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

The Chi-square test for 2x2 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 frequency in each cell
• \( E \) — Expected frequency under independence
• \( \sum \) — Sum over all four cells of the 2x2 table

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

3. Importance of Chi-square Test

Details: This test is widely used in medical research, social sciences, and business analytics to examine relationships between categorical variables like treatment vs outcome, gender vs preference, etc.

4. Using the Calculator

Tips: Enter the four cell counts of your 2x2 table. All values must be non-negative integers. The calculator will compute the chi-square statistic which you can compare to critical values from chi-square distribution tables.

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 (any expected cell count <5) or when dealing with very rare events.

Q2: What degrees of freedom does a 2x2 test have?
A: A 2x2 Chi-square test has 1 degree of freedom (df = (rows-1)*(columns-1)).

Q3: How do I interpret the chi-square value?
A: Compare your calculated χ² to critical values from chi-square distribution tables at your desired significance level (typically 0.05).

Q4: Can I use this for larger tables?
A: This calculator is for 2x2 tables only. Larger tables require different calculators but use the same basic formula.

Q5: What are the assumptions of this test?
A: The test assumes independent observations, adequate sample size (all expected counts ≥5), and categorical data.