# 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 .