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Chapter 16: One-Way Analysis of Variance
we can use some simple graphical techniques to help validate these
assumptions.
Validating the Assumptions for a One-way ANOVA Using Graphs
The assumptions for ANOVA should be validated before any inference is
made on the population means. If these assumptions are not met then the
inference on the population means may not be reliable.
The assumptions are necessary in order for the test statistic used in the
analysis to follow a certain probability distribution.
If the populations are not exactly normally distributed but are
approximately normally distributed, then the ANOVA procedure will
still produce reliable results.
If the distributions are highly skewed or very different from a normal
distribution, or if the population variances are not equal or
approximately equal, then ANOVA will not produce reliable results.
Note:
In cases where the assumptions are not met, other tests, such as equivalent
nonparametric tests, should be employed.
Two simple graphical techniques can be used to establish the assumptions
for a one-way ANOVA. We can use the histogram with summary statistics
to help establish the normality assumption, and we can use box plots to help
establish the equal variance assumption.
Example 16-7:
Equal dosages of three different drugs were used to ease a
certain level of headache. Drug 1 was administered to ten patients and Drug
2 and Drug 3 were administered to nine patients each. The times for
complete relief of the headache for the drugs are given in
Table 16-2
.