**Orthogonality**: A
cross factored design is orthogonal if each of its factors is independent of
each other. Two categorical cross factors are orthogonal by design if each
level of one is measured at every level of the other. Two covariates are
orthogonal only if they have a correlation coefficient of zero. Orthogonal designs
partition total variation in the response straightforwardly into independent
hypotheses using sequential sums of squares for each effect in turn. Although a
balanced design generally (but not inevitably) ensures orthogonality, this can
be difficult to achieve in practice, especially with covariates. Loss of orthogonality can
reduce or enhance the power of a design to detect effects,
and usually requires analysis with the aid of adjusted sums of squares
calculated in a General Linear Model (GLM).

Doncaster, C. P. & Davey, A. J. H. (2007) *Analysis of Variance and Covariance: How to
Choose and Construct Models for the Life Sciences*. Cambridge: Cambridge
University Press.

http://www.southampton.ac.uk/~cpd/anovas/datasets/