F Test Calculator
f-test calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
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Formula: F = s₁²/s₂² (larger variance on top)
Worked example — F=1.5625
F = s₁²/s₂² (larger variance on top)
Compares two sample variances to test if they are significantly different.
Problem:s₁²=25 (n=30), s₂²=16 (n=25)
Solution:F=25/16=1.5625, df=(29,24)
Result:F=1.5625
The F-test compares the ratio of two sample variances to determine whether they come from populations with equal variance. The F-statistic equals the larger variance divided by the smaller variance, so it is always ≥ 1 when arranged this way.
Use the F-test for variance equality when both samples are approximately normally distributed. Use Levene's test when normality cannot be assumed, as Levene's is more robust to departures from normality and less sensitive to outliers that would inflate the F-ratio.
The two samples must be independent of each other, each sample must be drawn from a normally distributed population, and the data should be measured on a continuous ratio or interval scale. Violations of normality, especially in small samples, can substantially inflate the Type I error rate.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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