1. What is the Chi-Square Test?

The Chi-Square (χ²) test is a statistical method used to determine if there is a significant difference between the expected and observed frequencies in categorical data. It's commonly used in hypothesis testing to assess goodness of fit or test for independence.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

Where:

• \( O \) — Observed frequency
• \( E \) — Expected frequency
• \( \sum \) — Summation across all categories

Explanation: The test compares observed counts to expected counts under the null hypothesis, with larger χ² values indicating greater divergence from expected.

3. Importance of Chi-Square Test

Details: The Chi-Square test is widely used in research to test relationships between categorical variables, validate survey results, and analyze experimental data in fields like biology, marketing, and social sciences.

4. Using the Calculator

Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between goodness-of-fit and test of independence?
A: Goodness-of-fit compares observed to theoretical distribution, while test of independence examines relationship between two categorical variables.

Q2: When is Chi-Square test not appropriate?
A: When expected counts are <5 (use Fisher's exact test) or with continuous/non-categorical data.

Q3: How do I interpret the Chi-Square value?
A: Compare to critical value from Chi-Square distribution table using appropriate degrees of freedom and significance level.

Q4: What are degrees of freedom in Chi-Square test?
A: For goodness-of-fit: (categories - 1). For test of independence: (rows - 1) × (columns - 1).

Q5: Can Chi-Square show direction of association?
A: No, it only indicates whether an association exists, not its nature or direction.