F-Test (Variance Ratio)

Compare the variances of two independent populations to see if they are significantly different.

Population Parameters

Group 1

Variance (s²)

Sample Size (n)

Group 2

Variance (s²)

Sample Size (n)

Test Significance

F-Statistic (G1 / G2)2.5000

No Significant Difference

Numerator df₁19

Denominator df₂14

Variance Ratio2.500

SensitivityHigh

Overview

The F-test determines if the variations in two groups are significantly different. It is calculated as the ratio of two variances. In science, we often want to know if a treatment not only changes the average but also makes the results more or less consistent. The F-test is also the foundation of ANOVA.

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Pro Tips

By convention, the larger variance is usually placed in the numerator so that the F-statistic is ≥ 1.
Degrees of freedom (df) are calculated as sample size minus one (n-1).
If the calculated F-value is significantly larger than the critical F-value, we reject the null hypothesis of equal variances.

Fun Facts

"The 'F' in F-test stands for Sir Ronald Fisher, who created it originally to compare crop yields."
"An F-statistic of 1 means the variances of the two groups are perfectly identical."
"The F-test is extremely sensitive to non-normality; if your data isn't bell-shaped, the result might be misleading."

Formula: F = Larger Variance / Smaller Variance

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F-Test (Variance Ratio)

Compare the variances of two independent populations to see if they are significantly different.

Population Parameters

Group 1

Variance (s²)

Sample Size (n)

Group 2

Variance (s²)

Sample Size (n)

Test Significance

F-Statistic (G1 / G2)2.5000

No Significant Difference

Numerator df₁19

Denominator df₂14

Variance Ratio2.500

SensitivityHigh

Overview

💡

Pro Tips

By convention, the larger variance is usually placed in the numerator so that the F-statistic is ≥ 1.
Degrees of freedom (df) are calculated as sample size minus one (n-1).
If the calculated F-value is significantly larger than the critical F-value, we reject the null hypothesis of equal variances.

Fun Facts

"The 'F' in F-test stands for Sir Ronald Fisher, who created it originally to compare crop yields."
"An F-statistic of 1 means the variances of the two groups are perfectly identical."
"The F-test is extremely sensitive to non-normality; if your data isn't bell-shaped, the result might be misleading."

Formula: F = Larger Variance / Smaller Variance

Used with this

Similar tools that might be useful

A/B Test Calculator

Determine if your test results are statistically significant.

Absolute vs Relative Uncertainty

Convert between Absolute (± unit) and Relative (%) uncertainty.

Adjusted R-Squared

Evaluate model fit while accounting for the number of predictors.