What is an F Distribution?
The f value, or f statistic, is a random variable that can be used in an f test to compare two variances. The f value has an f distribution. The f distribution is used most often in Analysis of Variance (ANOVA/MANOVA) and is a ratio of two Chi-square distributions. Each F distribution has a specific degrees of freedom in the numerator and in the denominator. The numerator degrees of freedom are always first, as changing the order of degrees of freedom changes the distribution; for example F(9,11) does not equal F(11,9)).
What is the F Statistic Table Used for?
When you have found the F value, you can compare it with an f critical value in the table. If your observed value of F is larger than the value in the F table, then you can reject the null hypothesis with 95 percent confidence that the variance between your two populations isn’t due to random chance.
How to use the F Statistic Table
The F Statistic Table is actually a collection of tables. Which specific table you use will depend on which alpha level you use. For example, if you have an alpha level of .05, then your right tail area is .05 (5 percent), and you’ll look up the f critical value in the alpha level = .05 table. The rows in the F Distribution Table represent denominator degrees of freedom and the columns represent numerator degrees of freedom.
For example, to determine the .10 critical value for an F distribution with 6 and 6 degrees of freedom, look in the 6 column (numerator) and the 6 row (denominator) of the F Table for alpha=.10. F(.10, 6, 6) = 3.05455.
Why Use the F Statistic Table? Why not just use a calculator?
A calculator will certainly give you a fast answer. But with many scenarios in statistics, you will look at a range of possibilities and a table is much better for visualizing a large number of probabilities at the same time.