F Distribution

The F distribution is a continuous probability distribution and is used within the analysis of variance (ANOVA) that uses the F-test in which the actual calculated value is compared to the F-test statistic for hypothesis testing.

This distribution is the probability of the ratio of two independent chi-square variables, with each divided by it's own degrees of freedom. 

Often used in ANOVA, which test whether population means are equal. 

It is used in both 1-Way ANOVA and 2-Way ANOVA. 

Rarely is the probability density function calculated mathematically. Thankfully that work has been done and F-tables with the most common levels of significance and degrees of freedom exist for reference.

BE CAREFUL when using tables. Some tables are for one-tailed test and others cover two-tailed test.

For a one-tailed test, the null hypothesis is rejected when the test statistic is greater than the value given in the F-table value. 

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