Thanks for the response, Steve. It's good to hear from another animal scientist! The contrast coefficients I have in the SAS file were calculated by multiplying the coefficients for unequal spacing and unequal sample size from ORPOL by the respective samples size for each treatment (4, 4, 3, 4 for the 0, 120, 240, and 480 treatments, respectively). After some more digging, I've concluded that this approach isn't appropriate because it changes the relationships among the coefficients. I came across a helpful paper (Gaito, 1965; Unequal intervals and unequal n in trend analyses; Psychological Bulletin 63(2):125-127) that detailed the hand calculations for linear and quadratic coefficients and for the contrast SS. When I applied this approach to my data, the coefficients from the Gaito calculations were equivalent to those from ORPOL. I subsequently found that I could use the Singular option with the contrasts in GLM or Mixed and allow them to be estimable. This required the value in the Singular option to 0.1 for the linear contrast and 0.3 for the quadratic contrast. The contrast SS and P-values from the GLM output were very close to those from the Gaito calculations, although not identical. At this point, I've concluded that using the ORPOL coefficients for unequal spacing and unequal sample size per mean with the Singular option in Mixed or GLM is the best approach, but I suppose using the ORPOL coefficients and then calculating the contrast SS and conducting the F-test by hand is also an option.
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