A definition of orthogonality in the context of statistics is
An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors.
Being a non-native speaker, I am not sure I understand that. With my favourite example of a latin square, how can I see this condition is satisfied?
123 1 ABC 2 BCA 3 CAB
How does this show the variables are orthogonal?