HDTenEightyP/NetNews huggingface dataset:
Newsgroups: bit.listserv.edstat-l
Date:         Sun, 4 Oct 1992 18:00:53 EDT
Reply-To:     J.Laurie.Snell@DARTMOUTH.EDU
From:         J.Laurie.Snell@DARTMOUTH.EDU
Subject:      two envelope problem

Well, at least the discussion on the two envelope problem has provided some
history of the problem.

As Johan Bring mentioned it is discussed in detail in "Bayesian Statistics,
proceedings of the third Valencia international meeting edited by Bernardo.
The discussion occurs on page 233 with Zabell discussing a paper of Bruce
Hill and Hill adds to this discussion in  his reply.

 Zabell  says that he believes the first instance of the problem was in
Kratchik's Mathematical Recreations (1953) where it is introduced as a
"Necktie Paradox" but explained in terms of a game  in which two people agree
that the one with the most pennies in his pocket must give them to the other
person.  The now familiar wrong argument convinces each that this is a
favorable game.

 Martin Gardner  discussed this version in  "Ah Gotcha: Paaradoxes to Puzzle
and Deligh" (1982) and Zabell particulary recommends the discussion by
McGilvery  in the "Journal of Recreational Mathematics"  19, 15-19.   Ed
Barbeau has mentioned the two envelopes  with x and 2x version  was discussed
in the College Mathematics Journal Vol. 22, No. 4, 1991 pp 308-309.

The fact that, when you randomly pick one of two envelopes containing two
distinct numbers, you can do better than fifty fifty at guessing whether you
have the larger of  two numbers,  knowing nothing about how the numbers were
put in the envelopes, was shown by Tom Cover using the idea of the auxillary
numberin the book he edited with Godinath "Open problems in Communication and
Computation (1987).  This trick was also discussed by David Gale in the
Mathematical Intelligencer Vol. 13, No. 2, 1991 who attributes it to David
Blackwell. This seems a likely source for this problem  and I would be
interested if anyone knows more about Blackwell's connection with the it.
Also if anyone happens to know where Bertrand introduced his "Box paradox" I
would love to know it.

Laurie Snell
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Newsgroups: bit.listserv.edstat-l
Date:         Sun, 27 Sep 1992 13:01:19 EDT
Reply-To:     Walt Pirie <WLTPIRIE@VTVM1.BITNET>
From:         Walt Pirie <WLTPIRIE@VTVM1.BITNET>
Subject:      Binomial

Allen Herzog writes:



         Kahn, Jones and several others have discussed the concept
of indpendence in probability.  An interesting view of this notion
is provided by David Ruelle in his fascinating philosophical and
relatively non-technical book "Chance and Chaos" (Princeton
University Press, 1991) from the point of view of a professional
physcist.  He writes in a footnote (pp. 169-170) to his chapter
on "Probabilities" as follows:

          "We insist on giving a physical definition of the indpendence
of events.  Saying that two events are independent when they 'have
nothing to do with each other' can hardly be called an operational
definition, though. It would be better to to say that it is a metaphysical
principle that suggests operational defintions in specific cases, and the
validity of these operational defintiions can then be checked from the
consequences. But why not rather use the mathematical defintion of
independence  ( If A & B are independent, then prob (A and B)=
prob(A) X prob(B) - my interperlation)and verify it by statistical tests?
This is a neat way to present things in principle, and it is the way
used in textbooks, but not the way used in practice.

           In fact, statistical tests are a heavy and often unconvincing
machinery. So ccientists first guessthat two events are independent because
they have nothing to do with each other. Then they will thing of possible
reasons why the independence would be spoiled.  And only as a last
resort will they use statistical testing."

                                                  Allen Herzog
                                                  U50161@UICVM
My first thought was ---Ah, nice in principle, if only we had a simple,
general, effective test of independence. Then I thought: well, couldn't
we put this into a 2x11 table and do just that? Finally I realized that
test of independence would be indistinguishable from a test of
homogeneity, which would be essentially the same as the original
question.
Testing a hypothesis of independence is not something we really know how
to do well.
Statistics
Va Tech
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Newsgroups: bit.listserv.edstat-l
Date:         Sat, 3 Oct 1992 09:43:20 EDT
Reply-To:     Frank Dane <FDANE@UGA.BITNET>
From:         Frank Dane <FDANE@UGA.BITNET>
Subject:      Re: men, women, ans stats
              2 Oct 1992 23:33:20 -0400 from <WENDELL@UHCCVX.UHCC.HAWAII.EDU>

John Wendell asks for more information about sex differences from
"psychology types."  There are two important caveats to any research
concerning sex differences.  First, most "sex" difference research
is more likely to be "gender" difference research.  That is, the
differences observed are more likely to result from socialization
than biology.  (The Barbie dollcontributes to this, BTW.)
Second, and perhaps more important, "differences" typically result
from mean diferences in the samples observed.  It is therefore more
important to understand the distributional overlap; how many women are
better (or worse) than how many men?
It is an oversimplification to consider separate instructional techniques
for men and women on the basis of mean differences; it would be akin to
designing different techniques for A- and B+ students because their
exam means differ.

Finally (I know I said 2 caveats, but I can't help adding a third),
any report of sex differences in any area must be considered in light
of all of the other research in the area.  Thereis a largebody of
research on gender differences in math (sorry, don't have references
handy, but check PsychLit), and my recollection of that literature
is that gender differences areminimal and easily overcome by enhancing
interest in math.

Dr. Francis C. Dane, Associate Professor and Chair
Department of Psychology, Mercer University
Macon, GA  31207-0001  USA
Bitnet: FDANE@UGA   Internet: FDANE@UGA.CC.UGA.EDU
Tel: (912) 752-2972
Fax: (912) 752-2108
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Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 08:59:17 EDT
Reply-To:     AJK@NIHCU.BITNET
From:         AJK@NIHCU.BITNET
Subject:      'about', 'approximately', '+/-'

> From:         Jerry Dallal <jerry@HNRC.TUFTS.EDU>
> Subject:      Re: what's a random variable
> How  can you *not* teach CIs in an intro course?  After you teach someone how
> to estimate something the next question is, "How accurate is it?"  How would
> you go about answering?  CI's may not be perfect, but they are a widely used
> method of answering the question.  Students should be familiar with them.

AMEN.

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.

art kendall
ajk@nihcu
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X-Acknowledge-To: <ELLEN@PACEVM>
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 13:05:13 EDT
Reply-To:     arthur s ellen <ELLEN@PACEVM.BITNET>
From:         arthur s ellen <ELLEN@PACEVM.BITNET>
Subject:      Teaching Correlation, Suggestions?

I have been teaching correlation by showing the usual plots of r =
-1.0, 1.0 and showing how to compute Rxy by way of Z-scores. I show how the
product of the z-scores gives positive or negative correlations by
pointing out the possible product of z-scores while examining points on
a plot of z-scores.

Teaching correlation this way leaves me without a good conceptual
explanation of why the average product of z-scores ranges from -1.0 to +1.0.

Does anyone have a suggestion for explaining the upper and lower limits
of r and some alternative methods to teach correlation?

------------------------------------------------------
      ART ELLEN             PSYCHOLOGY DEPARTMENT  
 BITNET:  ELLEN@PACEVM         PACE UNVERSITY      
  VOICE:  (212) 346-1506         41 PARK ROW       
                           NEW YORK, NY 10038-1502 
------------------------------------------------------
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Return-Path: <sbaker>
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 07:49:09 -0400
Reply-To:     Stephen Baker <sbaker@UMASSMED.UMMED.EDU>
From:         Stephen Baker <sbaker@UMASSMED.UMMED.EDU>
Subject:      applied statisticians - where are they?

While it is inconceivable that there wouldn't be some applied people in any
statistics department, it is conceivable that they might be in the minority
in their own department.  The place where you should nearly always find
applied statisticians is in a university's School of Public Health.
in their own department.  The place where you should nearly always find
applied statisticians is in a university's School of Public Health.  Other
likely departments:
	operations research
	marketing research


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
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Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 15:57:49 -0400
Reply-To:     Mike M Harde <mikeh@WORLD.STD.COM>
From:         Mike M Harde <mikeh@WORLD.STD.COM>
Subject:      Envelopes

OK. I think I have it.  Whether or not to switch depends on your judgement
about how likely it is that $100 is a "high" value or a "low" value.  So
the answer is, "It depends."

I never got away with this in school.

But I guess the SAT's would provide a choice,

      .
      .
      D. Can't tell

I don't know... In a problem like this, $100 doesn't seem all that high.
I think I'll switch.

Mike Harde
Lincoln Systems Corp
mikeh@world.std.com
,
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Envelopes: clarification for subscribers
Date: 4 Oct 92 21:35:40 GMT
Organization: USDA HNRC at Tufts University


            On  Saturday,  in the middle of a flurry of  responses  to 
        postings about the envelope problem,  I decided to examine the 
        question of why we wouldn't pay to swap unopened envelopes. 
            
            I posted a message stating . . . 
         
>      Pick an envelope but *don't* open it.  Is it *now* to your 
>  advantage to switch?  I hope you said no.  Let X be the amount 
>  of money in the chosen,  but unopened, envelope.  Let Y be the 
>  money in the other envelope.  [Continuation . . .]
        
            After posting the message, I  quickly realized that it was 
        imprecise  (unconditional  statements  were written when  they 
        should have been written conditional on X=x)  and,  therefore, 
        incorrect  and,   even  if corrected,  would only add  to  the 
        confusion, so I quickly REPOSTed with a notice that I withdrew 
        the comment, and then CANCELled it a few minutes later.  I did 
        this  rather than merely  CANCEL the original in order to  get 
        notice to those  who  subscribe  directly rather than use news 
        readers.   Apparently,  my CANCEL was too close to the REPOST, 
        so subscribers  never received the retraction.    Hence,  this 
        posting, which I'll cancel tomorrow. 
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 3 Oct 1992 08:44:09 EDT
Reply-To:     Lee <WOLFLE@VTVM1.BITNET>
From:         Lee <WOLFLE@VTVM1.BITNET>
Subject:      Math sure is tough!, says Barbie.

          MATTEL OFFERS TRADE OF MATH-HATING BARBIES

   El Segundo, Calif. -- The makers of "Teen Talk" Barbie, stung
by criticism that the talking dolls utter sexist remarks, offered
to let offended customers trade their toy in for a mute model.

   But the proposal didn't silence the American Association
of University Women, which this week demanded that Mattel Toys
recall the talking Barbies.

   The association says the new dolls promote sexism and could
discourage girls from success in math, since one of the phrases
they are programmed to say is: "Math class is tough!"

   Association President Sharon Schuster said girls who want a
talking doll are unlikely to be satisfied with a tongue-tied Barbie.

   Mattel refused to recall the dolls, which retail for about $25.

                                   --Associated Press
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Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 09:51:43 EDT
Reply-To:     Lee <WOLFLE@VTVM1.BITNET>
From:         Lee <WOLFLE@VTVM1.BITNET>
Subject:      Probabilities.

   I have what is probably a dumb question.  The Commonwealth of
Virginia operates a lottery in which the winner must guess six of
44 numbers, regardless of order.  I know that the odds of guessing
those numbers are 1 in 7,059,052.  But the Commonwealth also pays
a prize to people who guess five of those six numbers.  What are
those odds?
   (As an aside, I did indeed guess five numbers.  I picked the
months and days of my children's birth dates.  There was only
one problem, I didn't buy a lottery ticket that Saturday.)



   Thank you.

                             Lee Wolfle
                             WOLFLE@VTVM1
                             wolfle@vtvm1.cc.vt.edu
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Newsgroups: bit.listserv.edstat-l
Date:         Mon, 28 Sep 1992 12:34:27 ADT
Reply-To:     GLB0000 <GLB@UNB.CA>
Comments:     <28SEP92.13570370.0200.MUSIC@UNB.CA>
From:         GLB0000 <GLB@UNB.CA>
Subject:      The last word on who teaches stat

I subscribed to and for the past few months have been a
passive observer of this list because it raises some interesting
issues.  Now I realize that it has CHANGED MY LIFE!

It's time to come out of the closet.  I admit it.  I teach
statistics in something other than a statistics department.
And, horror of horrors, I learned statistics outside of a
statistics department.

But members of this list have made me recognize the error of my
ways.  It is now clear that I cannot hope to aspire to anything
beyond the blithering idiot level myself and to believe that
I could actually teach anything about statistics to others is
nothing short of delusional.

Not only have I seen the light, I am ready to mend my ways.
I am willing to give up the undergraduate course that I have
this term and the graduate statistics course that I begin in
January.  But my Department head is unpersuaded.  He says that
these courses must be offered.  Therefore, I extend this offer
to those members of the list who, through the strength of their
logic and rhetoric, have created this situation:  Come and teach
my courses.  I assume, since your commitment to the rightness
of your cause is so great, that you will be willing to do this
for free.  Surely the knowledge that my students will be getting
a real education, rather than the misguided one that they are
currently receiving, should be reward enough.

Gary Bowden
Sociology, University of New Brunswick
glb@unb.ca
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Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 08:14:00 EDT
Reply-To:     Dennis Roberts <DMR@PSUVM.BITNET>
Comments:     208 Cedar Bldg.
Comments:     University Park, PA USA
Comments:     AC 814-863-2401
From:         Dennis Roberts <DMR@PSUVM.BITNET>
Subject:      Observations on envelopes

I have been following the discussion on envelope problems and I make the
following observations.  First, whether one is a frequentist or a bayesian,
it is obvious that such a simple problem is not so simple, given the
testimony of all of our experts.  Second, this back and forth discussion is
precisely the reason why intro courses in stat find that the "probability"
section is so difficult to students.  Other than the most basic problem in
probability, like tossing a coin (and even there, there could be some PRIOR
to consider; one mathematician once told me that the actual p values for
heads/tails flips was NOT .5 since coins are minted to have a very slight
slant on the edge to make coin mold extractions easier!), students find the
probability section horrendous ...  and it probably messes up all the
material to follow.  Thus, it is no wonder that we, on this network, are
having exactly the same difficulty that our students do!  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.  Anyway, just an observation from
this end.
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Newsgroups: bit.listserv.edstat-l
Date:         Sat, 26 Sep 1992 11:11:22 EDT
Reply-To:     William Kahn <71020.1025@COMPUSERVE.COM>
From:         William Kahn <71020.1025@COMPUSERVE.COM>
Subject:      dependent outcomes

Albyn Jones writes

. . . <stuff deleted> . . .

>Even if we don't
>allow them to discuss the question with each other, I suspect that
>commonal training, background, methodology, etc. will produce
>common decisions (i.e. dependent outcomes).

. . . <stuff deleted> . . .

The idea of independent outcomes is rather subtle.  If we can consider
common training, background, and methodology as causing dependence, perhaps
we should go further.  They have a common genetic structure (homo-sapien).
It is hard to imagine decision making on a topic of interest to humans which
is better done by non-humans.  Perhaps we want this commonality (a community
of peers) in our decision making.  Ah, but what if the interested parties
have different backgrounds (King vs LAPD)?  What dependence do we want?  How
can it be modeled?  If we can be explicit about our assumptions we can model
with conditional independence.  Part of invention, or revolution, is the
identification of here-to-fore unarticulated assumptions or conditioning.

I've heard that in setting the odds on baseball games in the sports betting
in Nevada, the houses typically employ two "independent" experts.  One is a
baseball "statistician" with numbers and computers.  The other is a
seat-of-the-pants "intuitive" type.  If they're odds are significantly
different on a game I'm not sure what resolution technique is used.  Anyone
know if this hearsay is true?  If so, Nevada is trying to address Albyn's
concern about common backgrounds and methods.

Bill Kahn
W. L. Gore and Associates
71020.1025@compuserve.com
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Via:        UK.AC.LON.LHMC.UX;  5 OCT 92 19:22:31 BST
X-Mailer:   ELM [version 2.3 PL11]
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 19:21:47 GMT
Reply-To:     Stephen Evans <rdak001@UX.LHMC.LON.AC.UK>
From:         Stephen Evans <rdak001@UX.LHMC.LON.AC.UK>
Subject:      Edstat-l

For some time I had been puzzled over replies to emails for which I had
never seen the originals. At that time I tended to see about 2 to 3 postings
from edstat-l at most per day. In the last 10 days or so I have become
overwhelmed by the volume on envelopes and Barbie dolls which seem
unimportant from my perspective. I have done nothing to change the volume
received as far as I am aware.
Please can someone tell me if this phenomenon is a result of some technical
change perhaps in the gateway to Europe or is actually a real increase in the
volume of email being generated.

If this is the usual volume and it is unlikely to change I will have to signoff

Stephen Evans
The London Hospital Medical College
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X-Delivery-Notice:  SMTP MAIL FROM does not correspond to sender.
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 13:20:47 U
Reply-To:     Wolfe Chris <wolfe_chris@MSMAIL.MUOHIO.EDU>
From:         Wolfe Chris <wolfe_chris@MSMAIL.MUOHIO.EDU>
Subject:      GRE Math

I have agreed to help a group of seniors prepare for the quantitative portion
of the GRE test. Can anyone recommend a good study guide? (But please, let's
not start a discussion of who's qualified to tutor students for the GRE's!)
-Chris Wolfe
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Newsgroups: bit.listserv.edstat-l
Date:         Fri, 2 Oct 1992 09:18:51 -0400
Reply-To:     Mike M Harde <mikeh@WORLD.STD.COM>
From:         Mike M Harde <mikeh@WORLD.STD.COM>
Subject:      Envelope questions

Re: "probabilities"

Suppose the envelopes are marked "A" and "B".  Then by Jerry Dallal's
definition of probability, is the probability that the higher amount is in
A  either 1 or 0?  We just don't know which?  Has it been determined since
there is no physical process that can change it?  If so, is there no
random event left?

Was the random event the placing of the dollars into the envelopes?  Since
the problm gives us no information about this, might there never have
been any randomness to this either?

Re: p of doubling my money = 1/3 (William Kahn)

For the past few day I have been searching for two numbers hiding in this
problem that when either multipled or divided would yield 1/3 (the
empirical approach when all else fails :-) ); the "correct" odds of
doubling my money.  Is there a way to assess these odds without
calculating backwards from an expected value of zero?

Re: A nagging problem

If I pick an envelope but don't open it.  The p = .5 works because the
expeceted value of switching to the other envelope is 1.25 times whatever
is in my envelope is offset by the expected loss from giving up what I
already have.

But once I open the envelope, p = .5 becomes p = 1/3.  Why?

Mike Harde
Lincoln Systems Corp
mikeh@world.std.com
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Newsgroups: bit.listserv.edstat-l
Date:         Mon, 28 Sep 1992 16:11:11 EDT
Reply-To:     William Kahn <71020.1025@COMPUSERVE.COM>
From:         William Kahn <71020.1025@COMPUSERVE.COM>
Subject:      switch envelopes?

Laurie Snell writes that Marilyn Vos Savant writes that Barney Blissinger
writes:

>I am asked to select one of two envelopes and told only that one contains
>twice as much money as the other.  I find $100 in the envelope I select.
>Should I switch to the other one to improve my worldly gains?

Please help me understand why this calculation is wrong:

Decision 1: Don't switch.
Decision 2: Switch.

E1=expected amount of money gained making Decision 1.
E2=expected amount of money gained making Decision 2.

E1=100$.
E2=.5*200$ + .5*50$ = 125$

E2>E1, so switch.

Normally these arguments trip me up because I have conditioned on something
without knowing I have.  Is the probability of switching to a higher
envelope not .5?

How is this problem not the same as:
You can have 100$ or an envelope which contains, with equal chance, either
200$ or 50$.

I feel silly asking about this because another part of me says the game
strategy: pick a random envelope, see what is in it, then switch, clearly
just randomly picks one of the envelopes.

Of course, the nonlinear utility of money might fold into this ultimately,
but right now, let's assume linear utility.

Thanks for the help.

William Kahn
W. L. Gore and Associates
71020.1025@compuserve.com
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