Chi-Square Test Calculator (2×2)
Category
Group A
Group B
Outcome 1
Outcome 2
Test Results
Chi-Square Statistic (χ²):
0
Degrees of Freedom (df):
1
P-Value:
0
Result:
–
Understanding the Chi-Square Test of Independence
The Chi-Square test of independence is a statistical method used to determine if there is a significant relationship between two categorical variables. For example, you might use it to see if gender (Male/Female) is associated with voting preference (Candidate A/Candidate B).
How to Use This Calculator
- Input Data: Enter your observed frequencies into the 2×2 table. These must be raw counts, not percentages or means.
- Calculate: Click the "Calculate Significance" button to process the mathematical formula.
- Analyze P-Value: A p-value less than 0.05 usually suggests that the relationship between the variables is statistically significant.
The Mathematical Formula
The calculator uses the standard Chi-Square formula:
χ² = ∑ [ (Oi – Ei)² / Ei ]
Where:
- Oi: Observed frequency in each cell.
- Ei: Expected frequency, calculated as (Row Total × Column Total) / Grand Total.
Real-World Example
Imagine a medical study testing a new treatment:
| Group | Recovered | Not Recovered |
|---|---|---|
| Treatment Group | 85 | 15 |
| Placebo Group | 60 | 40 |
By entering these values (85, 15, 60, 40), the calculator will determine if the recovery rate is significantly different between the two groups or if the results could have occurred by chance.
Interpreting Your Results
If your P-Value is ≤ 0.05, you "Reject the Null Hypothesis." This means there is evidence that the two variables are related. If the P-Value is > 0.05, you "Fail to Reject the Null Hypothesis," suggesting any observed difference is likely due to random sampling variation.