> kb.mod1 <- lm(Deflect ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4) > anova(kb.mod1) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) X1 1 32085 32085 10.1578 0.001575 ** X2 1 1696 1696 0.5371 0.464181 X3 1 11307 11307 3.5798 0.059365 . X4 1 116342 116342 36.8329 3.552e-09 *** X1X4 1 0 0 0.0001 0.994156 X2X4 1 1360 1360 0.4306 0.512132 X3X4 1 81 81 0.0256 0.872927 Residuals 328 1036035 3159 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod2 <- lm(Deflect ~ X1 + X2 + X3 + X4) > anova(kb.mod2) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) X1 1 32085 32085 10.2365 0.00151 ** X2 1 1696 1696 0.5412 0.46245 X3 1 11307 11307 3.6076 0.05839 . X4 1 116342 116342 37.1181 3.088e-09 *** Residuals 331 1037476 3134 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(kb.mod2, kb.mod1) Analysis of Variance Table Model 1: Deflect ~ X1 + X2 + X3 + X4 Model 2: Deflect ~ X1 + X2 + X3 + X4 + X1X4 + X2X4 + X3X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 331 1037476 2 328 1036035 3 1441.4 0.1521 0.9283 > > ### As the interaction, is highly non-significant, Use Model 2 for > ### main effects tests > > kb.mod3 <- lm(Deflect ~ X4) > anova(kb.mod3) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) X4 1 115483 115483 35.601 6.175e-09 *** Residuals 334 1083424 3244 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod4 <- lm(Deflect ~ X1 + X2 + X3) > anova(kb.mod4) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) X1 1 32085 32085 9.2321 0.002567 ** X2 1 1696 1696 0.4881 0.485261 X3 1 11307 11307 3.2536 0.072173 . Residuals 332 1153818 3475 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(kb.mod3,kb.mod2) Analysis of Variance Table Model 1: Deflect ~ X4 Model 2: Deflect ~ X1 + X2 + X3 + X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 334 1083424 2 331 1037476 3 45948 4.8864 0.002448 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(kb.mod4,kb.mod2) Analysis of Variance Table Model 1: Deflect ~ X1 + X2 + X3 Model 2: Deflect ~ X1 + X2 + X3 + X4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 332 1153818 2 331 1037476 1 116342 37.118 3.088e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > kb.mod5 <- aov(Deflect ~ factor(Wood) + factor(Bdtype)) > anova(kb.mod5) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) factor(Wood) 3 45089 15030 4.7951 0.002769 ** factor(Bdtype) 1 116342 116342 37.1181 3.088e-09 *** Residuals 331 1037476 3134 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > drop1(kb.mod5) Single term deletions Model: Deflect ~ factor(Wood) + factor(Bdtype) Df Sum of Sq RSS AIC 1037476 2709.8 factor(Wood) 3 45948 1083424 2718.4 factor(Bdtype) 1 116342 1153818 2743.5 > TukeyHSD(kb.mod5) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Deflect ~ factor(Wood) + factor(Bdtype)) $`factor(Wood)` diff lwr upr p adj 2-1 -7.736325 -30.11939 14.646739 0.8087781 3-1 -25.284472 -47.81297 -2.755974 0.0207927 4-1 -27.069424 -48.86854 -5.270307 0.0080047 3-2 -17.548147 -40.40713 5.310840 0.1967711 4-2 -19.333099 -41.47359 2.807396 0.1109786 4-3 -1.784952 -24.07246 20.502560 0.9968674 $`factor(Bdtype)` diff lwr upr p adj 2-1 -37.25515 -49.30233 -25.20798 0 > > options(contrasts=c("contr.sum","contr.poly")) > > kb.mod6 <- aov(Deflect ~ factor(Wood)*factor(Bdtype)) > anova(kb.mod6) Analysis of Variance Table Response: Deflect Df Sum Sq Mean Sq F value Pr(>F) factor(Wood) 3 45089 15030 4.7582 0.002913 ** factor(Bdtype) 1 116342 116342 36.8329 3.552e-09 *** factor(Wood):factor(Bdtype) 3 1441 480 0.1521 0.928296 Residuals 328 1036035 3159 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > # library(car) > # Anova(kb.mod6,type="III") > > > >