1. What is the Chi-square Test?

The Chi-square test is a statistical method used to determine if there is a significant association between categorical variables in a contingency table. For a 6x6 table, it compares observed frequencies with expected frequencies under the assumption 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 for each cell (calculated as (row total × column total) / grand total)
• \( \sum \) — Summation over all cells in the table

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

3. Interpreting the Results

Details: The chi-square statistic is compared against critical values from the chi-square distribution with (rows-1)×(columns-1) degrees of freedom (25 for 6x6 table). A significant result (typically p < 0.05) suggests an association between variables.

4. Using the Calculator

Tips: Enter the observed counts for each cell in the 6x6 table. All values must be non-negative integers. The calculator will compute the chi-square statistic and degrees of freedom.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a chi-square test?
A: When you have categorical data in a contingency table and want to test for independence between the variables.

Q2: What are the assumptions of the test?
A: 1) Random sampling, 2) Observations are independent, and 3) Expected counts should be ≥5 in most cells (80% rule).

Q3: What if my expected counts are too small?
A: For small expected counts, consider Fisher's exact test or combine categories to increase expected frequencies.

Q4: How do I find the p-value?
A: Use the chi-square statistic and degrees of freedom with a chi-square distribution table or online calculator.

Q5: Can I use this for larger tables?
A: Yes, the chi-square test works for any r×c contingency table, though interpretation becomes more complex with larger tables.