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The F-Bomb dropped on the F-Statistic
What is the F-Statistic and why is it so frackin’ important?
F-tests are named after its test statistic, F, which was named in honor of Sir Ronald Fisher. The F-statistic is a ratio of two variances. As a reminder, variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion.
An F-statistic is the variance ratio you get when you run an ANOVA test or regression analysis. This allows you to detect whether the averages between the two populations differ significantly. The variances of two populations can provide crucial information about the means. Think of it as serving a function similar to the T-statistic from a T-test; A T-test will show you whether one variable is statistically significant, while an F-test will show whether a group of variables is significant in the aggregate.
You can use the F-statistic when deciding to support or reject the null hypothesis. In your F test results, you’ll have both an F-value and an F-critical value.
- The value you calculate from your data is called the F-statistic or F-value (without the “critical” part).
- The F-critical value is a specific value that is compared to the F-value.
Generally, if your calculated F-value in a test is larger than your F-critical value, you can reject the null hypothesis. There is some sort of extant relationship between the variables. However, the statistic is only one measure of significance in an F-test. You should also consider the p-value. Everybody knows and loves the p-value, but you may not have known that the p-value is actually determined by the F statistic. It is the probability your results could have happened by chance.
The F-statistic must be used in combination with the p-value when you are deciding if your overall results are significant. This is because if you have a significant result, it doesn’t mean that all your variables are significant. The statistic is just comparing the joint effect of all the variables in aggregate.
