On Deciding Whether Trend Surfaces of Progressively Higher Order Are Meaningful

In polynomial trend-surface analysis the only commonly used significance test is a comparison of the mean square associated with all terms of order ≤ k + 1with that for residual dispersion. Unless there is marked systematic association among deviations this test is basically irrelevant; once significance has been achieved at, say, order k , it is not likely to be lost by addition of terms of order greater than k, even if these terms do not reduce residual dispersion. A test of the mean square for variation associated with terms of order k + 1 only against residual dispersion at order k + 1 would be both more germane and more instructive. Examples are taken from the recent literature.