Chi-Square Test Calculator

Chi-Square Test Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
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

1Select the test type: Goodness of Fit or Independence.
2Enter your data as comma-separated observed and expected counts, or input a multi-row contingency table.
3Adjust the alpha level (significance level) and preferred decimal places for the output.
4The 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.

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.

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.

Test Type: independence
Contingency Table:
30, 20
15, 35

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Testing a Fair Die

2. Analyzing Survey Demographics

FAQ

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