Chi-Squared (χ²) Test Calculator
Use this calculator to perform a Chi-Squared test for independence on a 2×2 contingency table. Enter the observed frequencies in the fields below to determine if there is a significant association between two categorical variables.
Observed Frequencies (2×2 Table)
Enter the counts for each cell in your contingency table:
Understanding the Chi-Squared (χ²) Test
The Chi-Squared (χ²) test for independence is a non-parametric statistical test used to determine if there is a significant association between two categorical variables. In simpler terms, it helps you find out if two variables are related or if they are independent of each other.
When to Use It
This test is appropriate when you have two categorical variables, and you want to see if the observed frequencies in your sample differ significantly from the frequencies you would expect if there were no association between the variables. Common applications include:
- Analyzing survey data (e.g., is there a relationship between gender and political preference?).
- Medical research (e.g., is a new drug's effectiveness associated with patient age group?).
- Marketing studies (e.g., is there an association between advertising channel and customer purchase behavior?).
How the Test Works
The Chi-Squared test compares the observed frequencies (the actual counts from your data) with the expected frequencies (the counts you would expect if the two variables were truly independent). The core idea is that if the observed frequencies are very different from the expected frequencies, it suggests that there is an association between the variables.
The formula for the Chi-Squared statistic is:
χ² = Σ [(O – E)² / E]
- O represents the observed frequency in each cell of the contingency table.
- E represents the expected frequency in each cell, calculated as: (Row Total × Column Total) / Grand Total.
- Σ means "sum of" across all cells in the table.
Degrees of Freedom (df)
The degrees of freedom for a Chi-Squared test are calculated as: (Number of Rows – 1) × (Number of Columns – 1). For a 2×2 contingency table, the degrees of freedom will always be (2-1) × (2-1) = 1.
Interpreting the Results
Once you calculate the χ² value and the degrees of freedom, you compare your calculated χ² value to a critical value from a Chi-Squared distribution table (or use a p-value). A larger χ² value indicates a greater difference between observed and expected frequencies, suggesting a stronger association between the variables. If your calculated χ² value exceeds the critical value for your chosen significance level (e.g., 0.05), or if the p-value is less than your significance level, you would reject the null hypothesis of independence and conclude that there is a statistically significant association between the variables.
Example Scenario
Imagine a study investigating whether there's an association between a new teaching method and student pass rates. Researchers observed the following results:
- Group 1 (New Method), Passed: 30 students
- Group 1 (New Method), Failed: 20 students
- Group 2 (Traditional Method), Passed: 15 students
- Group 2 (Traditional Method), Failed: 35 students
Using the calculator with these values (30, 20, 15, 35), you can determine the Chi-Squared value and degrees of freedom to assess if the teaching method significantly impacts pass rates.