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7.8 POST HOC TESTS
7.8.1 A BRIEF HISTORY OF POST HOC TESTS
Kirk (1995) has estimated that there are around thirty post hoc tests that
have been presented in the professional literature. Each of these post hoc
procedures has acquired the endorsement of some very respected statis-
ticians, and instructors of research and statistics courses almost always
have distinct preferences for one or two over most of the others. Generally
speaking there appears to be more difference of opinion on the issue of
which of the post hoc tests should be used than on most of the other issues
covered in this topic. Excellent and somewhat detailed treatments of this
topic are provided by Jaccard, Becker, and Wood (1984), Kirk (1995),
Klockars and Sax (1986), and Toothaker (1993).
A couple of these post hoc tests can be dated back to the 1930s when
ANOVA was being popularized. Another wave of development of these
tests occurred in the 1950s. Oehlert (2000) provides a short summary of
this history that we quote below; do not be concerned if the names of the
tests are unfamiliar to you; we will cover the tests that he mentions (and
more) in the current section of this topic.
The first multiple comparisons technique appears to be the LSD suggested
by Fisher (1935) . . . the next proposal was the SNK (though not so labeled)
by Newman (1939). Multiple comparisons then lay dormant till around 1950,
when there was an explosion of ideas: Duncan's multiple range procedure
(Duncan, 1955), Tukey's HSD (Tukey, 1952), Scheffe's all contrasts method
(Scheffe, 1953), Dunnett's method (Dunnett, 1955), and another proposal for
SNK (Keuls, 1952). The pace of introduction then slowed again. The REGW
procedures appeared in 1960 and evolved through the 1970s (Ryan 1960; Einot
and Gabriel 1975; Welsch 1977) ...(Oehlert,2000, p. 107).
Our goals in treating the post hoc tests are as follows:
To supply you with a listing and description of the tests.
To give you a very general sense of the distributions underlying these
post hoc tests.
To provide you with some potentially useful guidelines and recom-
mendations in making your choices.
To illustrate a hand calculation on a selected post hoc test.
To show you how to perform and interpret a post hoc analysis in
SPSS and SAS.
7.8.2 THE SAMPLING DISTRIBUTIONS UNDERLYING POST HOC TESTS
One way to categorize the differences in these post hoc procedures is in
terms of the type of the test statistics and sampling distributions that
they use (Kirk, 1995). These procedures generally fall into one of the four
