To calculate the height at $x$ of the graph of the F Distribution function with $dfn$ degrees of freedom associated with the numerator and $dfd$ degrees of freedom associated with the denominator,

**R**: use the functiondF(x,dfn,dfd)

**Excel**: use the functionF.DIST(x, dfn, dfd, FALSE)

The last argument for this function, when $FALSE$, indicates that the height of the function should be returned, instead of an area under the curve.

To calculate the area to the left of some $x$ and under a curve corresponding to a F distribution with $dfn$ degrees of freedom associated with the numerator and $dfd$ degrees of freedom associated with the denominator,

**R**: use the functionpf(x,dfn,dfd)

**Excel**: use the functionF.DIST(x, dfn, dfd, TRUE)

The last argument for this function, when $TRUE$, indicates the probability returned should be an area under the curve and not a height of the function's graph.

To find the cut-off $x$-value for which a random variable following a F distribution with $dfn$ degrees of freedom associated with the numerator and $dfd$ degrees of freedom associated with the denominator will produce an outcome less than $x$ with some given probability of $p$ (or, said another way, to find the $x$ value where there is an area of $p$ to the left of $x$ and under the related F distribution curve) ...

**R**: use the functionqf(p,dfn,dfd)

**Excel**: use the functionF.INV(p,dfn,dfd)

To generate $n$ values randomly selected from a F distribution with $dfn$ degrees of freedom associated with the numerator and $dfd$ degrees of freedom associated with the denominator,

**R**: use the functionrf(n,dfn,dfd)

**Excel**: copy the formula below to $n$ cellsF.INV(RAND(),dfn,dfd)