EXST7015 : Statistical Techniques II Geaghan ANOVA – Treatment Arrangements Orthogonal polynomial multipliers Page 1 19f-OrthogonalPolynomialTables Orthogonal Polynomial multipliers (equally spaced X) levels = 3 levels = 4 X l q X l q c 1 -1 1 1 -3 1 -1 2 0 -2 2 -1 -1 3 3 1 1 3 1 -1 -3 4 3 1 1 levels = 5 X l q c q 1 -2 2 -1 1 2 -1 -1 2 -4 3 0 -2 0 6 4 1 -1 -2 -4 5 2 2 1 1 levels = 6 1 -5 5 -5 1 -1 2 -3 -1 7 -3 5 3 -1 -4 4 2 -10 4 1 -4 -4 2 10 5 3 -1 -7 -3 -5 6 5 5 5 1 1 levels = 7 1 -3 5 -1 3 -1 1 2 -2 0 1 -7 4 -6 3 -1 -3 1 1 -5 15 4 0 -4 0 6 0 -20 5 1 -3 -1 1 5 15 6 2 0 -1 -7 -4 -6 7 3 5 1 3 1 1 levels = 8 1 -7 7 -7 7 -7 1 -1 2 -5 1 5 -13 23 -5 7 3 -3 -3 7 -3 -17 9 -21 4 -1 -5 3 9 -15 -5 35 5 1 -5 -3 9 15 -5 -35 6 3 -3 -7 -3 17 9 21 7 5 1 -5 -13 -23 -5 -7 8 7 7 7 7 7 1 1 levels = 9 1 -4 28 -14 14 -4 4 -1 1 2 -3 7 7 -21 11 -17 6 -8 3 -2 -8 13 -11 -4 22 -14 28 4 -1 -17 9 9 -9 1 14 -56 5 0 -20 0 18 0 -20 0 70 6 1 -17 -9 9 9 1 -14 -56 7 2 -8 -13 -11 4 22 14 28 8 3 7 -7 -21 -11 -17 -6 -8 9 4 28 14 14 4 4 1 1EXST7015 : Statistical Techniques II Geaghan ANOVA – Treatment Arrangements Orthogonal polynomial multipliers Page 2 19f-OrthogonalPolynomialTables For levels of X that are not equally spaced there is a SAS IML instruction that will produce the orthogonal polynomial multipliers. The following statements will do this if you have SAS IML available. OPTIONS PS=60 LS=78; PROC IML; RESET PRINT; X={1 , 2 , 3 , 4 , 8}; O=ORPOL(X,3); RUN; QUIT; where the X vector gives the levels of the quantitative variable. The orpol function needs one parameter specifying the name of the quantitative variable vector and a second parameter specifying the number of orthogonal polynomials levels
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