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and Jackson [1984], McGuigan [1995], McKinney et al. [1989], Miller
[1986], Padaki [1989], Welch and Gabbe [1996], Westgard and Hunt
[1973], White [1979], and Yoccuz [1991].
Guidelines for reviewers are provided by Altman [1998a], Bacchetti
[2002], Finney [1997], Gardner, Machin, and Campbell [1986], George
[1985], Goodman, Altman, and George [1998], International Committee
of Medical Journal Editors [1997], Light and Pillemer [1984], Mulrow
[1987], Murray [1988], Schor and Karten [1966], and Vaisrub [1985].
For additional comments on the effects of the violation of assumptions,
see Box and Anderson [1955], Friedman [1937], Gastwirth and Rubin
[1971], Glass, Peckham, and Sanders [1972], and Pettitt and Siskind
[1981].
For the details of testing for equivalence, see Dixon [1998]. For a
review of the appropriate corrections for multiple tests, see Tukey [1991].
For procedures with which to analyze factorial and other multifactor
experimental designs, see Chapter 8 of Pesarin [2001].
Most of the problems with parametric tests reported here extend to and
are compounded by multivariate analysis. For some solutions, see Chapter
5 of Good [2000] and Chapter 6 of Pesarin [2001].
For a contrary view on the need for adjustments of
p
values in multiple
comparisons, see Rothman [1990a].
Venn [1888] and Reichenbach [1949] are among those who've at-
tempted to construct a mathematical bridge between what we observe and
the reality that underlies our observations. To the contrary, extrapolation
from the sample to the population is not a matter of applying Holmes-like
deductive logic but entails a leap of faith. A careful reading of Locke
[1700], Berkeley [1710], Hume [1748], and Lonergan [1992] is an
essential prerequisite to the application of statistics.
For more on the contemporary view of induction, see Berger [2002]
and Sterne, Smith, and Cox [2001]. The former notes that, “Dramatic
illustration of the non-frequentist nature of
p
-values can be seen from the
applet available at http://www.stat.duke.edu/~berger. The applet assumes
one faces a series of situations involving normal data with unknown mean
q and known variance, and tests of the form
H
: q = 0 versus
K
: q π 0.
The applet simulates a long series of such tests, and records how often
H
is true for
p
-values in given ranges.”
