## Function F-Significance

(

**f-significance** < f-statistic > < numerator-dof > < denominator-dof > &optional < one-tailed-p > )

This function occurs in the statistical test of whether two observed samples

have the same variance. A certain statistic, F, essentially the ratio of the

observed dispersion of the first sample to that of the second one, is

calculated. This function computes the tail areas of the null hypothesis: that

the variances of the numerator and denominator are equal. It can be used for

either a one-tailed or two-tailed test. The default is two-tailed, but

one-tailed can be computed by setting the optional argument ` one-tailed-p' to<br> true.<br> <br> For a two-tailed test, this function computes the probability that F would be as<br> different from 1.0 (larger or smaller) as it is, if the null hypothesis is<br> true.<br> <br> For a one-tailed test, this function computes the probability that F would be as<br> LARGE as it is if the first sample's underlying distribution actually has<br> SMALLER variance that the second's, where `

numerator-dof' and ` denominator-dof'<br> is the number of degrees of freedom in the numerator sample and the denominator<br> sample. In other words, this computes the significance level at which the<br> hypothesis `

` the numerator sample has smaller variance than the denominator<br> sample'' can be rejected.<br> <br> A small numerical value implies a very significant rejection.<br> <br> The `

f-statistic' must be a non-negative floating-point number. The degrees of

freedom arguments must be positive integers. The ` one-tailed-p' argument is<br> treated as a boolean.<br> <br> This implementation follows Numerical Recipes in C, section 6.3 and the `

ftest'

function in section 13.4. Some of the documentation is also drawn from the

section 6.3, since I couldn't improve on their explanation.