1. What is the Chi-square Test?

The Chi-square 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:

• \( \chi^2 \) — Chi-square statistic
• \( O \) — Observed count
• \( E \) — Expected count
• \( \sum \) — Sum over all categories

Explanation: The test compares observed values with expected values under the null hypothesis, calculating how likely the observed difference is due to chance.

3. Importance of Chi-square Test

Details: The Chi-square test is widely used in research to test relationships between categorical variables, check distribution assumptions, and analyze contingency tables.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should I use a Chi-square test?
A: Use it when you have categorical data and want to test if observed frequencies differ significantly from expected frequencies.

Q2: What are the assumptions of the Chi-square test?
A: The test assumes random sampling, independence of observations, and that expected frequencies are at least 5 in each category.

Q3: How do I interpret the Chi-square value?
A: Compare your calculated χ² value to critical values from a Chi-square distribution table with appropriate degrees of freedom.

Q4: 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 variables.

Q5: Can I use this for small sample sizes?
A: For small samples (expected counts < 5), consider Fisher's exact test instead.