Chi-Square Calculator
Calculate Chi-Square statistics, P-values, and degrees of freedom instantly. Supports Goodness of Fit and Test of Independence.
Enter your observed and expected values. Ensure the counts match.
Define your table dimensions and enter frequencies.
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. It compares observed data with the data we would expect to obtain according to a specific hypothesis.
Figure 1: The Chi-Square distribution showing the critical region for hypothesis testing.
The test is non-parametric and is widely used in research, quality control, and survey analysis. It helps answer questions like “Is this die fair?” or “Is there a relationship between gender and voting preference?”
Chi-Square Formula
- O: Observed frequency (actual count)
- E: Expected frequency (theoretical count under null hypothesis)
- χ²: The test statistic
Test of Independence Explained
This test analyzes the relationship between two categorical variables organized in a contingency table.
Figure 2: Structure of a contingency table used for Test of Independence.
The calculator automatically computes the Expected frequencies (E) for each cell using the formula: E = (Row Total × Column Total) / Grand Total.
Real-World Applications
Healthcare
Testing the effectiveness of treatments across patient groups.
Marketing
Analyzing customer preferences across different demographics.
Education
Comparing pass rates between different teaching methods.
Biology
Mendelian genetics experiments to check trait inheritance.
Frequently Asked Questions
Generally, a P-value less than 0.05 (5%) indicates statistical significance, meaning you reject the null hypothesis.
Fisher’s Exact Test is preferred when sample sizes are small (expected values less than 5 in any cell) for 2×2 tables.
No. The Chi-Square formula requires actual frequency counts (integers), not percentages or proportions.