The F-statistic
The test statistic that represents the ratio of the variance within and between the groups is called the F-statistic. The closer F-statistic is to one, the more alike the two variances are. The F-statistic is calculated very simply as follows:
Here, is the variance between the groups and is the variance within the groups.
As the ratio F gets larger, the larger the variance between the groups is compared to the variance within the groups. This implies that the grouping is doing a good job in explaining the variance observed in the sample as a whole. Where this ratio exceeds a critical threshold, we can say that the difference is statistically significant.
Note
The F-test is always a one-tailed test, because any variance among the groups tends to make F large. It is impossible for F to decrease below zero.
The variance within for an F-test is calculated as the mean squared deviation from the mean. We calculate this as the sum of squared deviations from the mean divided by the...