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Checking orthogonalityThe set of contrasts we considered in the More Information page was:
For an orthogonal set, the following conditions must be met:
For the set above, the sum of each set of coefficients [1 −1 + 0] and [1/2 + 1/2 −1] is equal to zero. The following set of comparisons is not orthogonal: Rewriting this set of contrasts with their coefficients we get: The sum of each set of coefficients is still equal to zero, but the sum of their cross products is not equal to zero, namely [(1 × 0) + (−1 × +1) + (0 × −1)] = −1. Note that this simple method for checking orthogonality is only valid if each group has the same sample size.
