CI for the Ratio of Two Variances
Computes the confidence interval for the ratio between the variances of two normal populations, σ₁²/σ₂². Instead of just testing whether the variances differ, it gives a plausible range for how many times one is larger than the other. If the interval contains the number 1, there's no evidence the spreads are different. The calculation uses the F distribution, and because it's asymmetric, the bounds come from F quantiles with the degrees of freedom swapped. Enter the two samples and the confidence level.
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CI for the Ratio of Two Variances
Computes the confidence interval for the ratio between the variances of two normal populations, σ₁²/σ₂². Instead of just testing whether the variances differ, it gives a plausible range for how many times one is larger than the other. If the interval contains the number 1, there's no evidence the spreads are different. The calculation uses the F distribution, and because it's asymmetric, the bounds come from F quantiles with the degrees of freedom swapped. Enter the two samples and the confidence level.
How many times does one variance exceed the other?
Comparing variances with a hypothesis test only says whether they differ. But when they do, the next question is by how much: is one process's spread twice the other's, or ten times larger? The confidence interval for the ratio of variances answers that, delivering a plausible range for σ₁²/σ₂².
The interval rests on the F distribution, which describes how the ratio of sample variances behaves. There's a subtlety that often confuses: because the F isn't symmetric and its two degrees of freedom play distinct roles, the lower and upper bounds use F quantiles with the order of the degrees of freedom swapped. The result is an interval that usually isn't centered on the observed ratio.
Enter the two samples and the confidence level. The tool returns the bounds of the interval for the variance ratio. A practical reading: if the entire interval falls above or below 1, there's evidence the spreads differ; if it spans 1, you can't claim one population varies more than the other.
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CI for Variance and Standard Deviation
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Prediction Interval (New Observation)
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.