# How to Use f-distributions in Excel

f-distributions are probability distributions in Excel that compare the ratio in variances of samples drawn from different populations. That comparison produces a conclusion regarding whether the variances in the underlying populations resemble each other.

## F.DIST: Left-tailed f-distribution probability

The F.DIST function returns the left-tailed probability of observing a ratio of two samples’ variances as large as a specified f-value. The function uses the syntax

=F.DIST(x,deg_freedom1,deg_freedom2,cumulative)

where x is specified f-value that you want to test;* *deg_freedom1 is the degrees of freedom in the first, or numerator, sample;* *deg_freedom2 is the degrees of freedom in the second, or denominator, sample, and cumulative is a logical value (0 or 1) that tells Excel whether you want to calculate the cumulative distribution (indicated by setting cumulative to 0) or the probability density (indicated by setting cumulative to 1).

As an example of how the F.DIST function works, suppose you compare two sample’s variances, one equal to and one equal to . This means the f-value equals . Further assume that both samples number 10 items, which means both samples have degrees of freedom equal to and that you want to calculate a cumulative probability. The formula

=F.DIST(2/4,9,9,0)

returns the value 0.6851816.

## F.DIST.RT: Right-tailed f-distribution probability

The F.DIST.RT function resembles the F.DIST function. F.DIST.RT returns the right-tailed probability of observing a ratio of two samples’ variances as large as a specified f-value. The function uses the syntax

=F.DIST.RT(x,deg_freedom1,deg_freedom2,cumulative)

where *x* is specified f-value that you want to test;* **deg_freedom1* is the degrees of freedom in the first, or numerator, sample; *deg_freedom2* is the degrees of freedom in the second, or denominator, sample, and *cumulative* is a logical value (0 or 1) that tells Excel whether you want to calculate the cumulative distribution (indicated by setting *cumulative* to 0) or the probability density (indicated by setting *cumulative* to 1).

As an example of how the F.DIST.RT function works, suppose you compare two sample’s variances, one equal to and one equal to . This means the f-value equals . Further assume that both samples number 10 items, which means both samples have degrees of freedom equal to and that you want to calculate a cumulative probability. The formula

=F.DIST.RT(2/4,9,9)

returns the value 0.841761 suggesting that there’s roughly an 84-percent probability that you might observe an f-value as large as if the samples’ variances were equivalent.

## F.INV:Left-tailed f-value given f-distribution probability

The F.INV function returns the left-tailed f-value equivalent to a given f-distribution probability. The function uses the syntax

=F.INV(probability,deg_freedom1,deg_freedom2)

where *probability* is probability of the f value that you want to find;* **deg_freedom1* is the degrees of freedom in the first, or numerator, sample; and *deg_freedom2* is the degrees of freedom in the second, or denominator, sample.

## F.INV.RT:Right-tailed f-value given f-distribution probability

The F.INV.RT function returns the right-sided f-value equivalent to a given f-distribution probability. The function uses the syntax

=F.INV.RT(probability,deg_freedom1,deg_freedom2)

where *probability* is probability of the f-value that you want to find; *deg_freedom1* is the degrees of freedom in the first, or numerator, sample;* **deg_freedom2* and is the degrees of freedom in the second, or denominator, sample.

## F.TEST: Probability data set variances not different

The F.TEST function compares the variances of two samples and returns the probability that variances aren’t significantly different. The function uses the syntax

=F.TEST(array1,array2)

where *array1* is a worksheet range holding the first sample and is a worksheet range holding the second sample.