Page 185 - Statistics II for Dummies

Chapter 9: Testing Lots of Means? Come On Over to ANOVA!
just choose the p-value of the F-statistic that’s closest to yours. However, if 169
you do have access to a computer while doing homework or an exam, statisti-
cal software packages automatically calculate all p-values exactly, so you can
see them on any computer output.
To approximate the p-value from your F-statistic in the event you don’t have a
computer or computer output available, you find a cutoff value on the
F-distribution with (k – 1, n – k) degrees of freedom that draws a line in the
sand between rejecting Ho and not rejecting Ho. This cutoff, also known as the
critical value, is determined by your predetermined α (typically 0.05). You
choose the critical value so that the area to its right on the F-distribution is
equal to α.

F-distribution tables are available in various statistics textbooks and Web
sites for other values of α; however, α = 0.05 is by far the most common α
level used for the F-distribution and is sufficient for your purposes.

This table of values for the F-distribution is called the F-table, and students
typically receive these with their exams. For the seed-spitting example, the
F-statistic has an F-distribution with degrees of freedom (3, 16), where
3 = k – 1, and 16 = n – k. To find the critical value, consult an F-table (Table
A-5 in the appendix). Look up the degrees of freedom (3, 16), and you’ll find
that the critical value is 3.2389 (or 3.24). Your F-statistic for the seed-spitting
example is 8.43, which is well beyond this critical value (you can see how 8.43
compares to 3.24 by looking at Figure 9-5). Your conclusion is to reject Ho at
level α. At least two of the age groups differ on mean seed-spitting distances.
With the critical value approach, any F-statistic that lies beyond the critical
value results in rejecting Ho, no matter how far from or close to the line it is. If
your F-statistic is beyond the value found in the F-table you consult, then you
reject Ho and say at least two of the treatments (or populations) have differ-
ent means.

What’s next?

After you’ve rejected Ho in the F-test and concluded that not all the popula-
tions means are the same, your next question may be: Which ones are dif-
ferent? You can answer that question by using a statistical technique called
multiple comparisons. Statisticians use many different multiple comparison
procedures to further explore the means themselves after the F-test has been
rejected. I discuss and apply some of the more common multiple comparison
techniques in Chapter 10.

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