1. What is the Chi-square Independence Test?

The Chi-square test of independence assesses whether two categorical variables are independent. It compares observed frequencies to expected frequencies if the variables were independent.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

Where:

• \( O \) — Observed frequency
• \( E \) — Expected frequency (calculated assuming independence)
• \( \sum \) — Sum over all cells in the contingency table

Explanation: The test measures how much the observed counts deviate from what we would expect if the variables were independent.

3. Importance of Chi-square Test

Details: This test is widely used in research to examine relationships between categorical variables, such as treatment vs. outcome or demographic characteristics vs. preferences.

4. Using the Calculator

Tips: Enter the observed counts for each cell in the 2×2 contingency table. All values must be non-negative integers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a Chi-square test?
A: When you have two categorical variables and want to test if they're related. Both variables should have two or more categories.

Q2: What are the assumptions of this test?
A: 1) Independent observations, 2) Expected count ≥5 in each cell (for 2×2 tables), 3) Random sampling.

Q3: What does a significant result mean?
A: It suggests an association between the variables, but doesn't indicate the strength or direction of the relationship.

Q4: What if my expected counts are too small?
A: For 2×2 tables with expected counts <5, consider Fisher's exact test instead.

Q5: Can I use this for larger tables?
A: Yes, the test generalizes to R×C tables, though this calculator handles 2×2 tables.