Page 189 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
To find descriptive statistics for each sample, go to Stat>Basic Statistics>
Display Descriptive Statistics. Click on each variable in the left-hand box for
which you want the descriptive statistics and then click Select. Click on the
Statistics option, and a new window appears with tons of different types of
statistics. Click on the ones you want and click off the ones you don’t want.
Click OK. Then click OK again. Your descriptive statistics are calculated.
Note that you don’t need the sample sizes in each group to be equal to carry
out ANOVA; however, in intermediate stats, you’ll typically see what statisti-
cians call a balanced design, where each sample from each population has the
same sample size. (For more precision in your data, the larger the sample
sizes, the better; see Chapter 3.)
Setting Up the Hypotheses
Step two of ANOVA is setting up the hypotheses to be tested. You’re testing
to see whether or not all the population means can be deemed equal to each
other. The null hypothesis for ANOVA is that all the population means are
equal. That is, Ho: µ 1 = µ 2 = . . . = µ k, where µ 1 is the mean of the first popula-
tion, µ 2 is the mean of the second population, and so on until you reach µ k
th
(the mean of the k population).
Now what appears in the alternative hypothesis (Ha) must be the opposite of
what is in the null hypothesis (Ho). What’s the opposite of having all k of the
population’s means equal to each other? You may think the opposite is that
they’re all different. But that’s not the case. In order to blow Ho wide open, all
you need is for at least two of those means to not be equal. The alternative
hypothesis, Ha, is that at least two of the population means are different from
each other. That is, Ha: At least two of µ 1 , µ 2 , . . . µ k are different.
Note that Ho and Ha for ANOVA are an extension of the hypotheses for a two
sample t-test (which only compares two independent populations). And while
the alternative hypothesis in a t-test may be that one mean is greater than, less
than, or not equal to the other, you don’t consider any alternative other than ≠
in ANOVA. You only want to know whether or not the means are equal — at this
stage of the game anyway. After you reach the conclusion that Ho is rejected in
ANOVA, you can proceed to figure out how the means are different, which ones
are bigger than others, and so on, using multiple comparisons. Those details
appear in Chapter 10.
Doing the F-Test
Step three, collecting the data, includes taking k random samples, one from
each population. Step four of ANOVA is doing the F-test on this data, which is