From: turpin@cs.utexas.edu (Russell Turpin)
Newsgroups: sci.med
Subject: Re: The null hypothesis  (was: Xanax)
Date: 14 Sep 1992 10:37:56 -0500
Organization: U Texas Dept of Computer Sciences, Austin TX
NNTP-Posting-Host: cs.utexas.edu
Summary: When is an assumption not an assumption?

-*----
In article <79667@ut-emx.uucp> llama@pooh.cc.utexas.edu (sine nomine) writes:
> i think you misunderstand the terminology being used here, russell.
> the foundation of the scientific method as taught in applied
> statistics and research methods classes is that you start with a null
> hypothesis (h0) (the variable being studied has no effect) and an
> alternative hypothesis (h1) (the variable being studied will produce
> an effect). please note that i'm using "effect" here in the
> statistical sense; the null hypothesis is that there will be no
> statistical difference between a group subjected to the variable being
> studied and a group not subjected to that variable.
>
> so, when you're setting up an experiment, your assumption is that the
> null hypothesis is true. in fact, studies generally refer to being
> able to reject the null hypothesis, not to accepting the alternative.

There are a variety of arguments in which one rhetorically
"assumes" some claim in order to proceed with the argument, which
then provides evidence for or against the claim.  For example, a
mathematician commonly begins an argument "by contradiction" with
the request "assume X."  But at the end of the argument, the
mathematician wants the audience to believe that he has disproved
X.  This should lead them to some suspicion that the initial
request, that they "assume X," was not meant literally!  A
listener who took this request literally would acknowledge "X is
true," and leave the presentation forthwith, the issue being
resolved.  On later hearing that the speaker had disproved X, the
listener would respond "nonsense, for X is true."  Fortunately,
the request is rhetorical shorthand, and its meaning is roughly:
"let's see what happens to our formal system if X is added as an 
axiom."

The "assumption" of the null hypothesis in statistical analysis
is similarly rhetorical.  When one compares the null hypothesis
against some other hypothesis using some set of data, and finds
that the null hypothesis is as good an explanation, by this
process one has marshalled *some* evidence for the null
hypothesis.  When one gets the same results with other competing
hypotheses and more data sets, one has marshalled more evidence
for the null hypothesis.  Eventually, medical researchers are
justified in saying, "this treatment is ineffective."

What I argue against is reifying the "assumption of the null
hypothesis" as part of statistical analysis into a more general
epistemological rule.  If one simply assumes the null hypothesis,
not as part of statistical analysis but *before* any analysis,
one proclaims "this treatment is ineffective," before one has any
evidence of this claim.  If one really believes this, there is
then no reason to do further study!  This is wrong.  From a
scientific viewpoint, one can only say that there is no evidence
that the treatment is effective.  (I will concur with Gordon that
from a practitioner's viewpoint, this is damning enough.)

To give a simple example outside medicine, one who says "there is
no life on other planets" is making a statement of faith, not a
conclusion of science.  It is not science to assume the negative
merely because there is no evidence of the positive.

> i think the misunderstanding here is that gordon was using the term
> "hypothesis" in the statistical/experimental sciences sense, and you
> were reading it in the more general sense. ...

But the issue in this thread is what should be said of proposed
treatments in the absence of any evidence, prior to experiment
and analysis.  In this case, statistical analysis has little say,
and any assumption almost has to be read in the general sense. 

I think this mistake is made for two reasons.  First, because
statisticians use the terminology "assume the null hypothesis,"
people come to think that that is really what the statistical
argument requires.  Second, some people mistakenly think that
statistical analysis is "the foundation of the scientific
method," rather than merely one form of argument.  Once one
recognizes that statistical analysis is merely one form of
argument, then it becomes fairly clear that the "assumption" made
within it is like a mathematician's "assumption" of the claim he
proceeds to disprove, to wit, that it is only part of a larger
argument and that it is not really an assumption in the larger
sense.

This may seem anathema to doctors and biologists who learned
their research methods *too* well.  (I never seem to have any
problem with statisticians, most of whom have a broader view of
what it is they do.)

> sine nomine
> debbie martinson

A contradiction in the signature.  How should we take the
assumption "sine nomine"?

Russell