LaTeX
\chi^2=\sum\frac{(O-E)^2}{E}Variables
- O: observed count
- E: expected count
How to use this formula
Compares observed and expected categorical counts.
Important notes
- Expected counts should be sufficiently large for the approximation.
Quick example
A large statistic indicates poor agreement with expectations.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Expected counts should be sufficiently large for the approximation.
- For the Chi-Square Statistic, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Chi-Square Statistic, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- For the Chi-Square Statistic, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
A large statistic indicates poor agreement with expectations.
Common mistakes
- When copying Chi-Square Statistic, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Chi-Square Statistic, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Chi-Square Statistic in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\chi^2=\sum\frac{(O-E)^2}{E}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Chi-Square Statistic used for?
Compares observed and expected categorical counts.
Can I copy this formula as LaTeX?
Yes. Copy \chi^2=\sum\frac{(O-E)^2}{E} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.