Chi-Square Test

Introduction: Chi-Square Test

The Chi-Square Test is a non-parametric statistical test used to examine relationships between categorical variables. It compares observed frequencies with expected frequencies to test if differences are due to chance.

Background

Developed by Karl Pearson in 1900, the Chi-Square test is widely used when dealing with attribute data and categorical outcomes.

Key Elements / Features

• Null Hypothesis (H₀): Assumes no relationship between variables.
• Chi-Square Statistic (χ²): Measures the difference between observed and expected counts.
• P-value: Determines statistical significance.

Applications / Examples

• Market research: Testing if customer preference differs by region.
• Healthcare: Analysing treatment outcomes by gender.
• Quality control: Checking if defect types occur equally often.

Example: A company tests if defect rates are the same across three factories.

Relevance / Impact

The Chi-Square Test is essential for categorical data analysis, helping organisations identify whether patterns or differences are significant. It supports evidence-based decisions without requiring normality assumptions.

See also

• Attribute Data
• Logistic Regression
• Hypothesis Testing
• Non-Parametric Tests