What is an F Distribution?
The f value, or f statistic, is a random variable that can be used 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 Chi-square and in the denominator Chi-square. 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 a critical F value in the table. If you use the alpha=.05, that means you are looking at the 95 percent confidence level. 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
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.