e-Statistics

## F-Test

In the comparison of population means in two independent groups, say Group 1'' and Group 2,'' test procedures (pooled t-test and Wilcoxon test) often assume that the two population variances are approximately equal. This assumption itself can be treated as hypothesis test, and F-test is introduced for the plausibility of equal variances. The test is actually concerned with how Group 1 and Group 2 differ in terms of their respective population variance and .

The test procedure is based upon the sample standard deviations and from Group 1 and 2 with the respective sample size and . The test statistic is likely observed around, greater than, or less than unity under the respective null hypothesis  ,''  ,'' or  .'' The opposite of such observation is expressed by p-value < , suggesting an evidence against the null hypothesis . To check the plausibility of equal variances, we reason that the null hypothesis  '' can be accepted when we fail to reject it. The F-test is known to be very sensitive to the appropriateness of normality assumption.