Database Reference
In-Depth Information
Unfortunately, Excel (without an “add-in”) does not have the capability to perform
the Newman-Keuls (or S-N-K) test. Therefore, our illustration of the test will be solely
using SPSS. However, later, we have a sidebar about what you can do using only Excel.
6.6
ILLUSTRATION OF THE S-N-K TEST
All of the S-N-K steps are performed by SPSS, but not all the steps are displayed. (Of
course, what is useful for you to know is shown to you.)
SIDEBAR: HOW DOES NEWMAN-KEULS WORK?
Basically, each of the column (sample) means in an S-N-K test is put into increasing order (from the
lowest value to the highest value) by the software. Then, using tried and true statistical methods (based
on a probability distribution called the “Studentized Range Distribution”), it is determined how far
apart the column means need to be so as to constitute a “signiicant difference.” As you might expect,
it depends on your input—How many columns do we have? How many data points per column? How
much variability is there within columns? What alpha value (usually 0.05) do you choose? (Actually,
you are choosing “a,” usually to be 0.05, where “a” is called the “overall error rate,” and is the prob-
ability of making at least one type I error among all the comparison conclusions.)
The S-N-K test recognizes that if there are, for example, ive columns, the highest column mean
is going to be moderately higher than the lowest column mean, even if the true means of all ive col-
umns are the same, while two column means that are adjacent in rank order (i.e., next to each other
in the rank order) will, of course, have a smaller difference in sample means than the difference
between the extreme columns. So, how far apart two means need to be to constitute a signiicant dif-
ference is dependent on how far apart in the rank order the two means are that are being compared.
As an analogy that should make this point abundantly clear, consider ive random 10-year-old
boys at a party. If you line up the ive boys in increasing height, obviously, the difference between
the tallest and shortest boy will be larger than the difference between two boys who are standing
next to each other in the lineup.
SIDEBAR: OTHER MULTIPLE COMPARISON TESTS
There is another multiple comparison test, the “Tukey HSD Test,” that is very popular—probably
used in practice more often than the S-N-K test—but it does not recognize this obvious fact: “How
far apart two means need to be to constitute a signiicant difference is dependent on how far apart
in the rank order the two means are that are being compared.” Thus, we have decided not to present
this test; we believe that it is a test that is inferior to the S-N-K test and is more frequently used than
the S-N-K test simply because there are many academic courses that have a “follow-the-leader”
mentality and teach the Tukey HSD Test and do not teach the S-N-K test. And, as you will see, right
under the S-N-K test option in SPSS is the Tukey HSD test option (called simply “Tukey” in SPSS).
If you have interest in exploring the other multiple comparison tests, there are many texts that you
can turn to. We are biased and recommend the text written by the authors
Berger and Maurer (2002)
.
When performing an ANOVA in SPSS, such as the one-factor ANOVA illustrated
earlier in the chapter, it is very simple to add to the analysis the S-N-K test (as well
as many other multiple comparison tests, as you shall see).
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