F F-Test Calculator
Compare two population variances with an F statistic and two-sided p-value.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Compare two population variances with an F statistic and two-sided p-value.
| Concept | Formula or rule |
|---|---|
| F-Test Calculator | F = s₁² / s₂² |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: Variance 25 divided by variance 16 gives F=1.5625.
✓ df₁=19 and df₂=17
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Entering standard deviations as variances
Square SDs first.
Square SDs first.
⚠️
Ignoring non-normality
The classical variance F-test is sensitive to departures from normality.
The classical variance F-test is sensitive to departures from normality.
⚠️
Forgetting numerator order
Swapping variances reciprocates F and swaps degrees of freedom.
Swapping variances reciprocates F and swaps degrees of freedom.
Practice Questions
1. If variances are equal, what is F?
Answer: 1
2. What is df1 when n1=10?
Answer: 9
3. Can F be zero?
Answer: Only if the numerator variance is zero, outside the positive-input test here.
Frequently Asked Questions
What is the null hypothesis?▾
The population variances are equal.
What are the degrees of freedom?▾
n1−1 and n2−1.
Is F negative?▾
No.