HDTenEightyP/NetNews huggingface dataset:
Newsgroups: bit.listserv.edstat-l
Date:         Thu, 1 Oct 1992 10:51:54 U
Reply-To:     dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
From:         dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Subject:      Envelope

                                                                    10:19 PM
  OFFICE MEMO                                                 Time:
                      Subject:
                      Envelope                                      09-25-92
                                                              Date:

I've really enjoyed the discussion of the envelope problem.  A curious feature
of it is that Dave Krantz and Jerry Dallal agree that there is no expected gain
from switching.  I agree; as Ronan Conroy points out so elegantly, otherwise we
have discovered a way to compound our money at approximately 25% every 10
seconds, if that's how long it takes us to switch envelopes.  But Krantz
reaches his conclusion by a Bayesian analysis while Dallal concludes that the
envelope problem illustrates the limitations of Bayesian analysis.  Maybe I've
missed Dallal's point, but it seems to me that Krantz is right.  You can
certainly find elementary expositions of Bayes' Theorem in classical texts on
probability, so we can't say that classicists are opposed to all uses of Bayes'
Theorem, such as the oversimplified use that leads to the false conclusion that
one gains by switching.  I believe Krantz has shown that the envelope problem
is a nice example of why some rather high-level Bayesian thinking is sometimes
necessary.
Dick Darlington, Psychology, Cornell
#000#
Newsgroups: bit.listserv.edstat-l
From: mcoffin@IASTATE.EDU (Marie Coffin)
Subject: Re:      quantitative literacy for elementary school kids?
Reply-To: mcoffin@IASTATE.EDU (Marie Coffin)
Organization: Iowa State University
Date: Tue, 29 Sep 1992 18:50:14 GMT

In article <9209290211.AA04416@>,         ataylor@LALA.ZOO.HAWAII.EDU writes:
> Does anyone know anything about teaching concepts of probability and
> statistics to elementary school kids (6-12 year olds)? Is it possible?
> Or, to put it another way, would I be crazy to volunteer myself as a
> resource person at my daughter's school? Would it be more effective with
> high school kids?
> 
> - Andy Taylor
>   Department of Zoology
>   University of Hawaii at Manoa
> 
>   taylor@lala.zoo.hawaii.edu
>   ataylor@uhunix.bitnet

Yes, it is possible, and no, you would not be crazy to volunteer.  
I did this last year at a local grade school.  I was tutoring a gifted
fifth-grader, but he had no advanced math (i.e. nothing beyond fractions
and decimals).  We covered the basics of probability, took samples, made
graphs, etc.  It was a lot of fun for both of us.  

I can send you more details via e-mail, if you like.

Marie Coffin
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: tests, CIs, Bayesism .... Who are we teaching and why?DIR
Date: 3 Oct 92 19:12:15 GMT
Organization: USDA HNRC at Tufts University

In article <9210030002.AA05369@>, ataylor@LALA.ZOO.HAWAII.EDU writes:

> I can guarantee you (no uncertainty here!) that much of the esoterica
> floating around in connection with this envelope puzzler is detrimental to
> these pragmatic purposes. 

On the contrary.  This newsgroup is for people who are (concerned about)
teaching statistics.  The envelope paradox gets right to fundamentals.  And
if teachers of statistics can't sort out paradoxes such as these, it's
no wonder that some students are poorly taught.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 18:04:00 PDT
Reply-To:     "Peter A. Lachenbruch" <IARSPAL@UCLAMVS.BITNET>
From:         "Peter A. Lachenbruch" <IARSPAL@UCLAMVS.BITNET>
Subject:      Teaching Statistics Journal

Recently I mentioned that Peter Holmes was the editor of the journal TEACHING
STATISTICS. This is incorrect - the editor is David Green of the Department of
Mathematical Sciences, University of Technology, Loughborough LE11 3TU in
United Kingdom.  Sorry if this caused any confusion, and my apologies to
Peter Holmes if he has received too large a volume of mail and submissions be-
cause of my error.
Tony
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: Envelope.
Date: 2 Oct 92 03:35:11 GMT
Organization: USDA HNRC at Tufts University

In article <EDSTAT-L%92100115052005@NCSUVM.CC.NCSU.EDU>, WLTPIRIE@VTVM1.BITNET (Walt Pirie) writes:

I'll try one more time and then I'm out of here . . .

It's *exactly* the same as confidence intervals.

opening the envelope = generating a particular confidence interval

probability was 1/2-1/2 of choosing envelope with larger or smaller amount  =
       probability *WAS* 95% that your (future) interval would cover parameter

knowing amount = knowing interval

other envelope contains $200 = interval contains population parameter

> I'm having trouble with Jerry Dallal's argument. Here's my problem. Once you've
>  opened the envelope, admittedly you know how much is in that envelope. But loo
> ked at another way, the probability was 1/2-1/2 that you'd choose the envelope
> with the larger or smaller amount of money. Without some additional information
>  on the amounts involved, your data provides no information relevant to the ori
> ginal probabilities. That's not at all like the Confidence Interval problem.
> Walt Pirie
> Stat, Va Tech

How do you explain to your students why it is incorrect to say "the probability
that the population mean lies in the interval (-1.3, 2.7) is 95%"?  
Or do you let them say it ?

Don't give me babble!  Give me mathematics!  (I'm flaming, but I'm an excitable
guy.  Don't take it personally.)  I've given you mathmatics.  I've said THERE
IS NO MORE RANDOM VARIABLE.  Give me a RANDOM VARIABLE.  Then we can talk 
about PROBABILITIES.  To repeat: (I'm flaming, but I'm an excitable
guy.  Don't take it personally.)  
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 6 Oct 1992 13:56:24 +1000
Reply-To:     Michael Smithson <bhmjs@MARLIN.JCU.EDU.AU>
From:         Michael Smithson <bhmjs@MARLIN.JCU.EDU.AU>
Subject:      Fudge Factors and False Precision

Art Kendall writes:
>One of the most important concepts (IMHO) to get across EARLY is
>that estimates are best communicated to a reader by saying that
>"15 to 27 percent of the..." rather than saying "21 percent of the..."
>In one study the following two sentences were considered for inclusion
>in a report. How many of you would choose A over B?
>A: At the xxxxxxxx Naval Supply Center, we estimated that value of
>the material on the shelves exceeded the value shown on the books
>by $1,039,875,603 (+/- $38,421,791).
>B: At the xxxxxxxx Naval Supply Center, we estimated that value of
>the material on the shelves exceeded the value shown on the books
>by $1.04 billion (+/- $.04 billion).
>
>Whether we callit precision, the plus-or-minus factor, fudge,
>sampling error, or ???, it is one of the most important
>concepts for students to obtain.
>

AMEN (to add to his AMEN)!

IMHO, and ironically, this basic point all too often gets lost even in data
analyses by professionals. Frequently variability, vagueness, ambiguity,
and other kinds of uncertainty are not systematically recorded at the point
of data-coding and entry, with the result that data are recorded as falsely
precise. Matters are not aided by the current default options of pointwise
values or 'system-missing' values for many stats packages.

An example I often use to introduce students to some ideas about uncertainties
in data consists of the following hypothetical responses-from-hell to a survey
question about monthly income:

Case    Numerical Info.     Epistemic status
 1      $1500               Really precise; respondent's true/constant income.
 2      $1000-$2000         Respondent can't remember exactly.
 3      $1000-$2000         Respondent's income fluctuates unpredictably.
 4      $1000-$2000         [oops] R's income oscillates periodically.
 5      $1000 or $2000      Interviewer's handwriting is unclear.
 6      $1000 or $2000      Respondent's income alternates monthly.

All of these give the same 'pointwise' guesstimate of $1500-- Moreover, the
numerical information by itself is insufficient to reveal the kinds of
measurement problems involved; qualitative information is needed to convey
epistemic 'pedigree'. And that's exactly the kind of information which gets
lost in the translation from raw, dirty data to sanitized analysis.

Mike Smithson
Behavioural Sciences
James Cook University
Queensland 4811 Australia     bhmjs@marlin.jcu.edu.au
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 6 Oct 1992 10:24:00 PDT
Reply-To:     Albyn Jones <jones@REED.EDU>
From:         Albyn Jones <jones@REED.EDU>
Subject:      RA Fisher

Paul Thompson, Ph.D. states:

"Essentially, Gould argued (in my reading of
the article) that smoking and cancer are now known to be related, and thus
Fisher's somewhat self-interested defense of smoking (he was a smoker, and
wished to reassure himself, Gould argued) was motivated by self-interest and
not science. "

Does Gould really argue this?  It seems far more likely that Fisher
was motivated by his belief in the primacy of genetics - he was
a seminal figure in the development of quantitative genetics, and a
vocal supporter of the eugenics movement (better people through good
breeding; he put his theories into practice, siring 15 children as i recall).
I suspect that the fact he was a smoker, and may even have been supported
by the tobacco industry in his later years (anyone know details?)
is much less important than his beliefs about genetics.

albyn jones
jones@reed.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 03:37:50 EST
Reply-To:     "Kirke B. Lawton" <LAWK@UORVM.BITNET>
From:         "Kirke B. Lawton" <LAWK@UORVM.BITNET>
Subject:      Switching envelopes

Interesting question!

I think the apparent paradox (that it makes sense always to pick an
envelope and then switch regardless of the contents) is the result of
an implicit assumption, namely that the one has no a priori expectations
about the stakes of the game.  The previous solution assumes that
the player believe that a $100 versus $200 game is just as likely
as a $50 versus $100 game.

Consider the following decision tree:

                          __0.5__($200)   X=$100, picked high (2X)
                         /
     ___ p ___(good game)
    /                    __0.5__($100)   X=$100, picked low (X)
   /
(Start)                   __0.5__($100)   X=$50, picked high (2X)
                        /
    __ 1-p _(cheap game)
                         __0.5__($50)    X=$50, picked low (X)

p is the player's expection that the game is a "good game" ($200 versus
$100) rather than a "cheap game."  In each case the probability is
.5 that the player happened to chose the higher of the available
envelopes.  The player must choose whether to switch envelopes without
knowing whether the game is Good or Cheap.  All she know is that she has
picked the low value if the game is Good and the high envelope if the
game is Cheap.

So the expected NET value of switching is p*($200-$100) + (1-p)*($50-$100)
 = $100p - $50 + $50p = $150p - $50.  This is at least zero (no expected loss)
if p is at least one-third.  Thus, the decision whether to switch or not
depends on how likely it is that the HOST is willing to risk an expected
$150/game versus $75/game.  If the richer game less than half as likely, then
the optimal choice is to stay with the initial $100.

Hmmm.  Maybe my subscription to this list will help me contruct less
verbose and more pedagogically appealing explanations :)

Kirke B. Lawton
Dept. of Political Science
University of Rochester


========================================================================
6
LINE 1 %DATE
LINE 3 %SUBJ
LINE 4 %IDEND   %IDSTART
LINE 5 %END
LINE 6 %DIV
LINE 51 V900101  %RESUME
Re: switch envelopes?
71020.1025
COMPUSERVE.COM
William Kahn

0
43
2 7
1
0 0 1 0 0
1 0 0 0
51
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 13:20:39 EDT
Reply-To:     Walt Pirie <WLTPIRIE@VTVM1.BITNET>
From:         Walt Pirie <WLTPIRIE@VTVM1.BITNET>
Subject:      Who....

Paul Thompson writes:


Biology    Chemistry   Physics
   Biochemistry   Physical chemistry

Biology    Physics
   Biophysics

If all these disciplines required that only pure persons engage in
them, many important collaborative ideas and research probably would
not have been done.  Too many walls = incestuous inbred research.


--
Paul Thompson, Ph.D.  |  Department of Psychiatry  |  (216) 844-7463
Case Western Reserve University  | Cleveland, OH  44106
------------------------------------------------------------------------------
When I hear "family values," I reach for my revolver. - para. Hans Jonst

I think we're getting off track, here. This is a red herring. "Engaging
in" and teaching basic coursework in are rather unrelated issues. Even
teaching basic coursework in (Statistics or any other "service discipline
" like those mentioned) is quite a different issue than following that up
 with more narrow topics of interest in a specific applications
 discipline.
Walt Pirie
Stat, Va Tech
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 28 Sep 1992 17:29:00 PDT
Reply-To:     "Peter A. Lachenbruch" <IARSPAL@UCLAMVS.BITNET>
From:         "Peter A. Lachenbruch" <IARSPAL@UCLAMVS.BITNET>
Subject:      teaching statistics

I am mildly surprised that nobody has mentioned Harold Hotelling's article on
"The Teaching of Statistics" which appeared in the Annals of Mathematical
Statistics in 1940. It seems that this topic is hardly a new one. It also is
reprinted in the Hotelling Festscrift volume edited by Ingram Olkin "Contri-
butions to Statistics" which appeared in the late 1950s or early 1960s.
The problem of staffing is clearly a vexing one, as is the problem of quality
control. I would be a disaster teaching a course in Factor Analysis and/or
Linear Structural Modelling (among the many) - but I would indicate that from
the start and try NOT to teach the course. Sometimes there are obvious problems
 like the person who taught students not to use the t distribution with small
degrees of freedom - I think the logic was that normality wasn't assured - he/
she may have been correct, but the reasoning was flawed. At my previous Uni-
versity, the vice-president convened a statistics advisory group which got a
lot of people talking to each other and resulted in lower duplication.
Walt Pirie suggested in his last note that Sensitivity and Specificity were not
widely used. In medicine I am always being asked about this, and they are quite
important in ROC analysis. Oh well, enough rambling . . .
Tony
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Wed, 30 Sep 1992 12:24:02 BST
Reply-To:     Jane L Hutton <MW12@LIVERPOOL.AC.UK>
From:         Jane L Hutton <MW12@LIVERPOOL.AC.UK>
Subject:      Textbook errors

I have just sent a textbook back to John Wiley, as it contained a number
of gross errors. The book is 'Exploring statistics with MINITAB' by A Monk
An early error is that the mode is incorrectly defined, and no sensible discuss
ion of its use is given. I suspect that the manuscript was not reviewed by a
statistician, and I note that the author belongs to a psychology department.
I expect the book will contribute to confusion about and misuse of statistics
in the behavioural sciences.

Perhaps instead of trying to disallow non-statisticians as teachers on applied
courses, statistician could offer to vet material. I think that exam questions
and full solutions should be checked by a person with postgraduate level
statistics and experience in applied stats
Jane L Hutton
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Apparently-To: EDSTAT-L@ncsuvm.cc.ncsu.edu
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 28 Sep 1992 11:16:10 -0500
Reply-To:     "via the vacation program" <marick@CS.UIUC.EDU>
From:         "via the vacation program" <marick@CS.UIUC.EDU>
Subject:      out of town

I am on the road for a while.  I'll read my mail when I return.

Brian Marick
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL11]
Newsgroups: bit.listserv.edstat-l
Date:         Fri, 2 Oct 1992 20:27:22 EDT
Reply-To:     Mary Ann Metzger <metzger@UMBC3.UMBC.EDU>
From:         Mary Ann Metzger <metzger@UMBC3.UMBC.EDU>
Subject:      For those who inquired about Barbie

For those who requested Barbie's solution:

The important part of the solution was described very nicely by an earlier
correspondent to edstat-l (I don't have the item for citation): Ken and the
teacher both accept the assumption that a number may be randomly chosen from
the positive integers.  But this assumption is self-contradictory (although not
obviously so) and therefore leads to a paradox.  The teacher must specify,
therefore, that the possible amounts in the envelopes have been selected from a
finite set of integers.

Best strategies can be determined for any given set of integers.  For example:
If the possibles run from 1 to 12, then the possible amounts (permissibles) in
any envelope are 1 2 3 4 5 6 8 10 12.  Notice that no odd numbers greater than
5 are in the set of permissibles.  The strategy for this interval is clear: if
the number is 1 3 or 5 then switch (the other envelope has 2 6 or 10,
respectively).  If the number is 2 or 4, then switch because Ken's argument
applies.  If the number is 8 10 or 12 then stay.

I don't have a general solution because I haven't thought of a way to
characterize the general properties of intervals.  For example, for the
interval between 11 and 25, the only permissible values for the contents of the
envelopes are 11 12 22 24.  My conjecture is that for any given finite interval
of consecutive integers, approximately 1/3 or fewer of the permissible integers
are odd while 2/3 are even and of the even integers, approximately 1/2 can only
be high amounts.

For every odd number in every set, it's best to switch, since an odd integer
can never be represented as 2X where X is a positive integer. My conjecture is
that the best strategy for even numbers will be to stay.

-Mary Ann
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 09:48:00 PDT
Reply-To:     Albyn Jones <jones@REED.EDU>
From:         Albyn Jones <jones@REED.EDU>
Subject:      envelopes, probability, obscurity

Dennis Roberts opines:

"I think it is not
so much (as someone questioned) that some of us don't know what we are
talking about but rather, probability material is inherently obscure and
difficult compared to many other topics."

I wonder.  Maybe it seems obscure because most people aren't used to
thinking about it.  Kahneman and Tversky make a career out of
demonstrating that people have trouble with probability.  This
doesn't convince me that probability is hard relative to lots of
other activities, just that people don't pratice enough to get good at it.
Calculus is equally obscure to those who haven't studied it, or who
had a cook-book course, or whatever.  Music has always seemed obscure
to me (whaddya mean i'm singing in the wrong key?)
albyn jones
jones@reed.edu
From: dick_darlington@QMRELAY.MAIL.CORNELL.EDU (dick darlington)
Newsgroups: bit.listserv.edstat-l
Subject: max r = 1
Date: 5 Oct 92 08:28:12 GMT
Reply-To: dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU


                                                                     7:57 PM
  OFFICE MEMO                                                 Time:
                      Subject:
                      max r = 1#000#                                    09-28-92
                                                              Date:

Dennis Roberts offered one way to explain why the maximum r is 1.  Another way
uses difference scores.  Let M(x) denote the mean of x, so that M(z1^2) =
M(z2^2) = 1 and M(z1*z2) = r.  Then
M(z1 - z2)^2 = M(z1^2) + M(z2^2) - 2M(z1*z2) = 2 - 2r
But the first term on the left has a lower limit of 0, which gives r an upper
limit of 1.
Dick Darlington, Psychology, Cornell
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Return-Path: <sbaker@umassmed.UMMED.EDU>
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 07:54:19 -0400
Reply-To:     Stephen Baker <sbaker@UMASSMED.UMMED.EDU>
From:         Stephen Baker <sbaker@UMASSMED.UMMED.EDU>
Subject:      quantitative literacy for elementary school kids.

I was amazed to find my 6th grade daughter doing combinatorics and binomial
problems for math homework!  Just a sprinkling, but encouraging.  I had
thought I had seen pascal's triangle out of the corner of my eye!



Stephen P. Baker                                phone:  (508) 856-2625
Lecturer in Biostatistics                               (508) 856-2440 fax
Department of Academic Computing                        (413) 253-3923 home
University of Massachusetts Medical School      e-mail: sbaker@umassmed.bitnet
55 Lake Avenue North                                    _. .____ __. _ __._
Worcester, MA 01655
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: Envelope questions
Date: 4 Oct 92 14:27:29 GMT
Organization: USDA HNRC at Tufts University

In article <9210040246.AA05659@>, ataylor@LALA.ZOO.HAWAII.EDU writes:
> Jerry Dallal, responding to Mie Harden(?)
 [ . . . it goes on . . . ]

Drat!  Andy sent this same message to me via E-mail and I responded in kind
by typing directly into the mailer without saving a copy.  Andy, would you 
kindly post my response?

Thanks.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Mail-System-Version: <VAX-MM(235)+TOPSLIB(133)+PONY(228)
                     @UHCCVX.UHCC.HAWAII.EDU>
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 26 Sep 1992 18:43:07 -0400
Reply-To:     John Wendell <WENDELL@UHCCVX.UHCC.HAWAII.EDU>
From:         John Wendell <WENDELL@UHCCVX.UHCC.HAWAII.EDU>
Subject:      Exact Binomial Probabilities

Well there have been some postings about the _exact_ probability of
the 11 experts, each with .95 chance that they are individually
correct, that the majority of these experts will be wrong. If you
assume that the probabilities are independent and that the .95
probability is known exactly (and those giving an _exact_ solution
have assumed these conditions) the _exact_ probability is
297,028,867/51,200,000,000,000. There is not an _exact_ solution to
this problem that can be given in decimal notation.

 Yes, I know that both of the conditions assumed cannot be expected to
apply to real world situations. This is my (sick) attempt at humor.

Aloha, - John WENDELL@UHCCVX.UHCC.HAWAII.EDU

P.S. hope you found this posting at least half as funny as I do.
-------
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU