ABSTRACT
IN Chapter 6 the N cases under discussion were treated as belonging to one group. We will now go on to consider the variation which becomes observable when they are separated into a certain number of groups, say g. ‘Canonical variate analysis’ as it is frequently called, or ‘canonical analysis of discriminance’ as I would prefer to call it, is an extension of principal component analysis to the variation observed between groups in a multidimensional space. To introduce the notation, let us start with a single variable X, used to measure N individuals forming representative samples of g groups, A, B …G. Any data originating from one of the groups can be indicated by one of the subscripts a, b … g. Thus https://www.w3.org/1998/Math/MathML"> n g = the number of cases in group G ∑ x g = the sum of the observed measurements in these cases ∑ x g 2 = the sum of the squares of the measurements https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203753477/d140bb0d-3d08-4a5a-95b0-80201b76fae6/content/math_22_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> (Note that x is now used for a raw, unstandardized score.)
