What is a Chi-square?

The chi-square (χ²) is a statistical value that indicates how the observed data align with the expected data in a test. To calculate it, you perform the chi-square statistic on a large sample of independent and mutually exclusive variables.

How to use the Chi-square calculator?

1. Select an option from the drop-down list: • Goodness of fit test • Test of independence • Find the critical value 2. Enter observed values separated by commas. Example: 18, 22, 20, 40 3. Enter expected values separated by commas. Example: 25, 25, 25, 25 4. Choose the significance level from the drop-down list: • 0.05 (95% confidence) • 0.01 (99% confidence) • 0.10 (90% confidence) 5. Enter the degree of freedom. 6. After entering the values, click 'Calculate', and in seconds, you will see the result.

Examples

Choose to Calculate “Goodness of fit test”

Observed values = 14, 17, 16, 22, 28, 23 Expected values = 20, 20, 20, 20, 20, 20 Significance level = 0.05 (95% confidence) Degree of freedom = 5 Step-By-Step Solution Step 1: Chi-Square Test Step 2: Significance level: α = 0.05 Step 3: Goodness of Fit Test Step 4: H₀: Data follows expected distribution Step 5: H₁: Data does not follow expected distribution Step 6: Degrees of freedom: df = categories - 1 = 6 - 1 = 5 Step 7: Category 1: (O-E)²/E = (14-20)²/20 = 1.8 Step 8: Category 2: (O-E)²/E = (17-20)²/20 = 0.45 Step 9: Category 3: (O-E)²/E = (16-20)²/20 = 0.8 Step 10: Category 4: (O-E)²/E = (22-20)²/20 = 0.2 Step 11: Category 5: (O-E)²/E = (28-20)²/20 = 3.2 Step 12: Category 6: (O-E)²/E = (23-20)²/20 = 0.45 Step 13: Chi-square statistic: χ² = 6.9 Result: Chi square statistic: 6.9 Degrees of freedom: 5 Critical value: Not available

Choose to Calculate “Test of independence”

Observed values = 20, 30, 40, 10 Expected values = 30, 20, 30, 20 Significance level = 0.05 (95% confidence) Degree of freedom = 1 Solution: H₀: Variables are independent H₁: Variables are dependent Contingency Table Analysis: Cell (0,0): O=20, E=20, (O-E)²/E=0 Cell (0,1): O=30, E=30, (O-E)²/E=0 Cell (0,2): O=40, E=40, (O-E)²/E=0 Cell (0,3): O=10, E=10, (O-E)²/E=0 Chi-square statistic: χ² = 0 Degrees of freedom: df = (rows-1)(cols-1) = 0 Result: chi-square statistics = 0

Choose to Calculate the critical value

Significance level = 0.05, Degree of freedom = 1 Step-By-Step Solution Step 1: Chi-square Critical Value Lookup Step 2: Degrees of freedom: 1 Step 3: Significance level: 0.05 Step 4: Critical value: Not available Result: Degrees of freedom: 1 Significance level: 0.05 Critical value: Not available

Why use the MathCalc chi-square calculator?

Get Quick Results

If you are finding the goodness of fit test, Test independence, or critical value by hand, it can be time-consuming, especially when dealing with large datasets. This free MathCalc chi-square calculator gives you accurate results in seconds.

Reduce Human Error

Manual math can lead to minor mistakes that cost you money or points. This tool provides proven formulas to reduce errors, and your results are always right. To avoid miscalculations, use the MathCalc Chi-square calculator.

User-Friendly

This free MathCalc Chi-square calculator calculates the exact goodness of fit test, test of independence, and critical value. It is helpful for students and teachers.

Tips for Best Results

• Always double-check your input.<br>• Choose a correct Test type.<br>• Always select the correct significance level.

FAQ

What does the X2 p-value mean?

It is the probability of seeing an x2 value at least as significant as yours if the null hypothesis is true. Small p-values suggest your data differ from what H0 null hypothesis predicts.

What is the difference between the goodness of fit test and the test of independence?

The goodness of fit test checks if a single categorical variable matches a specified distribution. Independence checks if two categorical variables are related.

Do my observed and expected lists must be the same length?

Yes! Each observed count must pair with one expected count.