14.10: Checking the Normality Assumption
Testing the normality assumption is relatively straightforward. We covered most of what you need to know in Section 13.9. The only thing we really need to know how to do is pull out the residuals (i.e., the ϵ
ik
values) so that we can draw our QQ plot and run our Shapiro-Wilk test. First, let’s extract the residuals. R provides a function called
residuals()
that will do this for us. If we pass our
my.anova
to this function, it will return the residuals. So let’s do that:
my.anova.residuals <- residuals( object = my.anova ) # extract the residuals
We can print them out too, though it’s not exactly an edifying experience. In fact, given that I’m on the verge of putting myself to sleep just typing this, it might be a good idea to skip that step. Instead, let’s draw some pictures and run ourselves a hypothesis test:
hist( x = my.anova.residuals ) # plot a histogram (similar to Figure @ref{fig:normalityanova}a)
qqnorm( y = my.anova.residuals ) # draw a QQ plot (similar to Figure @ref{fig:normalityanova}b)
shapiro.test( x = my.anova.residuals ) # run Shapiro-Wilk test
##
## Shapiro-Wilk normality test
##
## data: my.anova.residuals
## W = 0.96019, p-value = 0.6053
The histogram and QQ plot are both look pretty normal to me. 212 This is supported by the results of our Shapiro-Wilk test (W=.96, p=.61) which finds no indication that normality is violated.