1. What is Chi-square Test for 2x2 Tables?

The Chi-square test for 2x2 contingency tables examines whether there is a statistically significant association between two categorical variables. It compares observed frequencies to expected frequencies under the null hypothesis of independence.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

Where:

• \( O \) — Observed count in each cell
• \( E \) — Expected count under independence (row total × column total / grand total)

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

3. Interpretation of Results

Details: A significant p-value (typically < 0.05) suggests an association between the variables. The degrees of freedom for a 2x2 table is always 1.

4. Using the Calculator

Tips: Enter counts for all four cells of your 2x2 table. The calculator will compute the Chi-square statistic, degrees of freedom, and approximate p-value.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Fisher's exact test instead?
A: Use Fisher's exact test when sample sizes are small (expected counts < 5 in any cell).

Q2: What are the assumptions of the Chi-square test?
A: The test assumes random sampling, independence of observations, and sufficiently large expected counts (typically ≥5 in each cell).

Q3: Can I use this for larger tables?
A: This calculator is specifically for 2x2 tables. Larger tables require different degrees of freedom calculation.

Q4: What does degrees of freedom mean here?
A: For a 2x2 table, df=1 because knowing one cell value and the marginal totals determines all other cell values.

Q5: How accurate is the p-value calculation?
A: This provides an approximation. For exact p-values, consult Chi-square distribution tables or statistical software.