f(3)
NAME
Statistics::Table::F - Perl module for computing the
statistical F-ratio
SYNOPSIS
use Statistics::Table::F;
if (($F = anova($list_of_lists)) >= F(@$list_of_lists 1,
count_elements($list_of_lists - @$list_of_lists),
0.05)) {
print "F is $F; the difference between your data
sets is significant.0;
} else {
print "F is $F; the difference between your data
sets is not significant.0;
}
DESCRIPTION
See Orwant, Hietaniemi, and Macdonald, Mastering
Algorithms in Perl, O'Reilly 1999. From Chapter 15:
The significance tests covered so far can only pit one
group against another. Sure, we could do a t-test of
every possible pair of web design firms, but we'd have
trouble integrating the results.
An analysis of variance, or ANOVA, is necessary when you
need to consider not just the variance of one data set but
the variance between data sets. The sign, ChiSquare, and
t-tests all involved computing intrasample descriptive
statistics; we'd speak of the means and variances of
individual samples. Now we can jump up a level of
abstraction and start thinking of entire data sets as
elements in a larger data set -- a data set of data sets.
For our test of web designs, our null hypothesis is that
the design has no effect on the size of the average sale.
Our alternative is simply that some design is different
from the rest. This isn't a very strong statement; we'd
like a little matrix that show us how each design compares
to one another and to no design at all. Unfortunately,
ANOVA can't do that.
The key to the particular analysis of variance we'll study
here, a one-way ANOVA, is computing the F-ratio. The
F-ratio is defined as the mean square between (the
variance between the means of each data set) divided by
the mean square within (the mean of the variance
estimates). This is the most complex significance test
we've seen so far. Here's a Perl program that computes
the analysis of variance for all four designs. Note that
since ANOVA is ideal for multiple data sets with varying
numbers of elements, we choose a data structure to reflect
that: $designs, a list of lists.
AUTHOR
Jon Orwant, orwant@media.mit.edu
SEE ALSO
- Statistics::ChiSquare, Statistics::Table::t