> co2.mod1 <- manova(cbind(y2,y4,y6,y8) ~ trt_m) > summary(co2.mod1,test="Pillai") Df Pillai approx F num Df den Df Pr(>F) trt_m 3 1.4090 1.5497 12 21 0.1832 Residuals 8 > summary(co2.mod1,test="Wilks") Df Wilks approx F num Df den Df Pr(>F) trt_m 3 0.082194 1.7704 12 13.520 0.1565 Residuals 8 > summary(co2.mod1,test="Hotelling-Lawley") Df Hotelling-Lawley approx F num Df den Df Pr(>F) trt_m 3 5.8465 1.7864 12 11 0.1729 Residuals 8 > summary(co2.mod1,test="Roy") Df Roy approx F num Df den Df Pr(>F) trt_m 3 4.9268 8.6219 4 7 0.007714 ** Residuals 8 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > #################################################### > > dayLevels <- c(1,2,3,4) > dayFactor <- as.factor(dayLevels) > dayFrame <- data.frame(dayFactor) > dayBind <- cbind(y2,y4,y6,y8) > dayModel <- lm(dayBind ~ trt_m) > > library(car) Loading required package: MASS Loading required package: nnet Loading required package: survival Loading required package: splines Warning message: package 'car' was built under R version 2.12.2 > co2.mod2 <- Anova(dayModel, idata=dayFrame, idesign = ~dayFactor) > summary(co2.mod2) Type II Repeated Measures MANOVA Tests: ------------------------------------------ Term: (Intercept) Response transformation matrix: (Intercept) y2 1 y4 1 y6 1 y8 1 Sum of squares and products for the hypothesis: (Intercept) (Intercept) 134.0677 Sum of squares and products for error: (Intercept) (Intercept) 11.06053 Multivariate Tests: (Intercept) Df test stat approx F num Df den Df Pr(>F) Pillai 1 0.923788 96.97013 1 8 9.5201e-06 *** Wilks 1 0.076212 96.97013 1 8 9.5201e-06 *** Hotelling-Lawley 1 12.121267 96.97013 1 8 9.5201e-06 *** Roy 1 12.121267 96.97013 1 8 9.5201e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 ------------------------------------------ Term: trt_m Response transformation matrix: (Intercept) y2 1 y4 1 y6 1 y8 1 Sum of squares and products for the hypothesis: (Intercept) (Intercept) 46.25989 Sum of squares and products for error: (Intercept) (Intercept) 11.06053 Multivariate Tests: trt_m Df test stat approx F num Df den Df Pr(>F) Pillai 3 0.807040 11.15314 3 8 0.0031368 ** Wilks 3 0.192960 11.15314 3 8 0.0031368 ** Hotelling-Lawley 3 4.182429 11.15314 3 8 0.0031368 ** Roy 3 4.182429 11.15314 3 8 0.0031368 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 ------------------------------------------ Term: dayFactor Response transformation matrix: dayFactor1 dayFactor2 dayFactor3 y2 1 0 0 y4 0 1 0 y6 0 0 1 y8 -1 -1 -1 Sum of squares and products for the hypothesis: dayFactor1 dayFactor2 dayFactor3 dayFactor1 0.009633333 -0.0306 -0.07848333 dayFactor2 -0.030600000 0.0972 0.24930000 dayFactor3 -0.078483333 0.2493 0.63940833 Sum of squares and products for error: dayFactor1 dayFactor2 dayFactor3 dayFactor1 3.74560000 1.403733 0.09283333 dayFactor2 1.40373333 1.335533 0.19020000 dayFactor3 0.09283333 0.190200 0.32346667 Multivariate Tests: dayFactor Df test stat approx F num Df den Df Pr(>F) Pillai 1 0.6675236 4.015465 3 6 0.069592 . Wilks 1 0.3324764 4.015465 3 6 0.069592 . Hotelling-Lawley 1 2.0077325 4.015465 3 6 0.069592 . Roy 1 2.0077325 4.015465 3 6 0.069592 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 ------------------------------------------ Term: trt_m:dayFactor Response transformation matrix: dayFactor1 dayFactor2 dayFactor3 y2 1 0 0 y4 0 1 0 y6 0 0 1 y8 -1 -1 -1 Sum of squares and products for the hypothesis: dayFactor1 dayFactor2 dayFactor3 dayFactor1 2.562167 1.793267 1.273350 dayFactor2 1.793267 1.487667 0.994500 dayFactor3 1.273350 0.994500 0.718425 Sum of squares and products for error: dayFactor1 dayFactor2 dayFactor3 dayFactor1 3.74560000 1.403733 0.09283333 dayFactor2 1.40373333 1.335533 0.19020000 dayFactor3 0.09283333 0.190200 0.32346667 Multivariate Tests: trt_m:dayFactor Df test stat approx F num Df den Df Pr(>F) Pillai 3 0.9432211 1.222910 9 24.00000 0.327156 Wilks 3 0.2137918 1.450637 9 14.75303 0.253029 Hotelling-Lawley 3 2.9698262 1.539910 9 14.00000 0.226177 Roy 3 2.7234542 7.262545 3 8.00000 0.011340 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Univariate Type II Repeated-Measures ANOVA Assuming Sphericity SS num Df Error SS den Df F Pr(>F) (Intercept) 33.517 1 2.7651 8 96.9701 9.52e-06 *** trt_m 11.565 3 2.7651 8 11.1531 0.003137 ** dayFactor 0.490 3 3.2101 24 1.2201 0.323944 trt_m:dayFactor 1.546 9 3.2101 24 1.2840 0.295542 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Mauchly Tests for Sphericity Test statistic p-value dayFactor 0.18024 0.044103 trt_m:dayFactor 0.18024 0.044103 Greenhouse-Geisser and Huynh-Feldt Corrections for Departure from Sphericity GG eps Pr(>F[GG]) dayFactor 0.52446 0.3165 trt_m:dayFactor 0.52446 0.3298 HF eps Pr(>F[HF]) dayFactor 0.63073 0.3204 trt_m:dayFactor 0.63073 0.3217 > > > > ###################################################### > > trt_u <- rep(1:4,each=12) > unit_u <- rep(1:12,each=4) > day_u <- rep(c(2,4,6,8),times=12) > trt_u <- factor(trt_u) > unit_u <- factor(unit_u) > day_u <- factor(day_u,ordered=T) > > > co2.mod3 <- aov(y ~ trt_u + trt_u/unit_u + day_u + trt_u:day_u) > summary(co2.mod3) Df Sum Sq Mean Sq F value Pr(>F) trt_u 3 11.5650 3.8550 28.8218 3.985e-08 *** day_u 3 0.4896 0.1632 1.2201 0.32394 trt_u:unit_u 8 2.7651 0.3456 2.5842 0.03429 * trt_u:day_u 9 1.5456 0.1717 1.2840 0.29554 Residuals 24 3.2101 0.1338 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > co2.mod4 <- aov(y ~ trt_u*day_u + Error(unit_u)) > summary(co2.mod4) Error: unit_u Df Sum Sq Mean Sq F value Pr(>F) trt_u 3 11.5650 3.8550 11.153 0.003137 ** Residuals 8 2.7651 0.3456 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Error: Within Df Sum Sq Mean Sq F value Pr(>F) day_u 3 0.4896 0.16319 1.2201 0.3239 trt_u:day_u 9 1.5456 0.17174 1.2840 0.2955 Residuals 24 3.2101 0.13375 > > summary(co2.mod4,split=list(day_u=list(linear=1, quadratic=2, + cubic=3))) Error: unit_u Df Sum Sq Mean Sq F value Pr(>F) trt_u 3 11.5650 3.8550 11.153 0.003137 ** Residuals 8 2.7651 0.3456 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Error: Within Df Sum Sq Mean Sq F value Pr(>F) day_u 3 0.4896 0.16319 1.2201 0.32394 day_u: linear 1 0.0306 0.03060 0.2288 0.63676 day_u: quadratic 1 0.3658 0.36575 2.7345 0.11122 day_u: cubic 1 0.0932 0.09322 0.6970 0.41204 trt_u:day_u 9 1.5456 0.17174 1.2840 0.29554 trt_u:day_u: linear 3 1.3198 0.43993 3.2892 0.03791 * trt_u:day_u: quadratic 3 0.1560 0.05200 0.3888 0.76210 trt_u:day_u: cubic 3 0.0698 0.02327 0.1740 0.91292 Residuals 24 3.2101 0.13375 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >