Chi-Square Test Calculator - Free χ² Statistical Test
Chi-Square Test Calculator
Perform chi-square tests for independence and goodness of fit. Test relationships between categorical variables.
Test of Independence (Contingency Table)
| Column 1 | Column 2 | Row Total | |
| Row 1 | 20 | ||
| Row 2 | 20 | ||
| Column Total | 20 | 20 | 40 |
Enter whole numbers (counts) in each cell
Test Results
Chi-Square (χ²)
p-value
Degrees of Freedom
Observed vs Expected Frequencies
Detailed Calculations
Critical Values (α = 0.05)
Common significance levels:
- • α = 0.10: 10% significance (less strict)
- • α = 0.05: 5% significance (standard)
- • α = 0.01: 1% significance (more strict)
How to use this calculator
📊 How to Use This Calculator
- Choose test type: Independence or Goodness of Fit
- For Independence: Enter observed frequencies in contingency table
- For Goodness of Fit: Enter observed and expected frequencies
- Click calculate to see chi-square statistic and p-value
- Review the hypothesis test result and visualizations
📐 Understanding Chi-Square Tests
Test of Independence
Tests whether two categorical variables are related or independent.
Example: Is there a relationship between gender and voting preference?
Goodness of Fit Test
Tests whether observed data matches an expected distribution.
Example: Does dice roll frequency match expected fair dice?
Chi-Square Formula
χ² = Σ[(O - E)² / E]
Where O = observed, E = expected frequency
🌟 Real-World Examples
Example 1: Marketing Campaign
Test if response rates differ by customer segment
Independence test between segment and response
Example 2: Quality Control
Check if defect rates match expected proportions
Goodness of fit test for defect categories
Example 3: Medical Study
Test if treatment effectiveness varies by age group
Independence test between age and treatment outcome
💡 Pro Tips
- • Expected frequencies should be ≥ 5 for valid results
- • If expected < 5, consider combining categories
- • Large sample sizes can detect trivial differences
- • Always check practical significance, not just statistical
- • Use Cramér's V to measure effect size for independence
- • Consider Fisher's exact test for small samples
⚠️ Common Mistakes to Avoid
- • Don't use chi-square for continuous data
- • Ensure observations are independent
- • Don't use percentages - use actual counts
- • Check assumptions before interpreting results
- • Remember: association ≠ causation
- • Don't ignore cells with very low expected frequencies
About this calculator
Perform chi-square tests for independence and goodness of fit. Calculate chi-square statistic, p-value, and visualize expected vs observed frequencies.
Was this helpful?
Browse more in
Related Calculators
Mean, Median, Mode Calculator - Free Online Statistics Calculator
Calculate mean (average), median (middle value), and mode (most frequent) instantly. Includes step-by-step solutions and data visualization.
Standard Deviation Calculator - Free Online Variance & SD Calculator
Calculate standard deviation, variance, and coefficient of variation. Choose between population and sample calculations with visual distribution.
Correlation Coefficient Calculator - Free Pearson's r Calculator
Calculate Pearson correlation coefficient (r) between two variables. Includes scatter plot, regression line, and coefficient of determination (r²).
Z-Score Calculator - Free Standard Score & Probability Calculator
Calculate z-scores, find probabilities, and percentile ranks. Convert between raw scores and z-scores with visual normal distribution curve.
Confidence Interval Calculator - Free CI Calculator for Mean & Proportion
Calculate confidence intervals for population mean, proportion, and difference. Find margin of error and interpret results with visualization.
Linear Regression Calculator - Free Statistical Analysis Tool
Perform linear regression analysis. Calculate slope, intercept, R-squared, predictions, and residuals with scatter plot visualization.