HDTenEightyP/NetNews huggingface dataset:
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Date:         Mon, 5 Oct 1992 11:23:56 U
Reply-To:     dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
From:         dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Subject:      Bayes on envelopes

                                                                     2:27 PM
  OFFICE MEMO                                                 Time:
                      Subject:
                      Bayes on envelopes                            09-28-92
                                                              Date:

In response to Andy Taylor's request, let me try a fully Bayesian analysis of
the envelope problem.  To me an exponential distribution seems like a
reasonable prior; it recognizes that nobody is very likely to put 1 and 2
billion dollars into two envelopes.  This distribution can be written f(x) =
exp(-x/a)/a, where x >= 0 and a > 0.  Some calculus shows that the mean of this
distribution is _a_.  Let this distribution be the prior dist of the smaller of
the two amounts.  Since the difference between 200 and 100 is twice that
between 100 and 50, you would switch only if _a_ were such that f(100) >
f(50)/2.  Some algebra shows that this occurs only if a > $50/ln(2) or $72.13.
But the median of an exponential dist is a*ln(2), so we can restate this
condition as requriring that the median of the dist exceed $50. In other words,
if you think it's more likely that the envelope-stuffer used over $50 for the
smaller amount than under $50, then you maximize expected income by switching.
  This analysis of course differs from another one which worked with integers;
I'm assuming the envelopes might have contained odd amounts such as $71.14 and
$142.28.
Dick Darlington, Psychology, Cornell
#000#
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Date:         Fri, 2 Oct 1992 09:35:14 CDT
Reply-To:     eco_gxc@SHSU.EDU
From:         eco_gxc@SHSU.EDU
Subject:      CI/envelopes/explain CI to students

RE: How do I explain CI to students.

I tell my students that if you have a random sample, then any statistics
that are derived from that sample are random variables x-bar, s-squared,
or a confidence interval.  The interval is random.  So, you can talk
about the prob that an interval contains mu but the prob is associated
with the location of the interval - not the location of the parameter.

Parameters, such as mu (or such as the amount of money in the second
envelope), are not random variables - unkown means a variable in algebra
but not in statistics.  In statistics, unkown just means unkown.

I doubt this explanation has a lot of meaning to most of my students.
I know it didn't mean anything to me when I took undergraduate stat
methods.

RE: envelope.

I don't really have a solid understanding of why the intuition of EV=125
is wrong for the envelope problem.  I know it is wrong because of
a my rudimentary baysian skills tell me that knowing $100 provides no
information whatsoever about whether you've got the big envelope or
the small one.  I understand the result - you can reason that out
without worring about whether or not the amount of money in the second
envelope is a random variable, although the point that it is simply an
unknown parameter, not a random variable is a good point that was
helpful to me somewhat.

But, none of that really explains to me why EV=125 is wrong.  I know you
can't compute an EV without a prob dist.  And, without a RV you can't
have a prob dist.  But, somehow, deep in my gut I think an expected value
approach ought to work anyway.  It doesn't work and that bothers me.
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Date:         Mon, 28 Sep 1992 13:21:57 -0400
Reply-To:     John Wendell <WENDELL@UHCCVX.UHCC.HAWAII.EDU>
From:         John Wendell <WENDELL@UHCCVX.UHCC.HAWAII.EDU>
Subject:      exact binomial

I retract my previous posting. There is an exact decimal solution (although
it wasnot previously posted, it is 0.0000580134505859375, for the 11 experts
problem). It is obvious that the fraction I gave has a decimal solution as
pointed out to me by Robert Hayden. I have learned my lesson, never post
a message when you are taking codine to kill the pain from an infected root
canal! Aloha, -John  it only hurts when I laugh, Ha Ha ouch.
-------
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Date:         Sat, 3 Oct 1992 00:26:18 EDT
Reply-To:     "Dr. Robert Hayden" <hayden@OZ.PLYMOUTH.EDU>
From:         "Dr. Robert Hayden" <hayden@OZ.PLYMOUTH.EDU>
Subject:      switcheroo

		The Saga of J. Laurie Snell

In the wee hours of Sunday morning, J. Laurie Snell prepares 40
envelopes.  20 contain $100, and these he puts in the left inside
pocket of his sports coat.  10 contain $200 and 10 contain $50.  These
20 he puts in the right inside pocket of his sportscoat.

Monday morning he ventures out upon the campus of Dartmouth College.
He accosts the first 20 people he meets, and hands them one envelope
randomly selected from his R.I.P. and  one envelope
randomly selectehd from his L.I.P.  10 people will get (50,100) and 10
people will get (100,200).


He then asks them to open one of the envelopes.  If the envelope
opened contains $50 or $200, he tells them to keep both envelopes and have
a nice day.  Let us say that half the people who got (50,100) and half
the people who got (100,200) happened to open the $100 envelope.  To
these people he says

	One of the two envelopes contains twice as much as the
	other.  You may keep either the $100 or the contents of
	the unopened envelope.  Which do you choose?

Last Monday, they all chose the $100 and he gave out $2000.  However,
the week before they all chose the unopened envelope and he gave out
$2500.

Questions

1. Are there any errors in the arithmetic above?

2. Is this problem isomorphic to the Marilyn vos Savant problem?  If
   not, why not.

Please make it clear which question you are answering!
--


      _
     | |          Robert W. Hayden
     | |          Department of Mathematics
    /  |          Plymouth State College
   |   |          Plymouth, New Hampshire 03264  USA
   | * |
  /    |          (603) 536-2497
 |     )          (603) 535-2489
 L_____/          hayden@oz.plymouth.edu
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Date:         Fri, 2 Oct 1992 15:58:12 EDT
Reply-To:     William Kahn <71020.1025@COMPUSERVE.COM>
From:         William Kahn <71020.1025@COMPUSERVE.COM>
Subject:      hypothesis testing = CI

Dennis Roberts writes:

>. . . <stuff deleted> . . .
>
>Of course, maybe your position is that NEITHER <hypothesis testing or
>confidence intervals> should be tackled
>
>. . . <stuff deleted> . . .

Yes.  Confidence intervals are just an inversion of an hypothesis test (the
set of all null hypotheses which are not rejected), and I lump them together
as some of finery of beautiful mathematics with marginal utility.

To make my position clear, though, I do enjoy the abstraction of "testing"
and think that on occassion it may even be useful.  It should continue to be
taught, but not in introductory courses.  I think it should sit in the
catalog right next to the Kalman Filter course: beautiful math which is
exactly right for certain specialized problems.

Bill Kahn
W. L. Gore and Associates
71020.1025@compuserve.com
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Date:         Sat, 26 Sep 1992 16:56:50 -0700
Reply-To:     BERGERD@CGSVAX.CLAREMONT.EDU
From:         BERGERD@CGSVAX.CLAREMONT.EDU
Subject:      The Science of Polling

All right, who taught statistics to the Science editors of Newsweek?
In the Science section of Newsweek, Sept 28, 1992, pp 38-39 is an
article "The Science of Polling."  It has a nice discussion of some
of the real-world factors that make polls less accurate than many
statisticians would like to believe - context effects, people who
lie, sampling problems, etc.  You might find the article useful
to stimulate class discussion of sampling, etc.

Yet, the article includes a gross error.  I quote:
"The margin of error, calculated according to a textbook statistical
formula, varies inversely with the sample size.  In general, about
500 responses gives a possible error of 5 percent either way;
2500 responses decreases it to 1 percent."

I plan to have my students critique this article after we have
covered sampling.  It should help convince students that they need
to THINK when they interpret statistical presentations.

Dale Berger, Psychology, The Claremont Graduate School, CA
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Date:         Wed, 30 Sep 1992 13:46:42 EDT
Reply-To:     HARVEYRJ@VTVM1.BITNET
From:         HARVEYRJ@VTVM1.BITNET
Subject:      tom swift & factor analysis

  george cobb recently recommended the "tom swift" article from the 1960's
as one that should be included in any course on factor analysis.  having
been assigned it during a graduate course I took on factor analysis, I
would heartily concur with this recommentation.  however, the reason for
my agreement is less obvious -- in short, armstrong's (1967) article is
useful primarily because the point it claims to "prove" about factor analysis
(i.e., that it "may be misleading," and "fails to identify the known factors
of a model") is, in itself, very misleading.  in short, although his cautions
are well taken (especially re: deriving "theory" based on exploratory
analyses), armstrong's decisions that produced his then-discredicted 3-factor
solution are flawed at nearly every step.
  first, the principal components model was chosen; much research has been
reported to indicate that it will produced biased, inflated loadings.  second,
he used the "eigenvalues > 1.0" rule, which has been thoroughly discredited
in the literature using both monte carlo and "real data" studies.  finally,
(although other questionable decisions were also made), armstrong/"swift"
used orthogonal rotation because he "believed" that the "basic underlying
factors are statistically independent"; this decision, like the others, is
completely unjustifiable based on the quantitative literature (i.e., "forcing"
an orthogonal solution on correlated axes will unavoidably produce a distorted
solution that may bear little relation to the "true" structure).
  given this series of flawed decisions, it hardly comes as a surprise that
the 3-factor orthogonal components solution does not match the "true"
underlying structure!
  some of the criticisms armstrong raises are valid, especially the use of
an exploratory technique to "prove" a theory or "test" a model.  however,
it seems as though many people simply accept armstrong's conclusions at face
value, and cite the "tom swift" paper as "proof" that factor analytic methods
are not "valid".  on the contrary, all armonstrong "proves" is that the use of
arbitrary and empirically discredicted decision rules in factor analysis will
likely lead to garbage results.  how surprising!
   thus, although examples of the "improper" use of factor analysis are not
at all hard to find (perhaps due to the fact that so few students receive
any detailed instruction in this method!), the armstrong (1967) study provides
a nice pracical demonstration of (a) how NOT do to a factor analysis, and (b)
how to construct -- and then strike down -- a "straw man" argument.

r. j. harvey
psychology
virginia tech
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Newsgroups: bit.listserv.edstat-l
Date:         Tue, 6 Oct 1992 12:37:58 U
Reply-To:     dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
From:         dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Subject:      To Johan Bring

                                                                    10:08 AM
  OFFICE MEMO                                                 Time:
                      Subject:
                      To Johan Bring                                09-29-92
                                                              Date:

Sorry to bother the network with this message, but it's the only way I know to
get through.

Johan,
I am the person you are looking for.  Your e-mail message contains two return
addresses:
   johan.bring@lobster.hsc.uu.se
   johan.bring.14@statistik.uu.se
I tried each one twice.  All four messages were returned as undeliverable.
Please let me know how I can reach you.
Dick Darlington
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Date:         Sat, 26 Sep 1992 04:19:00 BSC
Reply-To:     GELSON GOMES <GELSON@BRFAPESP.BITNET>
Comments:     @FPSP.FAPESP.BR - @FPSP.HEPNET - @BRFAPESP.BITNET - .BR gateway
From:         GELSON GOMES <GELSON@BRFAPESP.BITNET>
Subject:      Mastering INTERNET TOOLS

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                    "The InterMeta Course"

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presented in the InterMeta Course are how to (1)Remote Login,
(2)Use Electronic Mail, (3)Move a File, (4)Find Software,
(5)Locate a Person, (3)Deal with Network Problems. An index that
covers a selection of resources available on the Internet,
ranging from Card Catalogs to Archives for USENET news will also
be delivered.
     In addition, some sessions will help UNIX, VMS, VAX and DOS
users to interface their systems to the Net.
     Resulting from five years of researching and using the
Network, the InterMeta Course is being prepared by Gelson
Gomes, Ph.D. The InterMeta is the first experience of a Global
Scale Course utilizing a matrix of connected networks, the
Metanetwork.
     Dr. Gomes is a professor at the Federal University of Parana
and is conducting research on the Computer Industries of Brazil
and Taiwan. He got his Doctoral Degree on Science and Technology
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D.C.).
     The course will be ministered from Brazil; to help
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Mail your check to:
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Via: uk.ac.leicester; Mon, 28 Sep 1992 22:31:54 +0100
Site: University of Leicester, Leicester, U.K.
X-Name: David D Stretch
Phone: +44 533 522522 ext 3251, or +44 533 523251 (direct line)
Fax: +44 533 523293
Organisation: Organisation??? Who?? Me??? Don't make me laugh!
X-Address: Lecturer in Psychology, Dept. of Psychiatry,
X-Address: Clinical Sciences Building, Leicester Royal Infirmary,
X-Address: PO Box 65, Leicester, LE2 7LX, United Kingdom.
X-Mailer: ELM [version 2.3 PL0 (LUT)]
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Date:         Mon, 28 Sep 1992 22:30:19 BST
Reply-To:     dds@leicester.ac.uk
From:         David Stretch <dds@LEICESTER.AC.UK>
Subject:      Re: Cyril Burt

By chance, I was reading my copy of The Psychologist (Bulletin of the
British Psychological Society) shortly after running through messages
in my mailbox.

Richard Marshall from Nottingham Clinical Psychology Services raises an
interesting issue with respect to Cyril Burt's rehabilitation.

He asks whether the "seemingly mythical research assistants, Howard
and Conway" have ever been located, and whether anyone has
been able to obtain copies of their birth certificates. I am surprised that
this particular aspect of the affair seems not to have been sorted out,
though I have not taken a very detailed interest in it, and so I don't
know what the answer to the questions raised by Richard Marshall.

David Stretch


  +-----------------------+---------------------------------------------+
  |  Dr. David D Stretch  | First get your facts;   then you can        |
  |  Dept. of Psychiatry  |     distort them at your leisure.           |
  |  dds@leicester.ac.uk  |                                  Mark Twain |
  +-----------------------+---------------------------------------------+
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Date:         Wed, 30 Sep 1992 13:22:53 EDT
Reply-To:     Walt Pirie <WLTPIRIE@VTVM1.BITNET>
From:         Walt Pirie <WLTPIRIE@VTVM1.BITNET>
Subject:      Which Intro Stat Course?

One of the difficulties in the discussion of teaching the intro stat course is
that underlying it is the fact that people were referring to several (at least
2, probably more) different courses. What most people think of as intro stat is
 often a general concepts course ala Moore or Pisani et. al. But the first cour
se that students for whom statistics is a required part of their program (e.g.
psych, eng., bus.) take is really a course that could be titled "Stat methods f
or -----(fill in your favorite discipline.)" I see two problems with such cours
es (specifically when they are the first, and often only stat course.) First, n
o matter who teaches it, the very nature of the course makes it difficult to sp
end time on concepts, interpretations, underlying assumptions, and perspective
in general. Often those matters are given lip service at best and the course be
comes rather "cook book" in nature. Secondly, if taught in a subject-matter dep
artment, even the focus on methods is very narrow and driven by what that teach
er has used, or is familiar with, providing even less perspective. Comments?
From: dick_darlington@QMRELAY.MAIL.CORNELL.EDU (dick darlington)
Newsgroups: bit.listserv.edstat-l
Subject: Enveloping Mr. Bayes
Date: 5 Oct 92 04:33:32 GMT
Reply-To: dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU


                                                                     4:03 PM
  OFFICE MEMO                                                 Time:
                      Subject:
                      Enveloping Mr. Bayes                          09-28-92
                                                              Date:

I just realized my last missive leads to a remarkably simple conclusion.  If
you assume an exponential prior distribution, then guess a "reasonable" amount
for the LARGER of the two amounts, defined specifically as the median of your
prior distribution.  Then open your envelope.  If the amount inside exceeds the
amount you chose, then stand pat; otherwise switch.
Dick Darlington, Psychology, Cornell
#000#
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Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 09:43:20 -0400
Reply-To:     Mike M Harde <mikeh@WORLD.STD.COM>
From:         Mike M Harde <mikeh@WORLD.STD.COM>
Subject:      The envelope problem

William Kahn writes

>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?

>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.

>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.

How about the following?

Assuming all the probabilities are .5:

On the first pick you have nothing to lose. On the switch decision you
always have MORE to gain than to lose because twice any positive value is
more than half.  But in order to have the oportunity of switching, you
must make your first pick.  The strategy of picking an envelope and then
switching makes sense becasue the first pick puts you in a position to
gain more than you can lose.

Making the first pick doesn't give you any useful information; it just
gets you to a place where you have an oportunity to double your money.

The order in which you pick the envelopes is random.  And you end up with
an envelope that is randomly picked.  You still have a .5 probability
of ending up with the smaller payoff.  But the strategy makes sense because
of the way the payoffs to the second decision are biased.

If the problem was restated, "select one of two envelopes where one
contains $50 more money than the other", then switching would always be a
wash.

Or if the payoffs could be negative as well as positive (you owed dollars)
then the strategy would not be to pick and always switch.

Mike Harde
Lincoln Systems Corp
mikeh@world.std.com
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Subject: (no subject given)
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 29 Sep 1992 10:32:43 EDT
Reply-To:     Walt Pirie <WLTPIRIE@VTVM1.BITNET>
From:         Walt Pirie <WLTPIRIE@VTVM1.BITNET>

Stephen Baker writes:



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

My impression is that things in Statistics departments have changed for
the better. In the 60s and 70s I had the impression that many Stat Depts
were either "theoretical" or "applied"  and in some sense they were like
opposing camps. It seems like the discipline as a whole has moved more
toward the applied. More generally while individual departments still
tend to one side or the other, almost all have a good mix, and in part-
icular even the more theoretical dept.'s pay a lot more attention to
applications. I don't know how much my view here is colored by the fact
that I am in a traditionally applied dept.
Walt Pirie
Statistics, Va. Tech
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