1. What is Chi-square Test?

The chi-square (χ²) test is a statistical method used to determine if there's a significant difference between observed and expected frequencies in categorical data. It's commonly used for goodness-of-fit tests and tests of independence.

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. A large χ² value indicates a significant difference.

3. Interpreting Results

Details: Compare your χ² statistic to critical values from chi-square distribution tables with appropriate degrees of freedom (df = number of categories - 1).

4. Using the Calculator

Tips: Enter comma-separated observed and expected counts. Both lists must have the same number of values. Expected counts should not be zero.

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 from expected frequencies.

Q2: What are the assumptions of chi-square test?
A: 1) Random sampling, 2) Independent observations, 3) Expected counts ≥5 for most categories.

Q3: What does a high chi-square value mean?
A: A high value suggests the observed data is unlikely under the null hypothesis (significant difference).

Q4: Can I use this for 2x2 contingency tables?
A: Yes, but for 2x2 tables with small samples, Fisher's exact test may be more appropriate.

Q5: How do I find the p-value from chi-square?
A: Use chi-square distribution tables or statistical software with your χ² value and degrees of freedom.