Latin Squares

There was a question during the Q&A about Latin Squares Design. Namely, what would a main effect of order indicate? Here is Dr. Clements' answer:

"That the time you were examining mattered (i.e., in a 4 X 4, that there were differences between 1, 2, 3, and 4...such as you might expect if there were cumulative effects of treatment [any treatment], but no differences among treatments)."