[ Pobierz całość w formacie PDF ]

In the penny-spinning example, Robin is making a personal decision and
is free to choose ± as she pleases. In the termite example, the researchers
were influenced by decades of scientific convention. In 1925, in his extremely
influential Statistical Methods for Research Workers, Ronald Fisher3 sug-
gested that ± = .05 and ± = .01 are often appropriate significance levels.
These suggestions were intended as practical guidelines, but they have be-
come enshrined (especially ± = .05) in the minds of many scientists as a sort
of Delphic determination of whether or not a hypothesized theory is true.
While some degree of conformity is desirable (it inhibits a researcher from
choosing after the fact a significance level that will permit rejecting the
null hypothesis in favor of the alternative in which s/he may be invested),
many statisticians are disturbed by the scientific community s slavish de-
votion to a single standard and by its often uncritical interpretation of the
resulting conclusions.4
The imposition of an arbitrary standard like ± = .05 is possible because
of the precision with which mathematics allows hypothesis testing to be
formulated. Applying this precision to legal paradigms reveals the issues
with great clarity, but is of little practical value when specifying a signifi-
cance level, i.e. when trying to define the meaning of  beyond a reasonable
doubt. Nevertheless, legal scholars have endeavored for centuries to po-
sition  beyond a reasonable doubt along the infinite gradations of assent
that correspond to the continuum [0, 1] from which ± is selected. The phrase
 beyond a reasonable doubt is still often connected to the archaic phrase
 to a moral certainty. This connection survived because moral certainty
was actually a significance level, intended to invoke an enormous body of
scholarly writings and specify a level of assent:
Throughout this development two ideas to be conveyed to the
jury have been central. The first idea is that there are two realms
of human knowledge. In one it is possible to obtain the absolute
3
Sir Ronald Fisher is properly regarded as the single most important figure in the
history of statistics. It should be noted that he did not subscribe to all of the particulars
of the Neyman-Pearson formulation of hypothesis testing. His fundamental objection to
it, that it may not be possible to fully specify the alternative hypothesis, does not impact
our development, since we are concerned with situations in which both hypotheses are
fully specified.
4
See, for example, J. Cohen (1994). The world is round (p
ogist, 49:997 1003.
8.3. HEURISTICS OF HYPOTHESIS TESTING 161
certainty of mathematical demonstration, as when we say that
the square of the hypotenuse is equal to the sum of the squares
of the other two sides of a right triangle. In the other, which is
the empirical realm of events, absolute certainty of this kind is
not possible. The second idea is that, in this realm of events, just
because absolute certainty is not possible, we ought not to treat
everything as merely a guess or a matter of opinion. Instead,
in this realm there are levels of certainty, and we reach higher
levels of certainty as the quantity and quality of the evidence
available to us increase. The highest level of certainty in this
empirical realm in which no absolute certainty is possible is what
traditionally was called  moral certainty, a certainty which there
was no reason to doubt.5
Although it is rarely (if ever) possible to quantify a juror s level of as-
sent, those comfortable with statistical hypothesis testing may be inclined
to wonder what values of ± correspond to conventional interpretations of
reasonable doubt. If a juror believes that there is a 5 percent probability
that chance alone could have produced the circumstantial evidence presented
against a defendant accused of pre-meditated murder, is the juror s level of
assent beyond a reasonable doubt and to a moral certainty? We hope not.
We may be willing to tolerate a 5 percent probability of a Type I error [ Pobierz całość w formacie PDF ]

  • zanotowane.pl
  • doc.pisz.pl
  • pdf.pisz.pl
  • moje-waterloo.xlx.pl

    •