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.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

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

Explanation: The test compares observed counts with expected counts under the null hypothesis, measuring how much they deviate from each other.

3. Importance of Chi-Square Test

Details: The chi-square test is widely used in research to test for independence between categorical variables or goodness-of-fit for distributions.

4. Using the Calculator

Tips: Enter comma-separated observed and expected values. Both lists must have the same number of values and all expected counts should be ≥5 for reliable results.

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'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.

Q3: What are the assumptions of chi-square test?
A: Independent observations, adequate sample size (all expected counts ≥5), and categorical data.

Q4: How do I interpret the chi-square statistic?
A: Higher values indicate greater divergence between observed and expected. Compare to critical value from chi-square distribution table.

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