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be pressured to give their imprimatur to what, in statistical terms, is clearly
an improper procedure, nor should statisticians mislabel suboptimal proce-
dures as the best that can be done.
2
We concur with Anscombe [1963], who writes, “. . . the concept of
error probabilities of the first and second kinds . . . has no direct relevance
to experimentation. . . . The formation of opinions, decisions concerning
further experimentation and other required actions, are not dictated ...by
the formal analysis of the experiment, but call for judgment and imagina-
tion. . . . It is unwise for the experimenter to view himself seriously as a
decision-maker....The experimenter pays the piper and calls the tune he
likes best; but the music is broadcast so that others might listen. . . .”
NULL HYPOTHESIS
“A major research failing seems to be the exploration of uninteresting or
even trivial questions. . . . In the 347 sampled articles in
Ecology
containing
null hypotheses tests, we found few examples of null hypotheses that
seemed biologically plausible.” Anderson, Burnham, and Thompson
[2000].
Test Only Relevant Null Hypotheses
The “null hypothesis” has taken on an almost mythic role in contempo-
rary statistics. Obsession with the “null” has been allowed to shape the
direction of our research. We've let the tool use us instead of our using
the tool.
3
While a null hypothesis can facilitate statistical inquiry—an exact permu-
tation test is impossible without it—it is never mandated. In any event,
virtually any quantifiable hypothesis can be converted into null form.
There is no excuse and no need to be content with a meaningless null.
To test that the mean value of a given characteristic is three, subtract
three from each observation and then test the “null hypothesis” that the
mean value is zero.
Often, we want to test that the size of some effect is inconsequential,
not zero but close to it, smaller than
d
, say, where
d
is the smallest
biological, medical, physical or socially relevant effect in your area of
research. Again, subtract
d
from each observation, before proceeding to
test a null hypothesis. In Chapter 5 we discuss an alternative approach
using confidence intervals for tests of equivalence.
2
One is reminded of the Dean, several of them in fact, who asked me to alter my grades.
“But that is something you can do as easily as I.” “Why Dr. Good, I would never dream of
overruling one of my instructors.”
3
See, for example, Hertwig and Todd [2000].
