Chi-Square Test of Independence Calculator

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Variables and Observed Data

Test Results

1. Expected Values Table

2. Chi-Square Test Statistic (χ²)

Calculated χ² =

Degrees of Freedom (df) =

3. Critical Values (χ²critical)

For α = 0.01 (1%): χ²critical ≈

For α = 0.05 (5%): χ²critical ≈

For α = 0.10 (10%): χ²critical ≈

Note: Critical values are approximate.

4. P-value

p =

5. Decision (at α = 0.05)

6. Conclusion (at α = 0.05)

7. Chi-Square Distribution Sketch (α = 0.05)

How to Use the Chi-Square Test of Independence Calculator

This guide will walk you through the process of setting up your data and interpreting the results for the Chi-Square Test of Independence, which determines if there is a statistically significant relationship between two categorical variables.

1

Understand the Hypothesis

The test aims to check the relationship between two variables. Your null hypothesis (H₀) is that the two variables are independent (no relationship). Your alternative hypothesis (H₁) is that they are dependent (a relationship exists).

Quick Check: Use this test only when both of your variables are categorical (for example, Gender and Favorite Color, or Political Party and Voting Intent).

2

Define Variables and Table Dimensions

Locate the input fields for the table setup:

  • Row Variable Name: Enter the descriptive name for the first categorical variable (for example, "Treatment Group").
  • Column Variable Name: Enter the descriptive name for the second categorical variable (for example, "Outcome").
  • Number of Rows (R): Set the number of categories for your Row Variable.
  • Number of Columns (C): Set the number of categories for your Column Variable.

The calculator will automatically generate a blank table based on the R x C dimensions you specify.

3

Input the Observed Data (Counts)

The contingency table is where you enter the observed frequencies (raw counts) for each combination of categories.

  • Enter Whole Numbers: Input the count of subjects or observations that fall into each cell of the table. These must be non-negative integers.
  • Ensure Totals: The calculator will calculate the marginal totals (row totals, column totals) and the grand total as you input the data.
  • Crucial: Do not enter percentages or probabilities; only enter the raw counts.
4

Analyze the Output

Once the data is entered, the calculator will immediately display the results, which include:

  • Degrees of Freedom (DF): Calculated as (R - 1) × (C - 1). This is used to determine the shape of the Chi-Square distribution.
  • Chi-Square Statistic (X²): The calculated test statistic value. Larger values indicate a greater difference between the observed counts and the expected counts (what you would expect if H₀ were true).
  • P-Value: The probability of observing a Chi-Square statistic as extreme as the one calculated, assuming the null hypothesis (independence) is true.

Making the Final Decision

Compare the P-Value to your chosen Significance Level (alpha), typically 0.05.

If P-Value ≤ alpha (for example, P ≤ 0.05): Reject H₀. Conclude that there is sufficient evidence to state that the two variables are dependent (related).

If P-Value > alpha (for example, P > 0.05): Fail to Reject H₀. Conclude that there is not enough evidence to state that the two variables are dependent; they are considered independent (no relationship).

Background: The Chi-Square Test of Independence

Σ

What Does This Test Measure?

The Chi-Square Test of Independence determines whether there is a statistically significant association between two categorical variables. It compares the observed frequencies in a contingency table to the frequencies you would expect if the variables were truly independent.

Formula: χ² = Σ [(Observed − Expected)² / Expected], where Expected = (Row Total × Column Total) / Grand Total. Degrees of freedom = (R − 1) × (C − 1).

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Worked Example

Suppose you survey 100 people on Gender (Male/Female) and Preference (Product A/Product B), and get: Male–A: 30, Male–B: 20, Female–A: 15, Female–B: 35. Running the test gives χ² ≈ 8.29 with df = 1, and p ≈ 0.004.

Since p < 0.05, we reject H₀. There is a statistically significant association between gender and product preference — the two variables are not independent.

R

How to Do This in R Studio?

Use the built-in chisq.test() function on a matrix of observed counts:

data <- matrix(c(30, 20, 15, 35), nrow = 2, byrow = TRUE)
        rownames(data) <- c("Male", "Female")
        colnames(data) <- c("Product A", "Product B")
        
        chisq.test(data, correct = FALSE)
S

How to Do This in SPSS?

Analyze → Descriptive Statistics → Crosstabs. Place one variable in Row(s) and the other in Column(s). Click Statistics and check Chi-square. Click Cells and check Expected under Counts. Click OK.

J

How to Do This in JASP?

Frequencies → Contingency Tables. Drag one variable into Rows and the other into Columns. Under Statistics, check χ² and Expected counts to view the test results and expected frequency table.

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