Function F-Significance

Part of:

package cl-mathstats
( 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&#39; 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&#39;s underlying distribution actually has<br> SMALLER variance that the second&#39;s, where numerator-dof' and denominator-dof&#39;<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&#39;&#39; 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&#39; 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.