Order matters in summary.aov
People are often disconcerted by the ANOVA table produced by summary.aov in analysis of covariance. Compare the tables produced for these two models:
summary.aov(lm(weight~sex*age))
Df Sum Sq Mean Sq F value Pr(>F)
sex 1 90.492 90.492 107.498 1.657e-08 ***
age 1 269.705 269.705 320.389 5.257e-12 ***
sex:age 1 13.150 13.150 15.621 0.001141 ***
Residuals 16 13.469 0.842
summary.aov(lm(weight-age*sex))
Df Sum Sq Mean Sq F value Pr(>F)
age 1 269.705 269.705 320.389 5.257e-12 ***
sex 1 90.492 90.492 107.498 1.657e-08 ***
age:sex 1 13.150 13.150 15.621 0.001141 ***
Residuals 16 13.469 0.842
Exactly the same sums of squares and p values. No problem. But look at these two models from the plant compensation example analysed in detail earlier (p. 490):
summary.aov(lm(Fruit-Grazing*Root)) Df Sum Sq Mean Sq F value Pr(>F) Grazing 1 2910.4 2910.4 62.3795 2.262e-09 *** Root 1 19148.9 19148.9 410.4201 <2.2e-16 *** Grazing:Root 1 4.8 4.8 0.1031 0.75 Residuals 36 1679.6 46.7 summary.aov(lm(Fruit-Root*Grazing)) Df Sum Sq Mean Sq F value Pr(>F) Root 1 16795.0 16795.0 359.9681 < 2.2e-16 *** Grazing 1 5264.4 5264.4 112.8316 1.209e-12 *** Root:Grazing 1 4.8 4.8 0.1031 0.75 Residuals 36 1679.6 46.7
In this case the order of variables within the model formula has a huge effect: it changes the sum of squares associated with the two main effects (root size is continuous and grazing is categorical, grazed or ungrazed) and alters their p values. The interaction term, the residual ...
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