Plots of residuals, , similar to the ones discussed in
the previous chapters on regression, are used to ensure that the assumptions
associated with the ANOVA model are not violated. [Note]
The ANOVA model assumes that the random error terms, , are normally and independently distributed
with the same variance for each treatment. The normality assumption can
be checked by obtaining a normal probability plot of the residuals. Equality
of variance is checked by plotting residuals against the treatments and
the treatment averages, (also referred to as fitted values),
and inspecting the spread in the residuals. If a pattern is seen in these
plots, then this indicates the need to use a suitable transformation on
the response that will ensure variance equality. Box-Cox
transformations are discussed in the next section. To check for independence
of the random error terms residuals are plotted against time or run-order
to ensure that a pattern does not exist in these plots. Residual plots
for the given example are shown in Figures 6.5 and
6.6. The plots show that the assumptions associated
with the ANOVA model are not violated.
Figure 6.5: Normal probability plot of residuals for the
single factor experiment in Table 6.1.
Figure 6.6: Plot of residuals against fitted values for
the single factor experiment in Table 6.1.
, similar to the ones discussed in
the previous chapters on regression, are used to ensure that the assumptions
associated with the ANOVA model are not violated. [Note]
The ANOVA model assumes that the random error terms, 
, are normally and independently distributed
with the same variance for each treatment. The normality assumption can
be checked by obtaining a normal probability plot of the residuals. Equality
of variance is checked by plotting residuals against the treatments and
the treatment averages, 
(also referred to as fitted values),
and inspecting the spread in the residuals. If a pattern is seen in these
plots, then this indicates the need to use a suitable transformation on
the response that will ensure variance equality. Box-Cox
transformations are discussed in the next section. To check for independence
of the random error terms residuals are plotted against time or run-order
to ensure that a pattern does not exist in these plots. Residual plots
for the given example are shown in Figures 6.5 and
6.6. The plots show that the assumptions associated
with the ANOVA model are not violated.
