FACT2K.PAS analyzes experimental data from a 2**k factorial
design. This is a common statistical technique used in examining
all possible combinations of two levels of k separate factors under
contorl of an experimentalist. As an illustration, a chemist may
wish to study the conversion yield of a catalytic reaction by running
experiments of two catalyst preparations, two temperatures, two
pressures, and two reactant ratios. Upon analyzing the data, the
chemist can determine the effects and interations of the various
treatments (temperature effect, pressure-catalyst interaction, ect.).
There are many variations of this technique: n**k designs, frac-
tional factorial, block designs, and replicated 2**k factorial designs.
They would be programmed similarly. For more information, study a book
on experimental statistics. Two elementary ones which I recommend are:
I. Guttman, S. Wilks, and J.S. Hunter, "Introductory
Engineering Statistics," (Wiley:1982).
G.E.P. Box, W.G. Hunter, and J.S. Hunter, "Statistics
for Experimentalist," (Wiley:1978).
The output from FACT2K using the input file FACT2K.IN is the same as
that shown in the appendix of Guttman, Wilks, and Hunter.
Of particular interest to me was the Yates' algorithm (1937) for
the 2**k factorial. This algorithm will manipulate specially ordered
data in (N log N) multiplications instead of the obvious N**2 method.
Its similarity to the fast Fourier transform is striking. John Tukey,
one of the world's foremost statisticians, only upon prompting outlined
his method of efficiently computing Fourier transforms. His total famil-
iarity with Yates' algorithm probably contributed to his under-estimation
of the FFT's inportance to computing.