Our Chi-Square Test Calculator helps you determine the statistical significance of observed versus expected data distribution. This tool is ideal for data analysts and statisticians who need to perform chi-square tests efficiently.

Data Source and Methodology

All calculations are rigorously based on the formulas and data provided by authoritative statistical sources. Please refer to this source for more information. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Glossary of Variables

  • Oi: Observed frequency for category i.
  • Ei: Expected frequency for category i.
  • \(\chi^2\): Chi-square statistic.

How It Works: A Step-by-Step Example

Consider observed values of 20, 30, and 50, with expected values of 25, 25, and 50. The chi-square statistic is calculated by summing the squared difference between observed and expected values, divided by the expected values.

Frequently Asked Questions (FAQ)

What is the chi-square test used for?

The chi-square test is used to determine if there is a significant difference between expected and observed data distributions.

How do I interpret the chi-square results?

A high chi-square statistic indicates a large discrepancy between observed and expected data, suggesting statistical significance.

What is degrees of freedom in chi-square test?

Degrees of freedom in the chi-square test are calculated as the number of categories minus one.

What is a p-value in chi-square test?

The p-value indicates the probability of observing the data if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.

Can I use this calculator for large datasets?

Yes, but ensure your input data is well-formatted and within reasonable limits for accurate computation.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\]
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
Formula (extracted text)
\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
``` , ', svg: { fontCache: 'global' } };

Our Chi-Square Test Calculator helps you determine the statistical significance of observed versus expected data distribution. This tool is ideal for data analysts and statisticians who need to perform chi-square tests efficiently.

Data Source and Methodology

All calculations are rigorously based on the formulas and data provided by authoritative statistical sources. Please refer to this source for more information. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Glossary of Variables

  • Oi: Observed frequency for category i.
  • Ei: Expected frequency for category i.
  • \(\chi^2\): Chi-square statistic.

How It Works: A Step-by-Step Example

Consider observed values of 20, 30, and 50, with expected values of 25, 25, and 50. The chi-square statistic is calculated by summing the squared difference between observed and expected values, divided by the expected values.

Frequently Asked Questions (FAQ)

What is the chi-square test used for?

The chi-square test is used to determine if there is a significant difference between expected and observed data distributions.

How do I interpret the chi-square results?

A high chi-square statistic indicates a large discrepancy between observed and expected data, suggesting statistical significance.

What is degrees of freedom in chi-square test?

Degrees of freedom in the chi-square test are calculated as the number of categories minus one.

What is a p-value in chi-square test?

The p-value indicates the probability of observing the data if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.

Can I use this calculator for large datasets?

Yes, but ensure your input data is well-formatted and within reasonable limits for accurate computation.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\]
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
Formula (extracted text)
\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
``` ]], displayMath: [['\\[','\\]']] }, svg: { fontCache: 'global' } };, svg: { fontCache: 'global' } };

Our Chi-Square Test Calculator helps you determine the statistical significance of observed versus expected data distribution. This tool is ideal for data analysts and statisticians who need to perform chi-square tests efficiently.

Data Source and Methodology

All calculations are rigorously based on the formulas and data provided by authoritative statistical sources. Please refer to this source for more information. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Glossary of Variables

  • Oi: Observed frequency for category i.
  • Ei: Expected frequency for category i.
  • \(\chi^2\): Chi-square statistic.

How It Works: A Step-by-Step Example

Consider observed values of 20, 30, and 50, with expected values of 25, 25, and 50. The chi-square statistic is calculated by summing the squared difference between observed and expected values, divided by the expected values.

Frequently Asked Questions (FAQ)

What is the chi-square test used for?

The chi-square test is used to determine if there is a significant difference between expected and observed data distributions.

How do I interpret the chi-square results?

A high chi-square statistic indicates a large discrepancy between observed and expected data, suggesting statistical significance.

What is degrees of freedom in chi-square test?

Degrees of freedom in the chi-square test are calculated as the number of categories minus one.

What is a p-value in chi-square test?

The p-value indicates the probability of observing the data if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.

Can I use this calculator for large datasets?

Yes, but ensure your input data is well-formatted and within reasonable limits for accurate computation.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\]
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
Formula (extracted text)
\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
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