20, 20, 20, 20, 20
- **Contingency Table** (textarea): One row per line, e.g. 30, 20 15, 35
- **Alpha** (number)
- **Decimal Places** (number)

## 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.

## Frequently asked questions

### 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.

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