> woolfrict.sp1 <- aov(shrink ~ trt + runnum + trt:runnum + revs + revs:trt) > summary(woolfrict.sp1) Df Sum Sq Mean Sq F value Pr(>F) trt 3 3012.5 1004.18 729.1367 < 2.2e-16 *** runnum 3 124.3 41.43 30.0815 1.024e-12 *** revs 6 11051.8 1841.96 1337.4577 < 2.2e-16 *** trt:runnum 9 114.6 12.74 9.2487 3.546e-09 *** trt:revs 18 269.5 14.97 10.8718 4.620e-14 *** Residuals 72 99.2 1.38 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > # This model uses correct error terms for trt and revs and interaction > woolfrict.sp2 <- aov(shrink ~ trt*revs + Error(runnum/trt)) > summary(woolfrict.sp2) Error: runnum Df Sum Sq Mean Sq F value Pr(>F) Residuals 3 124.29 41.429 Error: runnum:trt Df Sum Sq Mean Sq F value Pr(>F) trt 3 3012.53 1004.18 78.836 8.81e-07 *** Residuals 9 114.64 12.74 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Error: Within Df Sum Sq Mean Sq F value Pr(>F) revs 6 11051.8 1841.96 1337.458 < 2.2e-16 *** trt:revs 18 269.5 14.97 10.872 4.62e-14 *** Residuals 72 99.2 1.38 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > # Partitions the Revs SS into orthogonal polynomials > summary(woolfrict.sp2,split=list(revs=list(linear=1, quadratic=2, + cubic=3, quartic=4, quintic=5, sextic=6))) Error: runnum Df Sum Sq Mean Sq F value Pr(>F) Residuals 3 124.29 41.429 Error: runnum:trt Df Sum Sq Mean Sq F value Pr(>F) trt 3 3012.53 1004.18 78.836 8.81e-07 *** Residuals 9 114.64 12.74 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Error: Within Df Sum Sq Mean Sq F value Pr(>F) revs 6 11051.8 1842.0 1337.4577 < 2.2e-16 *** revs: linear 1 10846.8 10846.8 7875.9309 < 2.2e-16 *** revs: quadratic 1 198.9 198.9 144.4046 < 2.2e-16 *** revs: cubic 1 2.9 2.9 2.0842 0.1532 revs: quartic 1 1.4 1.4 1.0398 0.3113 revs: quintic 1 0.1 0.1 0.0885 0.7669 revs: sextic 1 1.7 1.7 1.1983 0.2773 trt:revs 18 269.5 15.0 10.8718 4.620e-14 *** trt:revs: linear 3 154.4 51.5 37.3624 1.133e-14 *** trt:revs: quadratic 3 104.8 34.9 25.3581 2.646e-11 *** trt:revs: cubic 3 7.4 2.5 1.7944 0.1559 trt:revs: quartic 3 0.8 0.3 0.1861 0.9055 trt:revs: quintic 3 0.9 0.3 0.2099 0.8892 trt:revs: sextic 3 1.3 0.4 0.3199 0.8110 Residuals 72 99.2 1.4 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >