# SSQ decomposition and contrasts with ANOVA

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## SSQ decomposition and contrasts with ANOVA

 Dear R list, Please, could someone help me with SSQ decomposition and contrasts. Below my data, graphic, ANOVAs and my doubt: # Data a   = paste('a', gl(3, 8), sep='') b   = paste('b', gl(2, 4, 24), sep='') tra = sort(paste('t', rep(1:6, 4), sep='')) y   = c(26.2, 26.0, 25.0, 25.4, 24.8, 24.6, 26.7, 25.2,          25.7, 26.3, 25.1, 26.4, 19.6, 21.1, 19.0, 18.6,          22.8, 19.4, 18.8, 19.2, 19.8, 21.4, 22.8, 21.3) dF  = data.frame(a, b, tra, y) # Graphic par(mfrow=c(2,1)) interaction.plot(dF\$a, dF\$b, dF\$y,                   ylab = 'y', xlab = 'a') interaction.plot(dF\$b, dF\$a, dF\$y,                   ylab = 'y', xlab = 'b') # ANOVAs av0 = aov(y ~ tra, data=dF) summary(av0) av1 = aov(y ~ a*b, data=dF) summary(av1) av2 = aov(y ~ a/b, data=dF) b_a = summary(av2, split = list('a:b' = list(                'b1 vs b2/a1' = 1, 'b1 vs b2/a2' = 2, 'b1 vs b2/a3' = 3))) b_a av3 = aov(y ~ b/a, data=dF) a_b = summary(av3, split = list('b:a' = list(               'a/b1' = c(1,3), 'a/b2' = c(2,4)))) a_b # My doubts a) How to make the SSQ decomposition to complete the ANOVA below? --------------------------------------------------------                     Df   Sum Sq Mean Sq F value    Pr(>F) b                   1   19.082  19.082  14.875  0.001155 b:a                 4  156.622  39.155  30.524 8.438e-08 --------------------------------------------------------   b:a: a/b1         (2) (87.122) 43.561  33.958 7.776e-07 --------------------------------------------------------     a1 vs (a2, a3)   1        ?       ?       ?         ?     a2 vs a3         1        ?       ?       ?         ? --------------------------------------------------------   b:a: a/b2         (2) (69.500) 34.750  27.090 3.730e-06 --------------------------------------------------------     a1 vs (a2, a3)   1        ?       ?       ?         ?     a2 vs a3         1        ?       ?       ?         ? -------------------------------------------------------- Residuals   18  23.090   1.283 -------------------------------------------------------- b) How to make the SSQ decomposition to complete the ANOVA below? --------------------------------------------------------                     Df   Sum Sq Mean Sq F value    Pr(>F) b                   1   19.082  19.082  14.875  0.001155 b:a                 4  156.622  39.155  30.524 8.438e-08 --------------------------------------------------------   b:a: a/b1         (2) (87.122) 43.561  33.958 7.776e-07 --------------------------------------------------------     a2 vs (a1, a3)   1        ?       ?       ?         ?     a1 vs a3         1        ?       ?       ?         ? --------------------------------------------------------   b:a: a/b2         (2) (69.500) 34.750  27.090 3.730e-06 --------------------------------------------------------     a2 vs (a1, a3)   1        ?       ?       ?         ?     a1 vs a3         1        ?       ?       ?         ? -------------------------------------------------------- Residuals   18  23.090   1.283 -------------------------------------------------------- Or, In this case, how can I to test these constrasts? Thanks for any help, -- Jose Claudio Faria Brasil/Bahia/UESC/DCET Estatistica Experimental/Prof. Adjunto mails:   [hidden email]   [hidden email]   [hidden email]   [hidden email] tel: 73-3634.2779 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html