> tapply(gadd, brand, mean) # marginal mean for brand SHC SCHAF SCHUL BUL 1070.300 1069.850 1116.650 1359.650 > > tapply(gadd, side, mean) # marginal mean for side Front Back 1090.875 1217.350 > > tapply(gadd, list(brand,side), mean) # cell means Front Back SHC 1166.0999 974.4998 SCHAF 1117.5999 1022.1000 SCHUL 857.0001 1376.3000 BUL 1222.8001 1496.5001 > > tapply(gadd, list(brand,side), sd) # cell SDs Front Back SHC 152.3998 72.99994 SCHAF 216.2000 105.09994 SCHUL 151.4998 211.40010 BUL 123.1000 183.99987 > > # Fit Model with Interaction (A*B says to include main effects and interactions) > > lacrosse1.aov <- aov(gadd ~ brand*side) > > summary(lacrosse1.aov) Df Sum Sq Mean Sq F value Pr(>F) brand 3 1155478 385159 15.179 9.459e-08 *** side 1 319918 319918 12.608 0.0006816 *** brand:side 3 1632156 544052 21.441 4.988e-10 *** Residuals 72 1826954 25374 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > # Plot Means of Front and Back versus Brand > interaction.plot(brand,side,gadd) > > # Plot residuals versus predicted values > yhat <- predict(lacrosse1.aov) > e <- resid(lacrosse1.aov) > plot(yhat,e) >