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 independence.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed frequency
• \( E \) — Expected frequency
• \( \sum \) — Sum over all categories

Explanation: The test compares observed counts with expected counts under the null hypothesis. Larger χ² values indicate greater discrepancy between observed and expected values.

3. When to Use Chi-square Test

Details: Use chi-square test for categorical data when:

• Testing goodness of fit (does data match expected distribution?)
• Testing independence between two categorical variables
• Sample size is large enough (expected counts ≥5 in most cells)

4. Using the Calculator

Tips:

• Enter observed counts in one text area
• Enter corresponding expected counts in the other
• Values can be separated by commas or spaces
• Number of observed and expected values must match
• Expected values should not be zero

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between chi-square 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: What are the assumptions of chi-square test?
A: Independent observations, categorical data, sufficiently large sample size (expected counts ≥5 in most cells).

Q3: How do I interpret the chi-square statistic?
A: Compare to critical value from chi-square distribution table with appropriate degrees of freedom. Larger values indicate stronger evidence against null hypothesis.

Q4: What if my expected counts are too small?
A: Consider Fisher's exact test for small sample sizes or combine categories if appropriate.

Q5: Can I use chi-square for continuous data?
A: No, chi-square is for categorical data. For continuous data, consider t-tests or ANOVA.