A Unifying Computational Method for the
Analysis of Complete Factorial Experiments

A computational method which may be used for
the calculation of sums of squares in the analysis 
of variance of complete factorial experiments and in
the computation of main effect or interaction means 
is described.  The method is elucidated as unifying since
one method can be used for a variety of purposes 
each previously requiring different methods.  The programming
advantages of such a method are obvious. 
 The following variants are discussed: (1) the standard
analysis of variance; (2) analyses omitting certain 
levels of one or more factors; (3) separate analyses
for some levels of a factor or for combinations 
of levels of more than one factor.  These are performed
simultaneously; (4) the calculation of main effect 
or interaction means.  The mean expects the data in standard
order and it leaves the data in that order 
so that many analyses of the same data can be performed
without rearrangement.  The total sum of squares, 
excluding a replication sum of squares, is partitioned
into all polynomial partitions and their interactions 
each with one degree of freedom.  This is so even
if factors have unequally spaced factor levels.

CACM January, 1967

Cooper, B. E.

CA670105 JB February 28, 1978  4:49 PM

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