In article <[EMAIL PROTECTED]>,
Richard A. Beldin, Ph.D. <[EMAIL PROTECTED]> wrote:
>The question is: If you don't teach by rules, what will you use?
Teach the concepts and reasons. If you teach the rules, these
become much harder to learn. Statistics is not a religion,
where performing the sacrifices and making the appropriate
incantations is important.
>In the Elementary Statistics course I used to teach, I had several different
>objectives.
>1) Students should develop arithmetic reliability.
In a practical problem, all computations will be performed
by machine. Knowing how to add does not help in understanding
when. The converse is also true, but the how can get done.
>2) Students should learn how they can be tricked by statistical wizardry.
Give them the concepts, and it will be much harder to trick
them. These concepts involve probability from the beginning.
>3) Students should learn how to understand what is written by responsible
>statisticians.
They will not be able to do this if they do not know enough
mathematics. They must understand algebra, not just know
the rules, and they must be able to formulate, not solve.
>In the Applied Statistics course, my objectives were different.
>1) Students should learn to read and evaluate the professional literature in
>their discipline.
>2) Students should learn to apply the basic ideas of statistical description
>and inference: estimation, simple hypothesis testing, regression, etc.
Again, they had better understand the problems, and how to
formulate problems, including stating assumptions. These
assumptions do not come from statistics, but from the field
to which statistics is applied.
>3) Students should learn that their experience is limited and gain the
>confidence to consult a professional statistician.
>In the Mathematical Statistics course, my objectives were primarily
>mathematical, not statistical. Statistics was seen as a technology built on
>the foundations of the infinitesimal and finite difference calculus.
These are NOT the foundations. They are tools only. I am
unaware of texts using the finite different calculus; it is
useful, but even quite a few with doctorates in statistics
do not know anything about the finite difference calculus.
Statistics is not a technology; it is more a framework,
enabling the formulation of problems so that mathematical
reasoning concerning the handling of probabilistic
uncertainty can be applied.
The concepts can be taught. One can even present, with
understanding, the Neyman-Pearson Lemma in any decent
elementary statistics course. Do it for the discrete
case, with some added restrictions. Everything is
discrete or limits of discrete, and separating the
discrete from the continuous, as is usually done, just
adds to the obfuscation. This holds in elementary
courses as well.
--
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
