Re: A good Q???

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 06/18/04 

Date: 18 Jun 2004 14:49:47 -0500

In article <pllAc.33107$nY.1045712@news20.bellglobal.com>,
Georg Friedrich <gf@rie.mann> wrote:

>Herman Rubin wrote:
>> In article <kLhAc.43174$7H1.1458623@news20.bellglobal.com>,
>> Georg Friedrich <gf@rie.mann> wrote:

>>>This is not a psychology question. It is an applied mathematics
>>>question: You are given an incomplete set of data, and your task is to
>>>find a mathematical model (in this case a formula or a rule) that
>>>captures the "essence" of the data set.

>>>You are right that there are infinitely many mathematically correct
>>>answers. But that does not mean they are all equally acceptable.

>>>The art of applying mathematics is to take ill-posed questions and
>>>transform them to well defined mathematical problems.

>> I disagree. It is the person with the applied problem who
>> needs to make the assumptions, after which mathematics or
>> statistics or numerical analysis or whatever can be applied
>> to the well-formulated problem. So the question asked is
>> about which assumptions are being made; as to which are more
>> reasonable, not only can I not answer that as a mathematician,
>> I MUST NOT. This arises very often in statistics, and what is
>> generally done is unfounded religion.

>> I am often requested to repost my five commandments. These are
>> posted here without exegesis.

>> For the client:

>> 1. Thou shalt know that thou must make assumptions.

>> 2. Thou shalt not believe thy assumptions.

>> For the consultant:

>> 3. Thou shalt not make thy client's assumptions for him.

>> 4. Thou shalt inform thy client of the consequences
>> of his assumptions.

>> For the person who is both (e. g., a biostatistician or psychometrician):

>> 5. Thou shalt keep thy roles distinct, lest thou violate
>> some of the other commandments.

>> The consultant is obligated to point out how their assumptions affect
>> their views of their domain; this is in the 4-th commandment. But the
>> consultant should be very careful in the assumption-making process not
>> to intrude beyond possibly pointing out that certain assumptions make
>> large differences, while others do not. A good example here is regression
>> analysis, where often normality has little effect, but the linearity of
>> the model is of great importance. Thus, it is very important for the
>> client to have to justify transformations.

>> There are, unfortunately, many fields in which much of the activity
>> consists of using statistical procedures without regard for any assumptions.

>Note the distinction between mathematics and applied mathematics.
>Applied mathematics is not mathematics. The mathematician deals with
>well defined problems in a formal universe, with well defined criteria
>of correctness. The applied mathematician deals with ill posed problems
>defined in an informal language, with missing assumptions and open
>interpretations.

>In an ideal world, the client would make all the necessary assumptions
>and present the problem as a well defined mathematical problem. In the
>real world, this hardly ever happens. That's why the applied
>mathematician is paid big bucks, to bridge the gap between the client's
>world and formal mathematics. That's the art of applying mathematics ---
>figuring out what the missing assumptions are, and validating them with
>the client.

>I have nothing against the five commandments in some ideal sense, but if
>you insist on dealing only with the clients who follow 1 and 2, you will
>have to send many clients somewhere else. In many situations, the
>applied mathematician (consultant) must guess what the right assumptions
>are (violation of 3) and then verify them with the client (in agreement
>with 4).

This is permissible, but the clients who do not understand
1 and 2 are likely to agree with any assumptions the
consultant produces. The typical situation in statistical
consulting is that the client comes in with the data, some
idea about how the data is collected, and asks to get the
state of the universe.

The consultant can give some advice, such as point out
which assumptions are not important and which are. If
the applied mathematician makes the assumption that the
equations valid for a perfect gas hold, and this is not
the case, the results are likely not to be very good.
Or if a linear differential equation is used when it is
not even a fair approximation.

Fortunately in engineering, the errors usually show up
in testing; one rarely just goes ahead on the basis of
calculations from a model. And differences in the
assumptions in physics and engineering, especially in
complicated situations, can make huge differences.

However, in statistics, the errors may not show up for
decades, and much harm can be done. Medicine is replete
with examples of this, and psychology and education are
suffering badly from the misapplication. Even when those
in the hard sciences deal with randomness, they are prone
to make assumptions, such as a non-Gaussian process with
stationary independent increments and continuous time
paths, which do not exist. 

-- 
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, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

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