Hi Joe,
Why should the value 0.05 be adopted as the universally
accepted value for statistical significance?
It is an overstatement to say the 5% level is universally accepted. The
customary (in academic circles) 5% level for rejecting the no-effect
hypothesis is arbitrary, and whether or not it is appropriate depends
on what the decision is going to be used for. For example, if the
practice under consideration is cheap, one should use a less
conservative criterion for accepting or rejecting the practice, maybe
the 0.2 level or higher. Farmers understand this intuitively. There
are also formal methods such as the Waller-Duncan K-ratio test, that
balance the relative risks of making the two kinds of wrong decisions
(accepting a useless practice vs rejecting a useful practice). Cost
can be considered a risk.
http://www.unizh.ch/RZU/software/unix/statmath/sas/sasdoc/stat/chap17/sect26.htm
Why has this approach to hypothesis testing not been supplanted
in the intervening three-quarters of a century?
Well, it has in several ways. Most traditionally, Bayesian statistics,
the germ of which predates Student and Fisher, makes a lot of sense.
http://yudkowsky.net/bayes/bayes.html
We almost never study a problem or formulate a hypothesis without
having some prior knowledge about the veracity of different
explanations. Bayesian methods provide a way to plow existing
knowledge into new hypothesis tests.
Finally, Fisherian-style analysis, as brilliant as it is, is based on
the assumption of normality (that error is distributed in a bell-shaped
curve). I encounter situations all the time where this assumption is
catastrophically incorrect, leading to bad decisions (especially true
in the quality control arena). Fisher developed his methods at a time
where calculation was expensive. But now computing power is so cheap,
one can write simulation programs that do a better job by using
observed error distributions and numerically banging out millions of
calculations a second. One can also specify distributions in routines
such as SAS Proc Genmod and do the same kind of thing.
Dale
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