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Chapter 9: Going One-Way with Analysis of Variance
Just to get a feeling for what an ANOVA procedure involves and to give you a
quick reference for a later time, here are the general steps in a one-way ANOVA:
1. Check the ANOVA conditions, using the data collected from each of
the k populations.
See the next section, “Checking the conditions,” for the specifics on
these conditions.
2. Set up the hypotheses Ho: µ 1 = µ 2 = . . . = µ k versus Ha: At least two of
the population means are different.
Another way to state your alternative hypothesis is by saying Ha: At
least two of µ 1 , µ 2 , . . . µ k are different.
3. Collect data from k random samples, one from each population.
4. Conduct an F-test on the data from step three, using the hypotheses
from step two, and find the p-value.
See the section “Doing the F-test” later in this chapter for these 165
instructions.
5. Make your conclusions: If you reject Ho (when your p-value is less
than 0.05 or your prespecified α level), you conclude that at least two
of the population means are different; otherwise, you conclude that
you didn’t have enough evidence to reject Ho (you can’t say the
means are different).
If these steps look like a foreign language to you, don’t fear — I describe each
of these steps in detail in the sections to follow.
Checking the Conditions
Step one of ANOVA is checking to be sure all necessary conditions are met
before diving into the data analysis. The conditions for using ANOVA are just
an extension of the conditions for a t-test (see the section “Comparing Two
Means with a t-Test”). The following conditions all need to hold in order for
ANOVA to be conducted:
The k populations are independent (in other words, their outcomes
don’t affect each other).
The k populations each have a normal distribution.
The variances of the k normal distributions are equal.

I go into more detail about these conditions in the following sections.