In article <email@example.com>, Reef Fish <Large_Nassau_Groupen@yahoo.com> wrote:
>DZ wrote: >> Herman Rubin <firstname.lastname@example.org> wrote: >> > The fundamental concepts in statistics are probability, >> > and the problem of decision making under uncertainty. >> > There are a few books which start with probability, >> > which is represented by measure theory with the whole >> > space having measure 1. Now there are intuitive ideas >> > which can be used to exemplify this, but start with it >> > and continue. I can present measure theory and integration, >> > including countable additivity and why it is important, >> > at the high school algebra level; the ideas are much >> > simpler than usually made.
>> > After the basics, they can understand how to formulate >> > their problems and understand the answers. It matters >> > not that they do not know how to carry out the procedures; >> > it takes someone with a strong background to use these >> > in even slightly complex problems.
>> > Back to psychology. I have a SHORT derivation of the >> > asymptotics for factor analysis, which just carries >> > out my 1955 abstract, and which also points out that >> > everything gets worse if the usual normalizations are >> > used; variation which is irrelevant adds to the >> > deviations in the results. Where to publish this?
>> In your own book along with the above ideas? I'll buy it.
>Just buy a copy of Loeve's Probability Theory book. Herman can >teach any high school student measure theory and theory of >integration (ala measure theory type) in THREE WEEKS, because >that's about how long he covered a one-year advanced Graduate >Course in mathematics/statistics, with Loeve's textbook. The students
>in that course learned as much as Herman's high school students >would have learned in the subject of Probability OR Statistics.
The students in that course knew measure theory; it was a prerequisite. What I covered in three weeks was the concept of integration, with details.
Few courses teach concepts. Learning details is not og much help in understanding concepts unless the concepts have already been presented.
How many students understand the very simple conceptual approach to the Neyman-Pearson Lemma? I do not mean the usual formal proof; I mean the high school level ideas.
-- 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 email@example.com Phone: (765)494-6054 FAX: (765)494-0558