Re: Gen random numbers from distribution

[Robert J. MacG. Dawson]

Jim Snow wrote:
> 
> 1. George Marsaglia and Wal Wan Tsang published a paper dealing with
> your problem which gives an efficient procedure for all values of
> parameters. It is
> 
> "The Monty Python Method for Generating Gamma Variables"
> 
> in the Journal of Statistical Software ,vol3,issue 3,1998
> .
> 
> This is an online journal. The paper is available at
> 
> www.jstatsoft.org/v03/i03/
^^^  
you'll need this!

Thanks for the tip, it's a good paper.

-Robert Dawson


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Re: Stat question

[Dennis Roberts]

the reality of this is ... sometimes getting notes from other students is 
helpful ... sometimes it is not ... there is no generalization one can make 
about this

most student who NEED notes are not likely to ask people other than their 
friends ... and, in doing so, probably know which of their friends they 
have the best chance of getting good notes from ... (at least READABLE!) 
...even lazy students are not likely to ask for notes from people that even 
THEY know are not going to be able to do them any good

but i don't think we can say anything really systematic about this activity 
other than, sometimes it helps ... sometimes it does not help

At 06:24 PM 12/5/01 -0800, Glen wrote:
>Jon Miller <[EMAIL PROTECTED]> wrote in message >
> > You can ask the top students to look at their notes, but you should be 
> prepared
> > to find that their notes are highly idiosyncratic.  Maybe even unusable.
>
>Having seen notes of some top students on a variety of occasions
>(as a student and as a lecturer), that certainly does happen
>sometimes. But just about as likely is to find a set of notes that
>are actually better than the lecturer would prepare themselves.
>
>Glen
>
>
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dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



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Slutsky's theorem

[kjetil halvorsen]

Slutsky's theorem says that if Xn ->(D) X and Yn ->(P) y0, y0 a
constant, then

Xn + Yn ->(D) X+y0. It is easy to make a counterexample if both Xn and
Yn converges in distribution. Anybody have an counterexample when Yn
converges in probability to a non-constant random variable?

Kjetil Halvorsen


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Re: When does correlation imply causation?

[Alex Yu]

Whether we can get causal inferences out of correlation and equations has 
been a dispute between two camps:

For causation: Clark Glymour (Philosopher), Pearl (Computer scientist), 
James Woodward (Philosopher) 

Against: Nancy Cartwright (Economist and philosopher), David Freedman 
(Mathematician)

One comment fromm this list is about that causal inferences cannot be 
drawn from non-experimental design. Clark Glymour asserts that using 
Causal Markov condition and faithfulness assumption, we can make causal 
interpretation to non-experimental data.


Chong-ho (Alex) Yu, Ph.D., MCSE, CNE, CCNA
Psychometrician and Data Analyst
Assessment, Research and Evaulation
Cisco Systems, Inc.
Email: [EMAIL PROTECTED]
URL:http://seamonkey.ed.asu.edu/~alex/
  



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Re: Evaluating students: A Statistical Perspective

[Rich Ulrich]

Just in case someone is interested in the Harvard instance 
that I mentioned -- while you might get the article from a newsstand
or a friend --

On Sun, 02 Dec 2001 19:19:38 -0500, Rich Ulrich <[EMAIL PROTECTED]>
wrote:

[ ... ]
> 
> Now, in the NY Times, just a week or two ago.  The
> dean of undergraduates at Harvard has a complaint 
> about grade inflation.  More than 48% of all undergraduate
> grades last year were A.  (In 1986, it was only 34% or so.)
> Only 6% or present grades were C or D or F.
> 
> The dean has asked the faculty to discuss it, which is
> as much as she can do.  I don't know: Would the A's 
> emerge as scores on-a-curve, or are the lessons so
> easy that all the answers are right?
[ snip, rest]
Section A  of the  NY Times on Wed., Dec 5, had another 
article (page 14) and a column (page 21).

There were specific comments *contrary*  to some obvious notions
of grade "inflation" as an arbitrary and bad thing:  some were
presented as opinion, and other as apparent fact.  Recent Harvard
students have higher SATs than ever.  Students at a particular level
(of SAT, or otherwise) supposedly are performing better.  
The Dean of Harvard College (a subunit, I think)  says that his
students (in computer science) handle some previously-tough 
problems much more easily.  [ And I wonder, Is that peculiar to cs.]
Someone else was quoted,  that the performance needed for an A 
had not changed.

Amongst the commentary in the column -
Comments on educational research:  Good students (some 
research says) learn more if top grades are kept lower, but 
lower grading can discourage poorer students and increase 
dropout rates.   - Both effects are easy to imagine, somewhere,
sometime, 

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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Re: When does correlation imply causation?

[Dennis Roberts]

i repeat ... the r value shows the extent to which a straight line (in a 2 
variable problem) can pass through a scatterplot and, be close TO the data 
points

in that sense, r is an index value for the extent to which a straight line 
MODEL fits the data ...

knowing how the dots on the scatterplot got to be ... is totally outside 
the realm of what r can know



At 10:06 AM 12/6/01 -0700, Alex Yu wrote:

>Whether we can get causal inferences out of correlation and equations has
>been a dispute between two camps:
>
>For causation: Clark Glymour (Philosopher), Pearl (Computer scientist),
>James Woodward (Philosopher)
>
>Against: Nancy Cartwright (Economist and philosopher), David Freedman
>(Mathematician)
>
>One comment fromm this list is about that causal inferences cannot be
>drawn from non-experimental design. Clark Glymour asserts that using
>Causal Markov condition and faithfulness assumption, we can make causal
>interpretation to non-experimental data.
>
>
>Chong-ho (Alex) Yu, Ph.D., MCSE, CNE, CCNA
>Psychometrician and Data Analyst
>Assessment, Research and Evaulation
>Cisco Systems, Inc.
>Email: [EMAIL PROTECTED]
>URL:http://seamonkey.ed.asu.edu/~alex/
>
>
>
>
>=
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>the problem of INAPPROPRIATE MESSAGES are available at
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>=

_
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



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Re: Evaluating students: A Statistical Perspective

[Dennis Roberts]

generally speaking, it is kind of difficult to muster sufficient evidence 
that the amount of grade inflation that is observed ... within and across 
schools or colleges ... is due to an  increase in student ability

i find it difficult to believe that the average ability at a place like 
harvard has gone up ... but if so, very much over the years ...

if anything, selectivity has decreased at some of these top schools due to 
the fact that given their extremely high tuition ... they need to keep 
their dorms full and, making standards higher and higher would have the 
opposite effect on keep dorms filled





At 11:58 AM 12/6/01 -0500, Rich Ulrich wrote:
>Just in case someone is interested in the Harvard instance
>that I mentioned -- while you might get the article from a newsstand
>or a friend --
>
>On Sun, 02 Dec 2001 19:19:38 -0500, Rich Ulrich <[EMAIL PROTECTED]>
>wrote:
>
>=

_
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



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Re: When does correlation imply causation?

[Art Kendall]

This is a multi-part message in MIME format.
--E98CFE9DA7C53331DB22D947
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

Is it a fair interpretation of what you are saying to say  that the
process of correlating phenomena needs to be distinguished from the
value of some form of correlation coefficient?  I certainly agree with
that.
- - -
The observation that a correlation exists is one point in an inductive
argument about causation.  The entire argument shows causation.  If we
cannot show some form of correlation an important element of a casual
inference is missing.  Of course, the mere existence of a correlation,
by itself, does not constitute a complete complete argument about
causation. 

Related to this, I don't put a lot of faith in any single study, but
find plausability in a range of studies about a phenomenon.
- - -
Where do you put dose-response curves in your epistemology? How do you
deal with statements like:
Larger speed differences resulted in larger doppler shifts.
More ionizing radiation resulted in more deaths.
More time spent memorizing vocabulary words resulted in more words
recalled a week later.
More stress increased performance up to a point and then increased
stress lowered performance.
More exposure to a treatment results in a higher probability of
recovery.
- - -
Usually I think of X in the manipulated range as causal of Y _in a
population_. Often we cannot get to a deterministic cause, but to
stochastic or probabilistic causation. BY ITSELF, the demonstration that
people who smoked more were more likely to get cancer was insufficient
for some researchers.  However, after DNA was discovered and better
understood, and the mechanism induced in vitro and in vivo, even the
Tobacco Institute has recognized the causation.

Dennis Roberts wrote:

> At 07:36 AM 12/5/01 -0500, Karl L. Wuensch wrote:
>
> >   Accordingly, I argue that correlation is a necessary but not a
> > sufficient condition to make causal inferences with reasonable
> > confidence.  Also necessary is an appropriate method of data
> > collection.  To make such causal inferences one must gather the data by
> > experimental means, controlling extraneous variables which might confound
> > the results.  Having gathered the data in this fashion, if one can
> > establish that the experimentally manipulated variable is correlated with
> > the dependent variable (and that correlation does not need to be linear),
> > then one should be (somewhat) comfortable in making a causal
> > inference.  That is, when the data have been gathered by experimental
> > means and confounds have been eliminated, correlation does imply causation.
>
> the problem with this is ... does higher correlation mean MORE cause? lower
> r mean LESS cause?
>
> in what sense can think of cause being more or less? you HAVE to think that
> way IF you want to use the r value AS an INDEX MEASURE of cause ...
>
> personally, i think it is dangerous in ANY case to say that r = cause ...
>
> if you can establish that as A goes up ... so does B ... where you
> manipulated A and measured B ... (or vice versa) ... then it is fair to say
> that the causal connection THAT IS IMPLIED BECAUSE OF THE WAY THE DATA WERE
> MANIPULATED/COLLECTED also has a concomitant r ... BUT, i think one still
> needs to be cautious when then claiming that the r value itself is an
> indicant OF cause
>
> >
> >
> >   So why is it that many persons believe that one can make causal
> > inferences with confidence from the results of two-group t tests and
> > ANOVA but not with the results of correlation/regression techniques.  I
> > believe that this delusion stems from the fact that experimental research
> > typically involves a small number of experimental treatments that data
> > from such research are conveniently evaluated with two-group t tests and
> > ANOVA.  Accordingly, t tests and ANOVA are covered when students are
> > learning about experimental research.  Students then confuse the
> > statistical technique with the experimental method.  I also feel that the
> > use of the term "correlational design" contributes to the problem.  When
> > students are taught to use the term "correlational design" to describe
> > nonexperimental methods of collecting data, and cautioned regarding the
> > problems associated with inferring causality from such data, the students
> > mistake correlational statistical techniques with "correlational" data
> > collection methods.  I refuse to use the word "correlational" when
> > describing a design.  I much prefer "nonexperimental" or "observational."
> >
> >
> >
> >   In closing, let me be a bit picky about the meaning of the word
> > "imply."  Today this word is used most often to mean "to hint" or "to
> > suggest" rather than "to have as a necessary part."  Accordingly, I argue
> > that correlation does imply (hint at) causation, even when the
> > correlation is observed in data not collected b

Experimental Correlation Coefficients

[Wuensch, Karl L]

My experimental units are 100 classrooms on campus.  As I walk into
each room I flip a perfectly fair coin in a perfectly fair way to determine
whether I turn the room lights on (X = 1) or off (X = 0).  I then determine
whether or not I can read the fine print on my bottle of smart pills (Y = 0
for no, Y = 1 for yes).  From the resulting pairs of scores (one for each
classroom), I compute the phi coefficient (which is a Pearson r computed
with dichotomous data).  Phi = .5.  I test and reject the null hypothesis
that phi is zero in the population (using chi-square as the test statistic).
Does correlation (phi is not equal to zero) imply causation in this case?
That is, can I conclude that turning the lights on affects my ability to
read fine print?

I modify my experiment such that Y is now the reading on an
instrument that measure the intensity of light in the classroom.  I
correlate X with Y (point biserial r, a Pearson r between a dichotomous and
a continuous variable) and obtain r = .5.  I test and reject the null that
this r is zero in the population (using t or F as the test statistic).  Does
correlation (point biserial  r is not zero) imply causation in this case?
That is, can I conclude that one of things I can do to increase the
intensity of light in the room is to turn on the lights?

I modify this second experiment by creating three experimental
groups, with classrooms randomly assigned to groups.  In one group I turn
off the lights and close the blinds.  In a second group I raise the blinds
but turn off the lights.  In a third group I raise the blinds and turn on
the lights.  I compute eta, the nonlinear correlation coefficient relating
group membership to brightness of light in the room.  Alternatively I dummy
code group membership and conduct a multiple regression predicting
brightness from my dummy variables.  R = eta = .5.  I  test and reject the
null hypothesis that R and eta are zero in the population (using F as my
test statistic).  Does correlation (R or eta are not equal to zero) imply
causation in this case?

I could continue on with other correlations appropriate for various
experimental designs, but I would hope that you have gotten the point by
now.   

 ~~~  
Karl L. Wuensch, Department of Psychology,
East Carolina University, Greenville NC  27858-4353
Voice:  252-328-4102 Fax:  252-328-6283
mailto:[EMAIL PROTECTED]  
http://core.ecu.edu/psyc/wuenschk/klw.htm
 



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RE: When does correlation imply causation?

[hdaley]

Classic study:  Correlation between local stork population and local births.

-Original Message-
From: Stu [mailto:[EMAIL PROTECTED]]
Sent: Thursday, December 06, 2001 1:08 AM
To: [EMAIL PROTECTED]
Subject: Re: When does correlation imply causation?


> My favorite original example is the correlation between number of
> annual murders in a city and number of books in its libraries.
> Students have no trouble seeing that the two are going to have a
> fairly high correlation coefficient(*), but murders don't make
> people read and books don't make people kill.

There are many such examples. My favorites involve time series, for example,
hat size and shoe size (birth to adult); hair length and weight (birth to
age
1); and those with a third factor, for example, temperature and electric
bill.

Stu
Garfield High School
Los Angeles





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Re: Experimental Correlation Coefficients

[Dennis Roberts]

i would say that karl has demonstrated that IF we know conditions of 
manipulation or not ... we can have a better or lesser idea of what (if 
anything) impacted (caused?)  what

that i will grant him

to argue that r or eta has anything to do with this ... i would 
respectfully disagree

they are just byproducts of our manipulations ...

one cannot equate the byproducts with THE manipulations ..

At 03:23 PM 12/6/01 -0500, Wuensch, Karl L wrote:
> My experimental units are 100 classrooms on campus.  As I walk into
>each room I flip a perfectly fair coin in a perfectly fair way to determine
>whether I turn the room lights on (X = 1) or off (X = 0).  I then determine
>whether or not I can read the fine print on my bottle of smart pills (Y = 0
>for no, Y = 1 for yes).  From the resulting pairs of scores (one for each
>classroom), I compute the phi coefficient (which is a Pearson r computed
>with dichotomous data).  Phi = .5.  I test and reject the null hypothesis
>that phi is zero in the population (using chi-square as the test statistic).
>Does correlation (phi is not equal to zero) imply causation in this case?
>That is, can I conclude that turning the lights on affects my ability to
>read fine print?

could be here that if you did not have glasses ... you could not have read 
anything with or without light ... and, since you did have glasses ... the 
r you get is because of the implicit interaction between light or not, and 
glasses or not



>  ~~~
>Karl L. Wuensch, Department of Psychology,
>East Carolina University, Greenville NC  27858-4353
>Voice:  252-328-4102 Fax:  252-328-6283
>mailto:[EMAIL PROTECTED] 
>http://core.ecu.edu/psyc/wuenschk/klw.htm
>
>
>
>
>=
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>the problem of INAPPROPRIATE MESSAGES are available at
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_
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



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RE: When does correlation imply causation?

[David Heiser]

The issue of causality from the results of fitting a model to data has been
a major topic on SEMNET over the last many years.

If anyone wishes to pursue ideas on this and related issues, subscribe to
[EMAIL PROTECTED]

Most of the focus is on structural equation modeling (SEM). For
statisticians, a quick referral to Jim Steiger's article "Driving Fast in
Reverse" in JASA March 2001, p331-p338 (if you have it around) is a quick
discourse on SEM and the inherent problems of figuring out what is going on
from a model (I can send a copy via e-mail attachment if anyone asks)..

In SEMNET we have had some interesting open discussions over the years with
some of the book authors Wu casually name drops.

Judea Pearl's bottom line position is that a correlation between two
variables that is supported by data, "must mean something". The meaning has
to be deduced from path diagrams, a lot of rational logic, equation sets
with coefficients, and model outputs from very large, expensive software
packages.

The field is unfortunately dominated by those who have very large data sets,
do not have any physical measurements (i.e. use survey data, test
(examination, quiz, etc) results, results of "expert" opinions, etc.),  can
afford the computer resources to do the reduction, and are relying on the
fit of a model (and in many cases, any model) to the data to support a
logical claim of causation. In most cases, the model with the better fit
wins out.

Causation essentially is the "sizzle" that sells the paper and is a lead to
further grants.

DAHeiser




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Re: What usually should be done with missing values when I am conducting

[Richard J Burke]

jenny wrote:

> What should I do with the missing values in my data.  I ned to perform
> a t test of two samples to test the mean difference between them.
>
> How should I handle them in S-Plus or SAS?
>
> Thanks.
> JJ

If you are doing paired tests, then the pairs with missing values will
have to be ignored; otherwise, you will simply have two samples of
different sizes.





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