ANOVA
Example

We look at hypothetical data about the effect of drug treatment
on the amount of time (in seconds) a stimulus is endured.
We do an ANOVA following the formal hypothesis testing steps.
Note that the books steps are augmented here to reflect current
thinking about using visualizations to investigate the assumptions
underlying the analysis.
 State the Hypotheses:
The hypotheses, for ANOVA, are:
 Set the Decision Criterion
We arbitrarily set
 Gather the Data:
The data are obtained from 60 subjects, 20 in each of
3 different experimental conditions. The conditions are
a Placebo condition, and two different drug conditions.
The independent (classification) variable is the experimental
condition (Placebo, DrugA, DrugB). The dependent variable
is the time the stimulus is endured.
Here are the data as shown in ViSta's data report:
and here they are in ViSta's data object:
The data may be gotten from the ViSta
Data Applet. Then, you can do the analysis that
is shown below yourself.
 Visualize the Data
We visualize the data and the model in order to see if
the assumptions underlying the independentmeasures Ftest
are met. The assumptions are:
 The observations within each sample must be independent
(this assumption is satisfied by the nature of the
experimental design).
 The populations from which the samples are selected
must be normal (the data and model visualizations
can inform us about this).
 The populations from which the samples are selected
must have equal variance (the data and model visualizations
can inform us about this also). This is called homogeneity
of variance.
The data visualization is shown below.
The boxplot shows that there is somewhat more variance
in the "DrugA" group, and that there is an outlier in
the "DrugB" group. The Q plots (only the "DrugB" QPlot
is shown here) and the QQ plot show that the data are
normal, except for the outlier in the "DrugB" group.
 Evaluate the Null Hypothesis
We use ViSta to calculate the observed Fratio, and the
observed probability level. The report produced by ViSta
is shown below. The information we want is near the bottom:
We note that F=4.37 and p=.01721. Since the observed p
< .05, we reject the null hypothesis and conclude that
it is not the case that all group means are the same.
That is, at least one group mean is different than the
others.
Here is the F distribution for df=2,57 (3 groups, 60
observations). Note the location of the the observed
F=4.37.
 Visualize the Model
Finally, we also visualize the ANOVA model to see if the
assumptions underlying the independentmeasures Ftest
are met. The boxplots are the same as those for the data.
The partial regression plot shows that the model is significant
at the .05 level of significance, since the curved lines
cross the horizontal line. The residual plot shows the
outline in the "DrugB" group, and shows that the "DrugA"
group is not as well fit by the ANOVA model as the other
groups. Here is the model visualization:
