Confidence Interval for Ratio of two Variances Calculator


Instructions: Use this step-by-step Confidence Interval for Ratio of two Variances Calculator \((\displaystyle \frac{\sigma_1^2}{\sigma_2^2})\), by providing the sample data in the form below:

Standard Deviation 1 (\(s_1\)) =
Sample Size 1 (\(n_1\))
Standard Deviation 2 (\(s_2\)) =
Sample Size 2 (\(n_2\))
Confidence Level (Ex: 0.95, 95, 99, 99%) =



More about the confidence interval for the ratio of population variances

A confidence interval is an statistical concept that refers to an interval that has the property that we are confident at a certain specified confidence level that the population parameter, in this case, the ratio of two population variances, is contained by it. For the case the ratio of population variances (\(\sigma_1^2\sigma_2^2/\)), the following expression is used:

\[ CI = \displaystyle \left( \frac{s_1^2}{s_2^2} F_{1-\alpha/2, n_2-1, n_1-1}, \frac{s_1^2}{s_2^2} F_{\alpha/2, n_2-1, n_1-1} \right) \]

where the critical values corresponds to critical values associated to the F distribution. The critical values for the given \(\alpha\) and \(df_1 = n_1 - 1\) and \(df_2 = n_2 - 1\) degrees of freedom are \(F_L = F_{1-\alpha/2, n_2-1, n_1-1\) and \(F_U = F_{\alpha/2, n_2-1, n_1-1\).

Assumptions that need to be met

As with most parametric procedures, we need the samples 1 and 2 to come from a normally distributed populations, which is especially the case for small sample sizes.

Roughly speaking, every population parameter has a parametric expression to find a confidence interval. If you are interested in only one population variance, you can use this variance confidence interval calculator . Or you can use our confidence interval for the mean , or this confidence interval for variance when mean is known , or you can also use this confidence interval for mean regression responses .

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