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Statistical test comparing observed and expected frequencies to assess independence or goodness of fit for categorical data.
DESCRIPTION
The chi-square test evaluates whether observed categorical counts differ significantly from expected counts under a null hypothesis. Two common forms are the test of independence (contingency tables) and goodness-of-fit (single distribution). Assumptions include sufficiently large expected counts and independent observations; small samples may require Fisher’s exact test. Analysts report the chi-square statistic, degrees of freedom, and the p-value. It is widely used in A/B testing, survey analysis, and model diagnostics.
ALTERNATIVE DEFINITIONS
NIST/SEMATECH e-Handbook of Statistical Methods
The chi-square test is applied to a contingency table to test the hypothesis of independence between two variables.
Focuses on the independence test variant with contingency tables.
Penn State STAT 200
The Chi-Square Test of Independence is used to determine whether there is an association between two categorical variables.
Educational framing emphasizing association between categorical variables.
Encyclopaedia Britannica
Chi-square test, a statistical method of assessing the goodness of fit between observed values and those expected theoretically.
Highlights the goodness-of-fit form of the test.
RELATED TERMS
Contingency Table Pearson’s Chi-squared Goodness of Fit Independence Test p-value Degrees of Freedom Expected Frequencies Yates’ Correction
COMPETING TERMS
Fisher’s Exact Test G-test
RELATIONS
- Broader: Statistical Test
KNOWLEDGE AREAS
Mathematics Data Science Testing & Validation
TARGET AUDIENCE
Data Scientist Data Analyst Information Analyst BI Specialist
EXTERNAL SOURCES
- Wikipedia - Chi-square test
- NIST - Authoritative independence test guidance
- Penn State - Introductory course explanation
- UCLA OARC - Practical chi-square FAQ
TOP QUESTIONS
What is the Chi-square Test used for?
It evaluates whether observed counts deviate from expected counts. Commonly, it tests independence in contingency tables or goodness-of-fit to a theoretical distribution.
Category: Overview
When should I use a Chi-square Test of Independence?
Use it when you have two categorical variables and want to determine if they are associated. Data should be counts, not percentages.
Category: Requirements
What are the assumptions of the Chi-square Test?
Observations must be independent, expected cell counts sufficiently large, and categories mutually exclusive. Violations can inflate Type I or Type II errors.
Category: Requirements
What are common mistakes with the Chi-square Test?
Using percentages instead of counts, small expected frequencies, and multiple testing without correction are frequent errors. Misinterpreting p-values is also common.
Category: Mistakes
What is a competing test to the Chi-square Test?
Fisher’s Exact Test is preferred with small expected counts; the G-test is a likelihood-ratio alternative with similar goals.
Category: Alternatives
How do I interpret the Chi-square Test output?
Report the chi-square statistic, degrees of freedom, and p-value. A small p-value suggests a significant deviation from independence or expected distribution.
Category: Example
How is the Chi-square Test used in A/B testing?
It assesses differences in categorical outcomes across variants, like conversion vs. no conversion, to determine statistically significant effects.
Category: Application
What is Yates’ continuity correction in Chi-square Tests?
It adjusts for continuity in 2x2 tables, slightly reducing the chi-square statistic. Use cautiously; modern practice often favors exact or alternative methods.
Category: Opinion
Where can I learn Chi-square Test basics?
NIST’s e-Handbook and university course pages (UCLA, Penn State) provide clear tutorials and examples.
Category: Learning