Chi-Square Test for Independence

Chi-Square Test for Independence Calculator

Chi-Square Test for Independence

Contingency Table Setup

Observed Frequencies

Enter the observed counts for each cell. You can also name your row and column categories.

Assumptions: Data are counts/frequencies. Observations are independent. Expected frequencies should generally be ≥ 5 for most cells for test validity (this tool doesn't check this strictly).

Chi-Square Test Results

Setup table and click "Run Test" to see results.

Test Statistics:

Chi-Square Value (χ²):N/A
Degrees of Freedom (df):N/A
P-value:N/A
Significance Level (α):N/A
Awaiting calculation...

Expected Frequencies Table

Interpreting Results & Export

Chi-Square Test for Independence

The Chi-Square (χ²) test for independence is used to determine whether there is a statistically significant association between two categorical (nominal or ordinal) variables. It compares the observed frequencies in a contingency table with the frequencies that would be expected if the two variables were independent.

  • Null Hypothesis (H0): The two categorical variables are independent (i.e., there is no association between them).
  • Alternative Hypothesis (H1): The two categorical variables are dependent (i.e., there is an association between them).

Interpretation Steps:

  1. Calculate Chi-Square (χ²) Statistic: This measures the discrepancy between observed and expected frequencies. A larger χ² value suggests a greater difference.
  2. Determine Degrees of Freedom (df): Calculated as (Number of Rows - 1) * (Number of Columns - 1).
  3. Find the P-value: This is the probability of observing a χ² statistic as large as (or larger than) the one calculated, assuming the null hypothesis (independence) is true.
  4. Make a Decision:
    • If p-value ≤ α (significance level): Reject the null hypothesis (H0). Conclude there is a statistically significant association between the variables.
    • If p-value > α: Fail to reject the null hypothesis (H0). Conclude there is not enough evidence to say there's an association between the variables (this doesn't prove independence, just a lack of evidence for dependence).

Note on Expected Frequencies: The test is generally considered reliable if most (e.g., >80%) of the expected cell frequencies are 5 or greater, and no expected cell frequency is less than 1. If this condition is not met, other tests like Fisher's Exact Test might be more appropriate, especially for small tables (e.g., 2x2).

Export Results

© Chi-Square Test for Independence Calculator. For educational purposes.