F Distribution

The F Distribution is a continuous probability distribution based on the ratio of two random variances. It is formed from the ratios of two chi-squared variables with the following formula.

F-distribution

It is often used in the hypothesis testing of variances as in ANOVA, analysis of variance. Levene's Test is similar, but is used when analyzing data that is not from (and can not be assumed) a normal distribution.

The value of F represents the ratio of two variances, and comparing the F-test value to the F-critical value is used to make a decision on the null hypothesis.

In ANOVA, the value of F is the ratio of the treatment variance to the error variance.

Rarely is the probabality 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, there are many varieties out there and all can be correct but only when interpreted correctly. 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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