# 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.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.