Page 200 - Statistics II for Dummies

184 Part III: Analyzing Variance with ANOVA

Remember, you’re looking to see whether the confidence intervals for each
cereal group overlap; if they don’t, those cereals have different average ages
of consumers. If they do overlap, those cereals have mean ages that can’t be
declared different.

Based on the data in Figure 10-5, you can see that cereals one (C1) and two
(C2) aren’t significantly different, but for cereal three (C3), consumers have a
higher average age than C1 and C2. Cereal four (C4) has a significantly higher
age than the three others. After the multiple comparison procedure, you
know which cereals are different and how they compare to the others.

Individual 95% CIs For Mean Based on
Figure 10-5: Pooled StDev
Multiple Level N Mean StDev -------+---------+---------+---------+--
C1 10 8.800 1.687 (--*--)
comparison
C2 10 11.800 1.033 (--*--)
results for
C3 10 36.500 7.735 (--*--)
the cereal C4 10 55.400 10.309 (--*--)
example.

Sometimes multiple comparison procedures give you groups of means that
are equivalent to each other, different from each other, or overlapping. In
this case, the final result is μ = μ < μ < μ .
C1 C2 C3 C4

So Many Other Procedures,
So Little Time!

Many more multiple comparison procedures exist beyond Fisher’s and
Tukey’s imaginations. Those that I discuss in this section are a little more
specialized in what they were designed to look for, compared to Tukey’s and
Fisher’s. For example, you may want to know whether a certain combination
of means is larger than another combination of means; or you may want to
only compare specific means to each other, not all the pairs of means.
One thing to note, however, is that in many cases you don’t know exactly what
you’re looking for when comparing means — you’re just looking for differ-
ences, period. If that’s the case, one of the more general procedures, like
Fisher’s or Tukey’s, is the way to go. They’re built for general exploration and
do a better job of it than more-specialized procedures.

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