What is a Chi-Square test, and how is it used in statistics?

Answered on : 2024-01-23

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1. **Overview of Chi-Square Test:**

- The Chi-Square test is a statistical hypothesis test employed in the analysis of contingency tables, particularly when dealing with large sample sizes.

- It assesses the association or independence between categorical variables.

2. **Distribution Characteristics:**

- If χ is a Normally distributed variable with mean zero and variance 1, then χ² has a χ² distribution with one degree of freedom [8].

3. **Purpose and Application:**

- Used in hypothesis testing, especially for categorical variables, to compare observed and expected frequencies [3].

- Determines if two categorical variables are related or independent [11].

4. **Key Differences:**

- Chi-Square vs. Pearson R: Pearson R measures correlation, while Chi-Square is an inferential statistic for goodness of fit [6].

- Chi-Square vs. ANOVA: ANOVA compares means across groups with continuous dependent variables, while Chi-Square analyzes associations between categorical variables [9].

5. **Additional Resources:**

- For detailed information on calculations and examples, refer to statistical tutorials [11][13].

- A comprehensive guide on Chi-Square tests can be found in the BMJ Statistics Square One publication [1].