In article <9p2d8l$clk$[EMAIL PROTECTED]>,
Ronald Bloom <[EMAIL PROTECTED]> wrote:
>Herman Rubin <[EMAIL PROTECTED]> wrote:
>> Teaching people to use something without any understanding
>> can only be ritual; this is what most uses of statistics
>> are these days.
>> If one does not use numbers, it is opinion. I hope that the
>> pediatricians you have in your classes do not misuse data in
>> the manner you seem to be suggesting.
> If one *does* use numbers it still is "opinion". Anchoring
>numbers and mathematical models to claims about the way in
>which the world behaves (as opposed to claims about the way
>in which *numbers* behave) cannot but involve strong and
>deep assertions; which themselves *cannot* be theorems
>of mathematics. The specific nature of the tasks to which we
>put "numbers" to work reflects corresponding "opinions" we
>have about the relevance of specific mathematical models,
>and the underlying assumptions corresonding to each, in
>those specific instances.
>The use of Mathematics does not vanquish proto-mathematical hypotheses
>from the empirical questions upon which it is brought to bear.
One of the mistakes that philosophers of science make is that
one can just look at the data. It is the other way around;
the investigator must make the assumptions using whatever
information from the field of investigation is available, and
may consider alternative models. All one can do with the
numbers is to attempt to make decisions based on the assumptions.
The user needs to understand probability and probability
modeling, and to evaluate the consequences of the actions in
the various states of nature, as well as to formulate the
model, which describes how nature generates the data. It is
only then that the power of mathematics and statistics can
be applied. It is necessary to make approximations, as we
do not have infinitely large and infinitely fast computers
operating at zero cost; it does not take too large a problem
before we cannot just "put it on the computer".
Now the statistician can help by pointing out where one can
approximate with little risk of adverse consequences, and
when one cannot, and certainly can advise on how to calculate
the costs and procedures, which may take a numerical analyst
to carry out. What should be done is not likely to be at all
like what the ritual cookbooks indoctrinate.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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