Some myths concerning statistical hypothesis testing

Robert Dodier robert_dodier at yahoo.com
Sun Nov 17 21:27:42 EST 2002


"John H." <johnh at faraway.xxx> wrote:

> As a mathematical outsider I find it quite surprising that some of the
> fundamentals of statistical analysis, utilised so widely in the sciences,
> remains in hot dispute by many people who obviously are not intellectual
> outsiders. It just shows how even in such a 'pure' field as mathematics
> there remains plenty of room for debate.

Just to clarify the grounds of the debate, the questions of interest
are not mathematical in nature -- so far as I know all parties agree
on the theorems of probability, measure theory, etc. and nobody claims
that their opponents have a false derivation or some error like that.

The debate is best characterized as a scientific in nature -- 
specifically, there is disagreement as to what the A, B, C, and 
X, Y, Z in the equations can stand for. It is something like a
physicist exhibiting an equation for balance of phlogiston -- 
even if the equation itself is OK, some people will object to
interpreting the quantity P as a massless fluid that transfers energy.

Specifically, in the case of statistics, one group claims that it is
meaningful to assess probability for any proposition, be it concerning
random variables or otherwise. Another influential group claims that
is incorrect, and some mode of reasoning other than probability is
required for any proposition not concerning random variables. This 
disagreement as to the scope of probability has lead to vastly 
different methodologies, and never the twain shall meet, AFAICT.

Statistics courses for non-majors are almost entirely taught by
the "probability for random variables only" party; this is a 
historical and sociological phenomenon. OTOH, I am aware that the
other persuasion is popular in many computer science departments,
specifically as it makes automated reasoning much easier to formulate.

For what it's worth,
Robert Dodier
--
``He wins most who toys with the dies.'' -- David O'Bedlam



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