Tony Paletta wrote on Fri, Dec 12, 2003 02:24 PM UTC:
Mark,
Latin Squares are typically used when experimental plans involve
'treatment ordering' or 'incomplete block' (nesting of subjects under
some combination of treatments) designs where there is a possibility of
correlation between treatment and assignment. The 'orthogonal' is the
sense of 'uncorrelated' (== zero cosine == 'right angle'), meaning
that there no overall correlation or covariance is introduced between
treatment and assignment (which would otherwise 'confound' a treatment
effect, making it indistinguishable from the assignment or ordering
effect).
(Just a rough sketch from memory; if this sounds like Greek to you, rest
assured that the things called Greco-Latin Squares serve the same
'orthogonal' master).