Chi-Square Test Calculator Free SPSS Research Tool

Chi-Square Test of Independence Calculator

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

Chi-Square Test of Independence Calculator Guide

How to Use the Chi-Square Test Calculator

  1. Enter your contingency table values in the input cells of the table.
  2. Optionally, use the Add Row, Remove Row, Add Column, or Remove Column buttons to adjust the table size as needed.
  3. Click "Calculate Chi-Square Test" to compute the results.
  4. View the results, including:
    • Chi-Square Statistic (χ²).
    • Degrees of Freedom.
    • p-value.
    • Conclusion (whether to reject or fail to reject the null hypothesis).
  5. 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

    1. Enter your contingency table values in the input cells of the table.
    2. Optionally, use the Add Row, Remove Row, Add Column, or Remove Column buttons to adjust the table size as needed.
    3. Click "Calculate Chi-Square Test" to compute the results.
    4. View the results, including:
      • Chi-Square Statistic (χ²).
      • Degrees of Freedom.
      • p-value.
      • Conclusion (whether to reject or fail to reject the null hypothesis).
    5. 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.