> a = aov(iris$Petal.Width ~ iris$Species) > a Call: aov(formula = iris$Petal.Width ~ iris$Species) Terms: iris$Species Residuals Sum of Squares 80.41333 6.15660 Deg. of Freedom 2 147 Residual standard error: 0.20465 Estimated effects may be unbalanced

Look. You should call summary on the ret. val of aov to get the following statistics.

> summary(a) Df Sum Sq Mean Sq F value Pr(>F) iris$Species 2 80.413 40.207 960.01 < 2.2e-16 *** Residuals 147 6.157 0.042 — Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Because P value is very small, H0 is rejected; Petal.Width is different depending on Species.

We can draw a boxplot to visualize this:

Some texts[1] explain that F statistics in ANOVA is (between class variance) / (within class variance) while others say F is (treatment) / (random error), but they basically evaluate the same thing.

ANOVA assumes a couple of things.

a) variance should be the same across classes.

b) error should be independent, and gaussian.

c) data from each class is independent.

In the above, I didn’t do much to show that the assumption holds, but one can run

plot(a)

to get some graphs like ‘residual vs fitted’, ‘qq plot’, etc.

References)

1. http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/SHUTLER2/node1.html

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