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SIDEBAR: THE POTENTIAL OF SUBSET INCONSISTENCY
This is a “subtopic” that the authors wish they did not have to discuss. The Homogeneous Subsets
table can show an inconsistency. Figure 6.11 did not show an inconsistency. But, suppose, for dif-
ferent data, the S-N-K results are shown in Figure 6.12 .
In Figure 6.12 , the S-N-K results say that there are two subsets of (true) means, subset 1, 2,
and 4, and subset 4 and 3. You can see that column mean 4 is in both subsets (see arrow in Figure
6.12 )!! This is inconsistent. How can the true mean of column 4 be the same as the true mean of
columns 1 and 2 while also being the same as the true mean of column 3, when, at the same time,
the true mean of column 3 is different (i.e., in a different subset) from the means of columns 1
and 2?
Sadly, virtually all of the multiple comparison tests allow this possibility to occur. Naturally,
you always hope that it does not occur, but if it does, we basically view the mean or means that
cause the inconsistency as means whose place in the hierarchy is simply “not clear.” In other words,
in the above example, we would conclude that the true mean of column 3 is higher than the true
mean of column 1 and true mean of column 2, and we would also conclude that the true mean of
columns 1 and 2 are not different; inally, we would conclude that it is not clear where the mean of
column 4 belongs.
FIGURE 6.12
An illustration of an inconsistency in the S-N-K results; SPSS.
 
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