Chi-Square Test Calculator

How to calculate Chi-Square?

The Chi-Square test of independence is a statistical method used to determine if there is a significant association between two categorical variables. It works by comparing the observed frequencies in your data to the expected frequencies if the variables were completely independent.

Chi-Square = Σ[(O - E)² / E]

Using the Chi-Square calculator: an example

Consider a medical study where participants are split into a Treatment group and a Control group. Researchers track whether the participants Improved or Did Not Improve. This data forms a 2x2 contingency table used to calculate if the treatment had a statistically significant impact.

Step-by-step calculation:

1. Calculate expected frequencies: Based on the row and column totals, find the expected value for each cell.
2. Apply the formula: For each cell, subtract the expected value from the observed value, square the result, and divide by the expected value.
3. Sum the results: Add up the values calculated in the previous step for all cells in the table.
4. Compare to critical value: Use the final Chi-Square sum and the degrees of freedom to determine the p-value or compare against a distribution table.

Frequently Asked Questions

What is a 2x2 contingency table?

A 2x2 contingency table is a matrix used to display the frequency distribution of two categorical variables, each having exactly two levels (e.g., Male/Female and Pass/Fail).

What does a p-value less than 0.05 mean?

A p-value below 0.05 indicates that the observed association between variables is statistically significant, suggesting there is less than a 5% chance the results happened by coincidence.

When should I use this test instead of a T-test?

You should use a Chi-Square test when you are comparing categorical data (counts and groups). A T-test is intended for comparing the means of continuous numerical data between two groups.