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 6x2 table, it compares observed frequencies with 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 null hypothesis
• \( \sum \) — Sum over all cells in the table

Calculation Steps:

1. Calculate row and column totals
2. Compute expected counts: (row total × column total) / grand total
3. Calculate (O-E)²/E for each cell
4. Sum all values to get χ² statistic

3. Interpreting the Results

Details: Compare the calculated χ² value to critical values from the Chi-square distribution with (rows-1)×(columns-1) = 5 degrees of freedom. Higher values indicate greater deviation from expected counts.

4. Using the Calculator

Tips: Enter observed counts for each cell in the 6x2 table. All values must be non-negative integers. The calculator will compute the χ² statistic.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a Chi-square test?
A: When you have categorical data and want to test if distributions differ between groups or if variables are independent.

Q2: What are the assumptions?
A: Observations must be independent, categories mutually exclusive, and expected counts should be ≥5 in most cells.

Q3: What if my expected counts are too small?
A: Consider Fisher's exact test or combine categories if appropriate.

Q4: How do I find the p-value?
A: Use a Chi-square distribution table with (6-1)×(2-1)=5 degrees of freedom or statistical software.

Q5: Can I use this for larger tables?
A: The formula works for any RxC table, but this calculator is specifically designed for 6x2 tables.