Chi-Square Test of Independence Calculator
Enter Your Contingency Table
Category | Group 1 | Group 2 | Total |
---|---|---|---|
Category 1 | 50 | ||
Category 2 | 50 | ||
Total | 55 | 45 | 100 |
Interpretation Guide
- Null Hypothesis (H₀): The two variables are independent (no association)
- Alternative Hypothesis (H₁): The two variables are associated
- Significance Level (α): Typically 0.05
- Decision Rule: If p-value ≤ α, reject H₀ (significant association)
Chi-Square Test of Independence Calculator Guide
How to Use the Chi-Square Test Calculator
- Enter your contingency table values in the input cells of the table.
- Optionally, use the Add Row, Remove Row, Add Column, or Remove Column buttons to adjust the table size as needed.
- Click "Calculate Chi-Square Test" to compute the results.
- View the results, including:
- Chi-Square Statistic (χ²).
- Degrees of Freedom.
- p-value.
- Conclusion (whether to reject or fail to reject the null hypothesis).
- Review the expected frequencies and chi-square contributions tables for detailed calculations.
Key Features of the Chi-Square Test Calculator
User-Friendly Input
- Dynamic contingency table with adjustable rows and columns.
- Pre-filled example data for quick testing.
- Real-time row, column, and grand total calculations as you input data.
Accurate Calculations
- Implements the Chi-Square Test of Independence formula: χ² = Σ[(O - E)² / E], where O is observed frequency and E is expected frequency.
- Handles edge cases (e.g., zero values, invalid inputs) with clear error messages.
- Calculates degrees of freedom: (rows - 1) × (columns - 1).
- Computes p-value using an approximation of the chi-square distribution.
Detailed Results
Displays:
- Chi-Square Statistic (
Chi-Square Test of Independence Calculator Guide Chi-Square Test of Independence Calculator Guide
How to Use the Chi-Square Test Calculator
- Enter your contingency table values in the input cells of the table.
- Optionally, use the Add Row, Remove Row, Add Column, or Remove Column buttons to adjust the table size as needed.
- Click "Calculate Chi-Square Test" to compute the results.
- View the results, including:
- Chi-Square Statistic (χ²).
- Degrees of Freedom.
- p-value.
- Conclusion (whether to reject or fail to reject the null hypothesis).
- Review the expected frequencies and chi-square contributions tables for detailed calculations.
Key Features of the Chi-Square Test Calculator
User-Friendly Input
- Dynamic contingency table with adjustable rows and columns.
- Pre-filled example data for quick testing.
- Real-time row, column, and grand total calculations as you input data.
Accurate Calculations
- Implements the Chi-Square Test of Independence formula: χ² = Σ[(O - E)² / E], where O is observed frequency and E is expected frequency.
- Handles edge cases (e.g., zero values, invalid inputs) with clear error messages.
- Calculates degrees of freedom: (rows - 1) × (columns - 1).
- Computes p-value using an approximation of the chi-square distribution.
Detailed Results
Displays:
- Chi-Square Statistic (χ²).
- Degrees of Freedom.
- p-value.
- Conclusion based on significance level (typically α = 0.05).
- Expected frequencies table.
- Chi-square contributions table for each cell.
Robust Error Handling
- Displays clear error messages for invalid inputs (e.g., zero grand total, zero expected frequencies).
- Ensures at least one row and one column remain in the table for valid calculations.
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