From: maj@waikato.ac.nz
Newsgroups: bit.listserv.edstat-l
Subject: Niceties and esoterica
Date: 14 Oct 92 08:34:30 +1300
Organization: University of Waikato, Hamilton, New Zealand

Oh dear, I don't think these issues are going to sort themselves
out quickly, partly because they are not substantial ones of
RIGHT and WRONG, as one of my noisier sparring partners would
have it, but questions of stress and emphasis. Perhaps I should
retreat with my tail between my legs to some more natural 
habitat for me like STAT-L. Interesting thing that there are two
lists like this: you would think that the issues important for
statistical consulting would be those important for the teaching
of statistics. I wonder why that's not so?

Let        albyn = albyn jones  [jones@reed.edu]
           Jerry = Jerry Dallal [gdallal@pearl.tufts.edu] 
           Murray= Murray Jorgensen [maj@waikato.ac.nz]

This is near the end of the teaching year for me so I write from
a perspective of gloom and depression about how little I have
been able to get across to a large proportion of my first year
class. Most recently I have come to see that many still do not
really understand P-value. I have some ideas about how to cope
with this that I may share with the list if they work out with 
next year's class. It is from this pessimistic perspective that 
I wrote

Murray> To spend a large proportion of class time on 
Murray> explaining the difference between
Murray> various systems of statistical inference seems to me Murray> like
attending to the needs of the instructor, rather Murray> than most consumers of
statistics. Certainly this may be Murray> appropriate to explore later in the
education of a Murray> statistical specialist, but I don't think that was what
Murray> most people were talking about.

Murray> Isn't _any_ form of interval estimate an interval within
Murray> which it is reasonable to expect the parameter to lie?

Murray> Can anyone think of a situation where a user of 
Murray> statistics would come to serious harm in thinking that a Murray>
parameter belonged to a particular 95% confidence Murray> interval with
probability .95?

Albyn tries a bit of reductio ad absurdum :

albyn> Lets extend the "who cares what it really means" argument 
albyn> just a bit farther, to hypothesis tests.  why bother to 
albyn> get it right here either? After all, the .05 level  
albyn> hypothesis test for \mu = 0 is  just the answer to the 
albyn> question "is 0 in the 95% CI for \mu?". What's wrong with 
albyn> students thinking that the p-value is the probability 
albyn> that the null hypothesis is true? 

I don't think that the blurring of confidence with probability does 
lead to this particular misinterpretation of P-value. Under
the blurring "0 is not in the 95% CI for \mu" would translate
to "the probability that \mu = 0 is _at most_ .05". Another
misinterpretation, true, but not such a damaging one.

Jerry claims that I am changing the question that I asked

Jerry> The original question did not ask what should be taught 
Jerry> in an intro course.It asked if the distinction mattered.  
Jerry> It does.It's difficult to have an intelligent dialogue 
Jerry> if, when a quesiton is answered,the poser then changes 
Jerry> the question.
Jerry> Had the original question been, "Why shouldn't intro 
Jerry> students be allowed to confuse confidence with 
Jerry> probability?"  I would have replied, "BECAUSE IT'S 
Jerry> WRONG!!!"

I have repeated my original question above and I think that it 
is clear that the context is clear: that of an introductory 
course in which most students will not go on to become
practising statisticians.

My case is that the amount of time and effort needed to 
communicate the precise meaning of the frequentist confidence 
machinery can lead to the impression that the technical details 
are the important part of statistics. They aren't.

Statistics comprises several stages.

1. A Question

   [in a subject area such as Agronomy, Medicine, or Industry]

2. Gathering data

   [via experiment, survey, or observation]

3.  The translation of the situation into mathematical terms.

   [eg 3a  Deterministic formulation
       3b  Frequentist formulation
       3c  Bayesian formulation
       3d  Fuzzy set formulation {God help us}
       . . .]

4.  Mathematical manipulation of the data within the formulation
    of 3. 
    [4a,4b,4c,...]

5.  Translation of the results of 4 back into the subject area
    language.

So when we speak in loud capital letters of what's RIGHT and what's 
WRONG we are speaking about concepts and derivations
within a particular formalism, and not larger truths about
this universe we live in. I'm not saying that one should not
teach these concepts as clearly and accurately as you can. But
let's not spend a lot of time on clever little conundrums
designed to advance one particular formalism at the expense
of another. And let's use the time that we save by looking at
some important but only perfunctorily handled problems like
how do we get from stage 2 to 3 [translating real problems
into mathematical formalism] and from 4 to 5. It's my belief
that many of the concepts we keep so nicely separated at
stages 3 and 4 get mapped together at stage 5.

Futhermore a chain of inference is only as strong as its weakest
link, so to spend a lot of effort on making the formal part of the 
subject impeccable and to neglect the process of translating the
real problems into the formalism because it is less clear-cut runs
the risk of making statistics seem irrelevent.
-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
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