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What is the F Distribution?

The F distribution is a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). An F statistic is a value obtained when an ANOVA or regression analysis is conducted. The F statistic can be used with the F distribution in an F test to determine if a group of variables is statistically significant. The F test will give an F statistic that determines if you can reject the null hypothesis, and a p-value determines if the results are statistically significant. The null hypothesis states that there is no significant difference between specified populations.

Why is this Useful?

The F distribution allows us to use an F statistic to compare two populations. For ANOVA tests we can use the F distribution to determine if the variance between the means of two populations significantly differ. The F distribution can also be used in regression analysis to compare the fit of different models. The F distribution allows us to obtain an F value that determines the p-value. A p-value is the probability of getting a result as extreme or more extreme as the one that you observed, given that the null hypothesis is true. 

Applications of the F Distribution

Statistical Analysis