Hello all: I am seeking advice for the analysis of a field research study that used a 2 x 4 factorial plus control arrangement of treatments. The study investigated the effects of frequency (once or biweekly) and rate (0.075, 0.15, 0.3, and 0.6 L m^-2) of a product applied to a field crop. First I analyzed the data as a factorial (omitting the control) and used orthogonal polynomials to evaluate rate response (linear, quadratic, cubic). Second, I analyzed the data using one-way single degree-of-freedom contrasts to compare specific treatments (e.g., control vs. all treatments). I am curious if it is valid to use to the untreated control as a "0" level while evaluating response (linear, quadratic, cubic, and quartic) to rate (e.g. 0, 0.075, 0.15, 0.3 and 0.6) by using single degree of freedom contrast to represent the orthogonal polynomials. I used PROC IML to generate coefficients for these levels: 0 (control) 0.075 0.15 0.3 0.6 Linear -0.474342 -0.31623 -0.15811 0.158114 0.790569 Quadratic 0.5459642 0.035224 -0.33462 -0.65164 0.40507 Cubic -0.469987 0.422258 0.514346 -0.5705 0.10388 Quartic 0.2367184 -0.72143 0.631249 -0.15781 0.011272 The rates (0.075, 0.15, 0.3 and 0.6) appear in each level of the frequency factor (twice per replication) and there is only one control ("0") per replication. Is it possible to divide the above coefficients for the 4 rates (0.075, 0.15, 0.3 and 0.6) by 2 and construct contrast statements as follows: TRMT 1 2 3 4 5 6 7 8 9 FREQ Single Biweekly RATE Control (0) 0.075 0.15 0.3 0.6 0.075 0.15 0.3 0.6 Linear -0.474342 -0.15811 -0.07906 0.079057 0.395285 -0.15811 -0.07906 0.079057 0.395285 Quadratic 0.5459642 0.017612 -0.16731 -0.32582 0.202535 0.017612 -0.16731 -0.32582 0.202535 Cubic -0.469987 0.211129 0.257173 -0.28525 0.05194 0.211129 0.257173 -0.28525 0.05194 Quartic 0.2367184 -0.36071 0.315624 -0.07891 0.005636 -0.36071 0.315624 -0.07891 0.005636 I am having a very hard time finding any texts, articles, or online resources that answer my question. I can provide further information if needed. Your help would be greatly appreciated! Thanks!
... View more