Question

determine whether the difference in the variance values is significant at 95 % confidence level using suitable test.

Answer 1

Purpose: Test if variances from two populations are equal

An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal. The one-tailed version only tests in one direction, that is the variance from the first population is either greater than or less than (but not both) the second population variance. The choice is determined by the problem. For example, if we are testing a new process, we may only be interested in knowing if the new process is less variable than the old process.

Definition

The F hypothesis test is defined as: H0: σ21 = σ22 Ha: σ21<σ22     for a lower one-tailed test σ21>σ22     for an upper one-tailed test σ21≠σ22     for a two-tailed test Test Statistic: F = s21/s22 where s21 and s22 and are the sample variances. The more this ratio deviates from 1, the stronger the evidence for unequal population variances. Significance Level: α Critical Region: The hypothesis that the two variances are equal is rejected if F>Fα,N1−1,N2−1    for an upper one-tailed test F<F1−α,N1−1,N2−1    for a lower one-tailed test F<F1−α/2,N1−1,N2−1 or F>Fα/2,N1−1,N2−1    for a two-tailed test where Fα, N1-1, N2-1 is the critical value of the F distribution with N1-1 and N2-1 degrees of freedom and a significance level of α. In the above formulas for the critical regions, the Handbook follows the convention that Fα is the upper critical value from the F distribution and F1-α is the lower critical value from the F distribution. Note that this is the opposite of the designation used by some texts and software programs.