HDTenEightyP/NetNews huggingface dataset:
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 26 Sep 1992 22:24:31 EDT
Reply-To:     William Kahn <71020.1025@COMPUSERVE.COM>
From:         William Kahn <71020.1025@COMPUSERVE.COM>
Subject:      error proportional 1/n

Dale Berger writes that Newsweek writes:

>"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 don't know much about real surveys, but I know that there is some complex
conditioning and stratification going on.  Is it possible that given the
degree of hetergeneity in American society, it is indeed possible to get
stochastic error proportional to 1/n over the range 500 to 2500 respondents?
You may be able to start breaking up subgroups better with the larger
samples.  Clearly once your subgroups are as homogeneous as possible then
error goes inversely with root n.  Newsweek may have been referring to a
sophisticated textbook which has a more sophisticated formula than our
typical simple random sampling one.

As an exercise, what kind of hierarchical grouping of respondent types would
indeed generate the linear relationship if attacked with an "optimal"
survey.

Bill Kahn
W. L. Gore and Associates
71020.1025@compuserve.com
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: Query re Envelope Problemread/followup
Date: 6 Oct 92 18:52:03 GMT
Organization: USDA HNRC at Tufts University

In article <EDSTAT-L%92100518105411@NCSUVM.CC.NCSU.EDU>, KLAJMAN@APOLLO.MONTCLAIR.EDU (GILBERT KLAJMAN) writes:
> I feel somewhat out of my depth... particularly since I've looked in vain
> for the beginning of the thread on the problem.  I wonder whether anyone
> has tried a Monte Carlo approach to the problem, and if so, what results
> were obtained.
> 

Great idea!  You have to come to grips with all the problems that have been
discussed in order to set up the simulation.
From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: The envelope problem
Date: 30 Sep 92 20:55:17 GMT
Organization: USDA HNRC at Tufts University

In article <johan.bring.12@statistik.uu.se>, johan.bring@statistik.uu.se (Johan Bring) writes:
> Assume 
> that you find Y dollars in your envelope. Then it is either 2Y or 0.5Y in
> the other. Both possibilities are equally likely. So the expected reward if
> you switch is +*2Y++*0.5Y=1.25Y which is more then you have. 


There is a whole class of paradoxes that become paradoxes only because people
introduce elements of Bayesian analysis without acknowledging their
presence.  THERE IS NO PHYSICAL PROCESS THAT MAKES THE 
POSSIBILITIES 2Y AND .5Y EQUALLY LIKELY.  And, therefore, it is incorrect
to say P(2Y)=P(.5Y)=0.5.  Either 1=P(2Y)=1-P(.5y) or 0=P(2Y)=1-P(.5y).
Once you pick your envelope, there is no physical
chance mechanism at work and further probability statements are impossible.

To anyone who believes that the proper Bayesian analysis of this paradox is to
switch, I make you the following offer.  Let's play the game.  I'll stuff
the envelopes.  You pick one.  I'll let you switch.  At the end, you keep the
money in your envelope and pay me a fee equal to half the money in the two
envelopes combined . . . plus a modest fee of 5% of the money in the first
envelope you chose.  Since the trade was worth 25%, surely a rational
Bayesian would be only too eager to accept this arrangement.  ;-)

"Bayesian in my heart; classicist where my finger meet the keyboard."
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 3 Oct 1992 12:26:00 PDT
Reply-To:     Albyn Jones <jones@REED.EDU>
From:         Albyn Jones <jones@REED.EDU>
Subject:      re: men, women, ans stats

I too am curious what the social scientists think about the observed
differences between men and women in mathematical ability.  It
appears to me that the experiments one would like to do, involving
random assignment of babies (possibly at the point of conception)
to environments will simply never be done.  Hence it will be
difficult to make any statements about the biological basis of
ability, or other behavioral traits.

Some random thoughts, possibly relevant:

The same claims are made about other intellectual activities, for
example chess.  The first really strong women chess players (the
Polgar sisters from Hungary) were home schooled by their parents
to avoid the negative socialization that takes place in the
public schools.  I believe that the youngest of the three sisters
was the youngest international grandmaster in history, of either
sex.  The parents were not serious chess players.

Some researchers persist in studying the genetic basis for smoking,
presumably carrying the torch lit by R A Fisher.  A recently published
study found that identical twins were more likely to have similar
smoking behavior than fraternal twins.  Some people seem to take
this study seriously.

Just heard a talk by Sylvia Wiegand (mathematician), granddaughter of
Grace Chisolm Young, one of the first women to get a PhD in
mathematics (depends on whether you count S Kovalevski (sp?)).
Among other interesting tidbits, it seems that she (and many other
early women mathematicians) had unusually attentive fathers.

That's probably enough for now!

albyn jones
jones@reed.edu
From: dick_darlington@QMRELAY.MAIL.CORNELL.EDU (dick darlington)
Newsgroups: bit.listserv.edstat-l
Subject: Bayes reference
Date: 6 Oct 92 02:11:34 GMT
Reply-To: dick darlington <dick_darlington@QMRELAY.MAIL.CORNELL.EDU>
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU


                                                                     7:37 AM
  OFFICE MEMO                                                 Time:
                      Subject:
                      Bayes reference#000#                              09-29-92
                                                              Date:

Andy Taylor asks for a reference on Bayes.  I learned Bayesian statistics in
the sixties, from books now out of print.  I've lost interest over the years,
mainly because there seems little use for Bayesian statistics in the real world
of research articles published in nonstatistical journals.  But the envelope
problem has revived my interest somewhat, since a Bayesian approach seems to me
the only reasonable one.  I do have on my shelf a new book from a top
publisher: "Bayesian Statistics" by S. James Press: Wiley, 1989.  The Preface
says, "We assume a mathematical level of sophistication that includes a good
calculus course and some matrix algebra but nothing beyond that.  We also
assume that our audience includes those who are interested in using Bayesian
methods to model real problems..."  A quick glance through the pages suggests a
well-written book with many examples.
Dick Darlington, Psychology, Cornell
#000#
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 08:32:15 EDT
Reply-To:     AJK@NIHCU.BITNET
From:         AJK@NIHCU.BITNET
Subject: Re: men, women, ans stats

> From:         John Wendell <WENDELL@UHCCVX.UHCC.HAWAII.EDU>
> Subject:      men, women, ans stats
>
> Mary Anne Metzger mentioned the Barbie controversy. Briefly, the
> Barbie controversey says "Math is hard," and the feminists and other
...
> know there are lots of you psych types on this list that might have
> some insight into this.  In particular, are there implications for
> how we teach stats to men and women?  For example, men are supposed to
> be better at spatial rotation and women better at percetual speed in
> recognizing matching patterns, does this mean that co-variance can be
> better taught to men via scatter plots and women via star plots or
> Chernoff faces?  Are there ways of explaining statistical concepts
> that can be expected to work better for one sex than the other?  Or is
> this research still so much in its infancy that there is little that
> can be said in these regards?
As a psychologist, I would say that there is no ONE way to present
a concept to any individual or group.
Usually each individual benefits from having more than one
perspective on a concept.
Many of us memorized that (a+b)**2 = a**2 + 2ab + b**2  .
if contractions are eliminated for sake of presentation we get
 1*a*a + 1*b*a + 1*a*b + 1*b*b
which makes it clearer for some people.

I have often asked stat & math PhDs if they can use a rough
sketch to show that the equation above is reasonable (true?) or
intuitive (makes sense).  Many do not produce it in a 3 minute
period. sometimes not even by the next day!


As a math statistician, I would remind that a differencein central
tendency does not necessarily mean that there is no overlap in distribution.
research and common experience show that the following set of
statement are true AS A set:
The average height of the men is greater than the average height of
women.
some men are taller than some of the women.
some women are taller than some of the men.
not(every man is taller than every woman)
not(every woman is shorter tahn every man)

art kendall
ajk@nihcu
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 6 Oct 1992 10:09:00 PDT
Reply-To:     Albyn Jones <jones@REED.EDU>
From:         Albyn Jones <jones@REED.EDU>
Subject:      factor analysis

Steven R Brown <SBROWN%KENTVM.BITNET@ncsuvm.cc.ncsu.edu>
says:

"Burt's fudging his twins data has little to do with his contribution to
the metaphysics of factors, as found in his _The Factors of the Mind_,
London, 1940.  Burt was among the first to notice the close connection
between factor analysis and the mathematics of quantum mechanics."

OK I'll bite.  what is this close connection? They both have something
to do with projection operators in linear spaces?

albyn jones
jones@reed.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 20:05:10 EDT
Reply-To:     Steven R Brown <SBROWN@KENTVM.BITNET>
From:         Steven R Brown <SBROWN@KENTVM.BITNET>
Subject:      Re: factor analysis
              29 Sep 1992 15:19:44 -0400 from <gcobb@MHC.MTHOLYOKE.EDU>

On Tue, 29 Sep 1992 15:19:44 -0400 George W. Cobb said:
>........................  To anyone who teaches or uses factor analysis,
>whether that person be statistician, psychologist, or thespian, I
>recommend an old article from The Amercian Statistician (Dec. 1967,
>pp. 17-21), by J. Scott Armstrong:
>
>Derivation of Theory by Means of Factor Analysis
>                       or
>Tom Swift and His Electric Factor Analysis Machine.
>
Armstrong's article has been one of my favorites too, but its value to
me has been in demonstrating Armstrong's timidity and unwillingness to
take implications to their conclusion.  The stereotypical way in which
someone might stage a factor analysis would be to throw in a bunch of
variables and see what happens.  Armstrong's reform consists in recom-
mending that the factor analyst have an a priori conceptualization in
terms of which the output might be judged as adequate or not: otherwise
the entire operation is terribly atheoretical.

But Armstrong's stance is only slightly less passive than the factor-
analytic strategy against which he argues since his hero Tom Swift could
conceivably stand next to the computer and wait 'til the cows come home
for it to produce results that comport with his theory.  A more active
tack is to rotate the factors theoretically -- remember that old skill,
from back in the '40s? -- to see if the factors as extracted will sup-
port one's theory.  This is an active rather than passive stance vis-a-
vis factor analysis, and the only prominent factor analyst of which I am
aware who consistently advocated this was the late William Stephenson,
who tied judgmental rotation to Charles Peirce's theory of abductory
logic (in contrast to Armstrong's ad hoc inductive logic).  One of the
best defenses of Stephenson's view was in an article by John W.
Thompson, "Meaningful and Unmeaningful Rotation of Factors," _Psycholog-
ical Bulletin_, 1962, 59, 211-223.  Armstrong's position is certainly
better than the wait-and-see head-in-the-sand position of most factor
analyses (even today), but he is only a way-station in an intellectual
evolution that ends with Stephenson's use of factor rotation as a tool
for probing factor space in the same way that an astronomer would use a
telescope to probe the heavens -- i.e., by looking in directions dic-
tated by the scientist's interests rather than waiting passively for
nature to present itself all wrapped up in simple structure.

Another factor-analytic classic, precious for its simplicity, is C.J.
Adcock's _Factorial Analysis for Non-mathematicians_, Melbourne Univer-
sity Press, 1954, which is out of print but available (I believe) from
University Microfilms as one of their "Books on Demand."
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 14:10:00 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:      max r = 1

Art Allen asks about ways to intuitively explain to students why the max r is 1
. One way is to use the correlation formula of the ratio of the covariance to t
he product of the 2 standard deviations. Clearly, the denominator is 1 times 1
and therefore is one. What is the best case scenario for the numerator? Since t
he covariance is the product of the deviation scores, think about deviations as
 z scores, and the best case would be when the z's on X are the same as the z's
 on Y. If this were the case, then we could substitute the z's on X FOR the z's
on Y. Then, the numerator would be the products of the SAME z scores, and would
 be like z squared and would produce a VARIANCE OF z's which is 1. Thus, the be
st the numerator can be is 1 and with a denominator of 1, the max r = 1. It's o
ne way to do the trick.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 26 Sep 1992 12:27:38 EDT
Reply-To:     Dart.Chance@DARTMOUTH.EDU
From:         Dart.Chance@DARTMOUTH.EDU
Subject:      Current events

A group of us are developing a new introductory course called CHANCE that
deals with current events in the news that depend in some way on chance
concepts -- DNA fingerprinting, statistical questions about AIDS, etc.  We
distribute to our group a very informal weekly list of news items that we
find in the newspapers and journals that might interest our classes.  If you
would like to receive this just send a note to

dart.chance@dartmouth.edu

Of course, if you see interesting things in recent newspapers or journals
that we miss we would appreciate your sending references to the same address.

Incidentally, you may be amused by Marilyn Vos Savant's latest problem in the
Sept. 20 Parade magazine.  This is sure to generate a lot of discussion. Here
it is:

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?
Barney Blissinger, Hershey Pa.

Marilyn pretty much implies that it does not make any different since you
gain no information from knowing the amount in your envelope.  She is wrong
about this and the fact that she is wrong follows from a very nice related
paradox.

Suppose  you are just told that two distinct numbers are put in two evelopes
and you choose an envelope at random and look at your number.  Can you give a
strategy for telling if you have the larger or the smaller of the two numbers
that has a probability great than 1/2 of being correct? The answer is yes and
here is how you do it.

 Pick an auxiliary number say with normal distribution mean 0 and variance 1.
If the number you found in the envelope was bigger than this auxiliary number
say you have the bigger number.  If it was smaller say you have the smaller
number.  Then if  your auxiliary number falls between the two numbers  in the
envelopes you will be sure to be right. This will happen with positive
probability.  In other cases you will be right with probability 1/2.  Thus
your overall probability of being correct is greater than 1/2.  Applying this
to Marilyn's problem you see that you can determine a strategy for deciding
whether to switch that is better than never switching.

I hope I am right in all this!  Laurie Snell
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Tue, 6 Oct 1992 10:43:40 -0400
Reply-To:     "Paul A. Thompson" <pat@po.CWRU.Edu>
From:         "Paul A. Thompson" <pat@PO.CWRU.EDU>
Subject:      Re: FACTOR ANALYSIS

much omitted .

>
>According to the original post by MHORNEY@OREGON, Gould's new book, like
>_The Mismeasure of Man_, shows how scientists misinterpret because of
>their philosophic commitments.  What of Gould's?  How do we account for
>his having missed the mark?  I can only offer a tentative hypothesis,

I have another hypothesis to offer about Gould and his philosophical
prejudices, which are manifest in much of his critical popularizations
of science.

I was quite annoyed by Gould's book, being in a psychometrics grad program
at the time.  I feel that not only did he caricaturize certain figures from
the past, but that his history stopped in 1940 or so.  The recent history
of the entire area is just as politically correct and careful as any other
area.   Yet by omitting the recent history, he tarred all current research
with the same brush.  His underlying presumption seems to be that
mental measurement is ipso facto racist and elitist, and should be omitted.

I recently read another article by Gould in Nature, where he publishes a
monthly column.  This column discussed Fisher's statistical research into
the smoking-cancer connection.  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.  I believe that this argument, as well as much of Gould
critical work, is historical revisionism and hindsight insight.

Generally, Gould does not seem at all sensitive to the climate of thought
at the time of his research.  While racism today is uniformly bad, can
we state absolutely that every slave owner in 1820 was totally wrong?  It
certainly was condoned and encouraged by the climate of the time, and
was the most economically rational approach to take in the south.  It was
wrong also.  But, arguing that everyone in 1820 should have the same
thought processes as do persons in the 1990 is not a sensible approach.
I do believe that Gould has this implicitely in much of his writing.

--
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
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Mon, 5 Oct 1992 12:48:31 EDT
Reply-To:     Walt pirie <WLTPIRIE@VTVM1.BITNET>
From:         Walt pirie <WLTPIRIE@VTVM1.BITNET>
Subject:      Envelope

Jerry (excitable) Dallal asked me for a rando m variable. Choose an answer you
like:
1. There are no random variables. It's all deterministic from the start. There'
s only lack of information.
2. Sure, I've got lots of random variables. Which would you like? How about:
let X=1 if the envelope chosen has the larger amount and X=0 if the smaller amo
unt. Assume a dist'n of 1/2-1/2. Now open the envelope and observe the amount (
say, $100). What information has been learned about the random variable X? To a
 frequentist, none that I can discern.

Walt Pirie
Stat, Va Tech
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.edstat-l
Date:         Sat, 3 Oct 1992 19:48:19 EDT
Reply-To:     "Karl L. Wuensch" <PSWUENSC@ECUVM1.BITNET>
From:         "Karl L. Wuensch" <PSWUENSC@ECUVM1.BITNET>
Subject:      Re: men, women, and stats
              3 Oct 1992 08:16:15 EDT from <jvaughan@ITSMAIL1.HAMILTON.EDU>

     Regarding the finding that men do better on standardized tests of math
but women get higher grades in the classroom:

     Several years ago two of my female colleagues and I published the results
of some research we did on how to predict who is going to do well and who is
going to do lousy in physics courses.  Among the predictors we used were tests
of "general intelligence," tests of critical thinking, tests of math and
algebra skills, and a test of math anxiety.  Our criterion variable was
performance in the classroom.  One of my colleagues insisted that I
analyze the data separately for men and for women, I didn't want to, but did it
just to please her.  Turns out that analysis was most useful.  For the men not
one of the predictors was significantly related to classroom performance.  For
the women all of the predictors were significantly related to classroom
performance.  The results were not due to lack of variance in the women's data
-- the sexes differed little in variances or means on the variables, but
greatly on the covariances between classroom performance and measures of
ability.

     How to account for these sex differences?  I like this hypothesis, which
has some support in other research:  In the classroom women are much better
students than men, they do what the professor tells them to (they are more
'compliant' -- profs says read the book, the reserve readings, and work all the
problems at the end of chapters, they do it).  Because they all work hard, they
all perform as best they can, thus their performance is limited only by their
ability, so tests of ability predict their performance.  Men, on the other
hand, only study hard if the course turns them on, if not, they do just enough
to scrape by, if that.  For our study, which did not address motivation, the
variance in performance due to differences in men's level of motivation went
into the error term, resulting in nonsignificance of the correlations.

     We also considered the possibility that the women's level of motivation
was uniformly high because they were in a class in a discipline that is
thought of as being stereotypically 'male.'  That is, 'Physics is hard for
women, so we best work hard as we can in this class.'  The reference:


McCammon, S., Golden, J., & Wuensch, K. L.  (1988).  Predicting
     course performance in freshman and sophomore physics
     courses:  Women are more predictable than men.  Journal of
     Research in Science Teaching, 25, 501-510.

    Karl L. Wuensch, Dept. of Psychology, East Carolina Univ.
    Greenville, NC  27858-4353, phone 919-757-6800
    Bitnet Address: PSWUENSC@ECUVM1
    Internet Address:  PSWUENSC@ECUVM.CIS.ECU.EDU
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU