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 7x7 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 under independence (row total × column total / grand total)
• The sum is over all 49 cells in the 7×7 table

Explanation: Large deviations between observed and expected values result in a higher chi-square statistic, indicating a potential association between variables.

3. Interpreting Results

Details: Compare your chi-square statistic to critical values from the chi-square distribution with 36 degrees of freedom (for 7x7 table). Higher values indicate stronger evidence against the null hypothesis of independence.

4. Using the Calculator

Tips: Enter observed counts for each cell in the 7×7 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: What are the assumptions of the chi-square test?
A: The test assumes random sampling, independence of observations, and that expected counts are ≥5 in most cells.

Q2: What if my expected counts are too small?
A: For small expected counts, consider Fisher's exact test or combine categories to increase expected values.

Q3: Can I use this for tables smaller than 7×7?
A: Yes, but degrees of freedom will change (df = (rows-1)×(columns-1)).

Q4: How do I find the p-value?
A: Use a chi-square distribution table or statistical software with your χ² value and degrees of freedom.

Q5: What does a significant result mean?
A: It suggests an association between variables, but doesn't indicate the nature or strength of the relationship.