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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Re: Stat question

[Glen]

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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Re: Stat question

[Jon Miller]

Stan Brown wrote:

> Jon Miller <[EMAIL PROTECTED]> wrote in sci.stat.edu:
> >
> >Stan Brown wrote:
> >
> >> I would respectfully suggest that the OP _first_ carefully study the
> >> textbook sections that correspond to the missed lectures, get notes from
> >> a classmate
> >
> >This part is of doubtful usefulness.
>
> Doubtful? It is "of doubtful usefulness" to get notes from a classmate and
> study the covered section of the textbook? Huh?

Sorry, bad editing on my part.

Getting notes from a classmate is of doubtful usefulness.  Plenty of anecdotes
on request.

If Cathy Cheng is in your class, you can just photocopy her notes and use them
as a textbook.  But most students?  Why would you care what someone who is
struggling to pass thinks the prof might have said?

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.

Jon Miller



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Re: Stat question

[dennis roberts]

At 06:13 PM 12/1/01 -0500, Stan Brown wrote:
>Jon Miller <[EMAIL PROTECTED]> wrote in sci.stat.edu:
> >
> >Stan Brown wrote:
> >
> >> I would respectfully suggest that the OP _first_ carefully study the
> >> textbook sections that correspond to the missed lectures, get notes from
> >> a classmate
> >
> >This part is of doubtful usefulness.
>
>Doubtful? It is "of doubtful usefulness" to get notes from a
>classmate and study the covered section of the textbook? Huh?

perhaps doubtful IF the students OP asked to look at were terrible students 
who took terrible notes ... and/or ... OP when reading the text could not 
make anything of it ...

but, those are two big ifs

usually, students won't ask to see the notes of students whom they know are 
"not too swift" ... and, also ... usually students who read the book do get 
something out of it ... maybe not enough

the issue here is ... it appeared (though we have no proof of this) that 
the original poster did little, if anything, on his/her own ... prior to 
posting a HELP to the list

stan seemed to be reacting to that assumption and, i don't blame him


>--
>Stan Brown, Oak Road Systems, Cortland County, New York, USA
>   http://oakroadsystems.com/
>"My theory was a perfectly good one. The facts were misleading."
>-- /The Lady Vanishes/ (1938)
>
>
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dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



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Re: Stat question

[Stan Brown]

Jon Miller <[EMAIL PROTECTED]> wrote in sci.stat.edu:
>
>Stan Brown wrote:
>
>> I would respectfully suggest that the OP _first_ carefully study the
>> textbook sections that correspond to the missed lectures, get notes from
>> a classmate
>
>This part is of doubtful usefulness.

Doubtful? It is "of doubtful usefulness" to get notes from a 
classmate and study the covered section of the textbook? Huh?

-- 
Stan Brown, Oak Road Systems, Cortland County, New York, USA
  http://oakroadsystems.com/
"My theory was a perfectly good one. The facts were misleading."
   -- /The Lady Vanishes/ (1938)


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Re: Stat question

[Jon Miller]

Stan Brown wrote:

> I would respectfully suggest that the OP _first_ carefully study the
> textbook sections that correspond to the missed lectures, get notes from
> a classmate

This part is of doubtful usefulness.

> , and _then_ contact the instructor to fill in any remaining gaps or
> answer any questions.

Jon Miller



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Re: Stat question

[Stan Brown]

Elliot Cramer <[EMAIL PROTECTED]> wrote in sci.stat.edu:
>Sima <[EMAIL PROTECTED]> wrote:
>: I have missed some lectures on statistics due to heavy illness
>: and now i got an assignment which i cannot solve.
>
>We all feel sorry for you Sima, but perhaps you should talk to your
>instructor about it.  He undoubtedly has office hours.

While that's the conventional advice, speaking as an instructor I do 
get tired of students who miss class for whatever reason, don't 
crack the textbook, and expect me to give them a private lesson that 
duplicates what was done in class. I don't know what if anything the 
OP has done about making up the missed material.

I would respectfully suggest that the OP _first_ carefully study the 
textbook sections that correspond to the missed lectures, get notes 
from a classmate, and _then_ contact the instructor to fill in any 
remaining gaps or answer any questions.

-- 
Stan Brown, Oak Road Systems, Cortland County, New York, USA
  http://oakroadsystems.com
My reply address is correct as is. The courtesy of providing a correct
reply address is more important to me than time spent deleting spam.


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Re: Stat question

[Elliot Cramer]

Sima <[EMAIL PROTECTED]> wrote:
: Dear List Members,

: I have missed some lectures on statistics due to heavy illness
: and now i got an assignment which i cannot solve.

We all feel sorry for you Sima, but perhaps you should talk to your
instructor about it.  He undoubtedly has office hours.



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Re: stat question

[Tony T. Warnock]

David Heiser wrote:

>  There is a lot of stat work involving maximum likelihood estimates, where
> there is no probability
> support unless you take a Bayesian approach. (Which is infrequent.)

Cute



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Re: stat question

[Herman Rubin]

In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>the problem with herman's pronouncement is mainly ... it is all or nothing

..

>the main purpose of any intro course is to spark some interest in some
>students ... 

>how else would herman propose that we get people interested in statistics?
>they have to start somewhere and sometime

You would probably get many without the prerequisites for
a good chemistry course interested by using a philosophy
based alchemy course, with emphasis on such things as the
philosophers' stone.  If you made it appear to be science,
and did not have the simple experiments to show it to be
far off the mark, would they be willing to overthrow it 
for the much harder chemistry?

The major mistake in our educational system is to teach
to the moment without the foundations.  We have millions
of adults who read poorly because they were taught by the
whole word method, instead of getting the idea that the
alphabet was more than an arbitrary collection of symbols,
which could be used for words arbitrarily.

To understand statistics, not the methodological religion,
one needs probability, including expectation, and algebra, 
A student with that can read, for example, all of my 
foundational paper starting from consistency, except the
last step, with full understanding.  Nobody has come up
with a justification on decision grounds for the techniques
taught in the typical beginning courses, and this does not
mean that it has not been tried.  This even applies to them
being approximations.  
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: stat question

[Li0N_iN_0iL]

Dennis Roberts wrote about Herman's pronouncement:

>he takes the position that no one can benefit from
>any intro stat courses ... which we know is a silly
>position to take

It's worse than silly: it's false.


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Re: stat question

[dennis roberts]

the problem with herman's pronouncement is mainly ... it is all or nothing

now, in his case, instead of saying that he thinks that students at the
undergraduate level would be BETTER off taking some introductory course in
probability ... RATHER than what he perceives as being the only thing
taught in an intro STATISTICS course ... he takes the position that no one
can benefit from any intro stat courses ... which we know is a silly
position to take

personally, i would prefer that students have some introduction to
statistics ... and, while many of the courses that are offered might not be
the best (just like in any discipline) ... the issue is whether it is
helpful to have ANY introduction to a field ... or no introduction to a
field ...

i opt for some intro ... rather than no intro

we have to assume that some of the students in these intro courses will
gain some perspective as to what is useful knowledge from that which isn't
... and some students wetted with some curuiosity from this first exposure
to the discipline will want to take more and become more "learned" in the
discipline ...

the main purpose of any intro course is to spark some interest in some
students ... 

how else would herman propose that we get people interested in statistics?
they have to start somewhere and sometime



==
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm


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Re: stat question

[Herman Rubin]

In article <01c055d0$5408df40$6f38de9e@daheiser>,
David Heiser <[EMAIL PROTECTED]> wrote:

>- Original Message -
>From: Herman Rubin <[EMAIL PROTECTED]>
>To: <[EMAIL PROTECTED]>
>Sent: Thursday, November 23, 2000 4:55 PM
>Subject: Re: stat question


>> >Herman Rubin wrote:

>> >>anyone wanting to learn good statistics should not even
>> >>consider taking an "undergraduate" statistics course

>> >Nonsense.(Reply by this anonymous, lion soaking in oil)

>> Not only is that not nonsense, but it is quite difficult
>> to get students who have learned techniques to consider
>> what, if any, basis was behind those techniques.
>> Meaningful statistics is based on the concept of
>> probability, not the computation of probabilities, and
>> consideration of the totality of consequences.

>Wow, Herman, this is deep stuff. There is a huge literature on the attempt
>to understand what probability is. Even Fisher had problems trying to
>understand it outside of the frequentist viewpoint. There is a lot of stat
>work involving maximum likelihood estimates, where there is no probability
>support unless you take a Bayesian approach. (Which is infrequent.)

It has long been known that maximum likelihood is at best
a method, which may or may not be good.  In fact, we have
many reasonable problems where we know that maximum
likelihood is not good, and in which we can do better,
even asymptotically.

My last clause in what you quoted above is what I consider
the key point; consider the TOTALITY of consequence.  This,
without elaboration, rules out classical hypothesis testing,
and both classical and Bayesian confidence regions.

There is a huge literature in attempting to DEFINE
probability, which is quite different from trying to
understand what it is.  The same problem occurs in trying
to define length, or even to define integers.  Integers
have properties, and probabilities have properties, and
it is a mistake to pick a definition of either.

>Just look at the extent of the literature on the 2X2 table, and the
>difficulty there is in understanding the concepts behind an analysis for
>effects.

>I have been reading the absolutely wonderful discussion and raging arguments
>on SEMNET between Mulaik, Pearl, Hayduk, Shipley and others on the meaning
>of b in the simple linear equation Y=bX+e1, where X is one variable and e1
>is a combination of the effects of all other variables and random effects.
>When e1 is large with respect to Y, it becomes very difficult to define a
>simple meaning of b in terms of a quantitative causality. This is deep
>stuff, that even the professors have difficulty in understanding.

One cannot define causality by looking at observed relations.  
This is a place where the philosophers overreached; models do
not come from data, but from the mind, and objectivity is
just plain impossible.  But enough mathematics had to be 
developed to see this, although there were examples of the
contradictions which readily occur.  

>Considering most of the important work involving statistics is in
>psychology, marketing, medicine, economics, physics, social studies, and
>every other hard or soft science out there, we cannot assume that all these
>PhD practitioners understand probability or really understand the nuances of
>the models, equations and conclusions they arrive at. (I did it. One
>sentence per paragraph. Does this put me on Fisher's level?)

Those in economics, although they have not managed to do
too much with statistics, seem to understand the problems,
as do SOME in biology.  Marketing people go by results.
Usually, physicists have sufficiently accurate data that
there is not too much of a problem; however, the first
failure of what is now called meta-analysis which I heard
about came from a physicist.

What is done in the other fields is to use statistical
methods as a RELIGION, nothing more and nothing less.
There is now some progress in getting Bayesian methods into
medicine, and realizing that the protocols and rules in use
can increase suffering and death.  The psychologists and
social scientists, with their forcing of normality, are a
real danger to all.

>It would be nice if all these practitioners had graduate courses in stat,

I did not even hint that.  They need CONCEPTUAL courses in
statistics, not how to carry out religious rituals.  For those
who can understand mathematics, there is no point in taking a
course below the mathematical level which can be understood,
in any field.  The essentials of measure theory and integration,
not antidifferentiation, belong in high school at the latest.
The Greeks understood integration, although they could not 
calculate many.  Those coming out of calculus can calculate many,
but have no understanding.

>but more than likely it is a unde

Re: stat question

[Herman Rubin]

In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>At 07:55 PM 11/23/00 -0500, Herman Rubin wrote:
>>In article <8vk5h2$516l9$[EMAIL PROTECTED]>,
>>Li0N_iN_0iL <[EMAIL PROTECTED]> wrote:
>>>Herman Rubin wrote:

anyone wanting to learn good statistics should not even 
consider taking an "undergraduate" statistics course

>>>Nonsense.

>>Not only is that not nonsense, but it is quite difficult
>>to get students who have learned techniques to consider
>>what, if any, basis was behind those techniques.
>>Meaningful statistics is based on the concept of
>>probability, not the computation of probabilities, and
>>consideration of the totality of consequences.

>herman ... are you suggesting that we encourage students NOT to take any
>work of any type at the undergraduate level? just go from high school to
>graduate school?

Read what I wrote more carefully.  BTW, one should go 
from a good elementary school, where concepts are emphasized
instead of drill, to "rigorous" courses in all fields.
The word rigor is what is normally used, but it has nothing
to do with difficulty.  It is the use of concepts and proofs,
not "this is how we get the answer".

>don't take calculus

Not as a manipulative course.  The more manipulation, the
harder is becomes to understand what it means.  To most of
those taking calculus not, a derivative or integral means
nothing more than what one gets by following the formal
procedures.  

The problems start early; every additional thousand (no
exaggeration) arithmetic problems makes it harder to 
understand that numbers are what have certain properties,
and that one can use them without knowing how to compute
the answers.  The same holds for calculus, probability,
and statistics.  Knowing how to calculate seems to be a
major problem for all except geniuses to understand, and
it is a problem there.

Why is it that schoolteachers are incapable of understanding
the structures and concepts which go with the various number
systems?  Those who understand this can teach children, but
not most teachers or prospective teachers.

... or geography ... or intro humanities ... or english
>lit ... or physics ... or 

It depends how it is done.  If intro humanities starts 
with honest history, now generally Politically Incorrect,
this is a good idea.  But literature is, except for some
discussion of literary forms, entertainment and even more
so propaganda, and it should be considered such.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: stat question

[David Heiser]

- Original Message -
From: Herman Rubin <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, November 23, 2000 4:55 PM
Subject: Re: stat question


> >Herman Rubin wrote:
>
> >>anyone wanting to learn good statistics should not even
> >>consider taking an "undergraduate" statistics course
>
> >Nonsense.(Reply by this anonymous, lion soaking in oil)
>
> Not only is that not nonsense, but it is quite difficult
> to get students who have learned techniques to consider
> what, if any, basis was behind those techniques.
> Meaningful statistics is based on the concept of
> probability, not the computation of probabilities, and
> consideration of the totality of consequences.
>
Wow, Herman, this is deep stuff. There is a huge literature on the attempt
to understand what probability is. Even Fisher had problems trying to
understand it outside of the frequentist viewpoint. There is a lot of stat
work involving maximum likelihood estimates, where there is no probability
support unless you take a Bayesian approach. (Which is infrequent.)

Just look at the extent of the literature on the 2X2 table, and the
difficulty there is in understanding the concepts behind an analysis for
effects.

I have been reading the absolutely wonderful discussion and raging arguments
on SEMNET between Mulaik, Pearl, Hayduk, Shipley and others on the meaning
of b in the simple linear equation Y=bX+e1, where X is one variable and e1
is a combination of the effects of all other variables and random effects.
When e1 is large with respect to Y, it becomes very difficult to define a
simple meaning of b in terms of a quantitative causality. This is deep
stuff, that even the professors have difficulty in understanding.

Considering most of the important work involving statistics is in
psychology, marketing, medicine, economics, physics, social studies, and
every other hard or soft science out there, we cannot assume that all these
PhD practitioners understand probability or really understand the nuances of
the models, equations and conclusions they arrive at. (I did it. One
sentence per paragraph. Does this put me on Fisher's level?)

It would be nice if all these practitioners had graduate courses in stat,
but more than likely it is a undergraduate level course taught at the
graduate level to a student say in psychology, or medicine or...(e.g.,
Abelson in his book, "Statistics as Principled Argument", in the first
sentence of the introduction says, 'This book arises from 35 years of
teaching a first-year graduate statistics course in the Yale Psychology
Department." This is typical of most graduate schools, where the first year
stat course is all that the student gets.) People in these fields will get
exposed to huge data bases with large numbers of variables and find the
impossibility of assessing all the implications of any model, hypothesis or
set of conclusion made.

It is very clear that an education in statistics never stops. The
undergraduate level exposes you to the concepts, and the understanding comes
with continued education and experience.

There has been a long discussion previously on EDSTAT about the 0.05
probability value and the use of it. There was no common agreement, which is
typical of most of the basic fundamental things we use in statistics. Since
we as statisticians can't agree on what is significant (in terms of
probability), how can we expect practitioners to fully understand what
probability is?

DAHeiser



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Re: stat question

[dennis roberts]

At 07:55 PM 11/23/00 -0500, Herman Rubin wrote:
>In article <8vk5h2$516l9$[EMAIL PROTECTED]>,
>Li0N_iN_0iL <[EMAIL PROTECTED]> wrote:
>>Herman Rubin wrote:
>
>>>anyone wanting to learn good statistics should not even 
>>>consider taking an "undergraduate" statistics course
>
>>Nonsense.
>
>Not only is that not nonsense, but it is quite difficult
>to get students who have learned techniques to consider
>what, if any, basis was behind those techniques.
>Meaningful statistics is based on the concept of
>probability, not the computation of probabilities, and
>consideration of the totality of consequences.

herman ... are you suggesting that we encourage students NOT to take any
work of any type at the undergraduate level? just go from high school to
graduate school?

don't take calculus ... or geography ... or intro humanities ... or english
lit ... or physics ... or 




==
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educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm


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Re: stat question

[Herman Rubin]

In article <8vk5h2$516l9$[EMAIL PROTECTED]>,
Li0N_iN_0iL <[EMAIL PROTECTED]> wrote:
>Herman Rubin wrote:

>>anyone wanting to learn good statistics should not even 
>>consider taking an "undergraduate" statistics course

>Nonsense.

Not only is that not nonsense, but it is quite difficult
to get students who have learned techniques to consider
what, if any, basis was behind those techniques.
Meaningful statistics is based on the concept of
probability, not the computation of probabilities, and
consideration of the totality of consequences.

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: stat question

[Li0N_iN_0iL]

Herman Rubin wrote:

>anyone wanting to learn good statistics should not even 
>consider taking an "undergraduate" statistics course

Nonsense.


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Re: stat question

[Herman Rubin]

In article ,
FL <[EMAIL PROTECTED]> wrote:
>Are there any graduate programs in Statistics that do not require the
>GRE for admission?

>I have an undergraduate degree in Computer Science and want to pursue a MSc.
>in Statistics. However, I have not taken many undergraduate Statistics
>courses.

>Thanks



It might take a little longer, but not much.  In my opinion,
anyone wanting to learn good statistics should not even 
consider taking an "undergraduate" statistics course, but
should instead get a good mathematics education, not just
computational.


-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: ** Stat question

[Howard S. Hoffman]

I get your point. I see this sequence as an example of how good dialogue can lead
to education and interesting literary exchange.
  Howard S. Hoffman
Herman Rubin wrote:

> In article <[EMAIL PROTECTED]>,
> Howard S. Hoffman <[EMAIL PROTECTED]> wrote:
> >I stand corrected. I had not considered the requirement of homogeniety of
> >varience. Sure, if U=2 V must be 0. hence, for certain values of U , V can be
> >predicted exactly.
> > Howard S. Hoffman
>
> Homogeneity of variance is not enough, either.  It is easy to
> construct examples do the conditional means and variances are
> the same, and yet the two random variables are not independent.
>
> If the condition expectation of EVERY function of V is
> independent of U, the random variables are independent.
> --
> This address is for information only.  I do not claim that these views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
> [EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558



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Re: ** Stat question

[Herman Rubin]

In article <[EMAIL PROTECTED]>,
Howard S. Hoffman <[EMAIL PROTECTED]> wrote:
>I stand corrected. I had not considered the requirement of homogeniety of
>varience. Sure, if U=2 V must be 0. hence, for certain values of U , V can be
>predicted exactly.
> Howard S. Hoffman

Homogeneity of variance is not enough, either.  It is easy to
construct examples do the conditional means and variances are
the same, and yet the two random variables are not independent.

If the condition expectation of EVERY function of V is 
independent of U, the random variables are independent.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: ** Stat question

[Robert Dawson]

Jan de Leeuw took his vorpal sword in hand and wrote:


> Well ! I can't let that one pass. Let it be noted that Robert Dawson does
> not quote but paraphrases Humpty Dumpty. The correct quotation is:
> ===
> "When I use a word, " Humpty Dumpty said in rather a scornful tone, "it
means
> just what I choose it to mean--neither more nor less."
> "The question is," said Alice, "whether you make words mean so many
> different things."
> "The question is," said Humpty Dumpty, "which is to be master--that's
all."
> ===

You are, of course, correct. There's glory for you!

> Also see J.B. Priestley, A Note on Humpty Dumpty, from "I for One", 1921;
> and Roger Holmes, The Philosopher's Alice in Wonderland, Antioch Review,
> 1959.
>
> As for the original problem, it suffices to observe that if U=12 (or 2)
then
> V must be zero.

Well, if we're being pedantic , it does *not* suffice; it must
also be
shown, as I did, that it sometimes equals something else.

>> As (this may have been a homework question but I presume it's past
the
>>due date by now, so I can be explicit) U=12 implies V=0 whereas U=11 makes
>>this impossible, U and V are not independent.





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Re: ** Stat question

[Jan de Leeuw]

Well ! I can't let that one pass. Let it be noted that Robert Dawson does
not quote but paraphrases Humpty Dumpty. The correct quotation is:
===
"When I use a word, " Humpty Dumpty said in rather a scornful tone, "it means
just what I choose it to mean--neither more nor less."
"The question is," said Alice, "whether you make words mean so many
different things."
"The question is," said Humpty Dumpty, "which is to be master--that's all."
===
Also see J.B. Priestley, A Note on Humpty Dumpty, from "I for One", 1921;
and Roger Holmes, The Philosopher's Alice in Wonderland, Antioch Review,
1959.

As for the original problem, it suffices to observe that if U=12 (or 2) then
V must be zero.

At 9:54 AM -0400 2/7/00, Robert Dawson wrote:
>Guidi Chan wrote:
>  > > A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
>  > > 1st and 2nd rolls.
>  > >
>  > > U = X1 + X2;  V = X1 - X2.
>  > >
>  > > Show that U and V are NOT independent.
>
>Howard Hoffman responded:
>  > If you make a scatterplot of all possible values of U and V you will
>  > discover that for every value of U the mean value of V is 0.  In other
>  > words, the slope of the regression of U on V is zero. This, for me is
>proof
>  > that U and V are independent.
>
> "When I use a word" said Humpty Dumpty, "it means what I want it to
>mean.
>It all depends on who's going to be master, you or the word."
>
> The fact is that this is not the accepted meaning of independence. The
>accepted meaning of independence is that the conditional probability
>distribution of U does not depend on V. This can be rephrased usefully as:
>"there is no value of U that, if observed, would tell you anything about the
>value of V".
>
> As (this may have been a homework question but I presume it's past the
>due date by now, so I can be explicit) U=12 implies V=0 whereas U=11 makes
>this impossible, U and V are not independent. [End of proof.]
>
>
> Independence is actually quite hard to see from a scatterplot, as it
>is often hard to determine by eye if two conditional samples {U_i:V_i in
>(a1,a2)}
>and {U_i:V_i in (b1,b2)} have similar distributions or not when the numbers
>of
>data points differ significantly. For this purpose, I like to use an array
>of
>side-by-side boxplots of the dependent variable, one for each interval of
>the
>independent variable.
>
> Another frequently-confused-with-independence property of joint
>distributions is that the two marginal distributions are causally
>unrelated. This implies independence but does not follow from it (the
>canonical example involves the toss of two coins, with the events being
>A: heads on cent, B:exactly one head.)
>
> We have: causally independent => independent => regression slope = 0.
>
> -Robert Dawson
>
>
>
>
>
>
>===
>   This list is open to everyone. Occasionally, people lacking respect
>   for other members of the list send messages that are inappropriate
>   or unrelated to the list's discussion topics. Please just delete the
>   offensive email.
>
>   For information concerning the list, please see the following web page:
>   http://jse.stat.ncsu.edu/
>===

===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550;  fax (310)-206-5658;  email: [EMAIL PROTECTED]
http://www.stat.ucla.edu/~deleeuw and http://home1.gte.net/datamine/

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Re: ** Stat question

[Robert Dawson]

Guidi Chan wrote:
> > A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
> > 1st and 2nd rolls.
> >
> > U = X1 + X2;  V = X1 - X2.
> >
> > Show that U and V are NOT independent.

Howard Hoffman responded:
> If you make a scatterplot of all possible values of U and V you will
> discover that for every value of U the mean value of V is 0.  In other
> words, the slope of the regression of U on V is zero. This, for me is
proof
> that U and V are independent.

"When I use a word" said Humpty Dumpty, "it means what I want it to
mean.
It all depends on who's going to be master, you or the word."

The fact is that this is not the accepted meaning of independence. The
accepted meaning of independence is that the conditional probability
distribution of U does not depend on V. This can be rephrased usefully as:
"there is no value of U that, if observed, would tell you anything about the
value of V".

As (this may have been a homework question but I presume it's past the
due date by now, so I can be explicit) U=12 implies V=0 whereas U=11 makes
this impossible, U and V are not independent. [End of proof.]


Independence is actually quite hard to see from a scatterplot, as it
is often hard to determine by eye if two conditional samples {U_i:V_i in
(a1,a2)}
and {U_i:V_i in (b1,b2)} have similar distributions or not when the numbers
of
data points differ significantly. For this purpose, I like to use an array
of
side-by-side boxplots of the dependent variable, one for each interval of
the
independent variable.

Another frequently-confused-with-independence property of joint
distributions is that the two marginal distributions are causally
unrelated. This implies independence but does not follow from it (the
canonical example involves the toss of two coins, with the events being
A: heads on cent, B:exactly one head.)

We have: causally independent => independent => regression slope = 0.

-Robert Dawson






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Re: ** Stat question

[Howard S. Hoffman]

I stand corrected. I had not considered the requirement of homogeniety of
varience. Sure, if U=2 V must be 0. hence, for certain values of U , V can be
predicted exactly.
 Howard S. Hoffman
Radford Neal wrote:

> Guidi Chan wrote:
>
> >> A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
> >> 1st and 2nd rolls.
> >>
> >> U = X1 + X2;  V = X1 - X2.
> >>
> >> Show that U and V are NOT independent.
>
> In article <[EMAIL PROTECTED]>,
> Howard S. Hoffman <[EMAIL PROTECTED]> wrote:
>
> >If you make a scatterplot of all possible values of U and V you will
> >discover that for every value of U the mean value of V is 0.  In other
> >words, the slope of the regression of U on V is zero. This, for me is proof
> >that U and V are independent.
>
> For U and V to be independent, it is not enough that the mean of V
> conditional on any particular value for U is always the same.  It must
> be that the conditional distribution for V given any particular value
> for U is always the same.  It is quite possible for the mean to be the
> same while the conditional distribution is different in other ways,
> eg, the standard deviation might be different.
>
>Radford Neal



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Re: ** Stat question

[Zina Taran]

how's about enumerating (at least, partially so) and then looking?
say, if U=2, V can only take one value: 0.
if U=8, V can take 5 different values: -4, -2, 0, 2, 4

- Original Message -
From: Radford Neal <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, February 06, 2000 11:05 AM
Subject: Re: ** Stat question


>
> Guidi Chan wrote:
>
> >> A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
> >> 1st and 2nd rolls.
> >>
> >> U = X1 + X2;  V = X1 - X2.
> >>
> >> Show that U and V are NOT independent.
>
> In article <[EMAIL PROTECTED]>,
> Howard S. Hoffman <[EMAIL PROTECTED]> wrote:
>
> >If you make a scatterplot of all possible values of U and V you will
> >discover that for every value of U the mean value of V is 0.  In other
> >words, the slope of the regression of U on V is zero. This, for me is
proof
> >that U and V are independent.
>
> For U and V to be independent, it is not enough that the mean of V
> conditional on any particular value for U is always the same.  It must
> be that the conditional distribution for V given any particular value
> for U is always the same.  It is quite possible for the mean to be the
> same while the conditional distribution is different in other ways,
> eg, the standard deviation might be different.
>
>Radford Neal
>
>
>
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>   This list is open to everyone. Occasionally, people lacking respect
>   for other members of the list send messages that are inappropriate
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>
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>
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Re: ** Stat question

[Radford Neal]

Guidi Chan wrote:

>> A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
>> 1st and 2nd rolls.
>>
>> U = X1 + X2;  V = X1 - X2.
>>
>> Show that U and V are NOT independent.

In article <[EMAIL PROTECTED]>,
Howard S. Hoffman <[EMAIL PROTECTED]> wrote:

>If you make a scatterplot of all possible values of U and V you will
>discover that for every value of U the mean value of V is 0.  In other
>words, the slope of the regression of U on V is zero. This, for me is proof
>that U and V are independent.

For U and V to be independent, it is not enough that the mean of V
conditional on any particular value for U is always the same.  It must
be that the conditional distribution for V given any particular value
for U is always the same.  It is quite possible for the mean to be the
same while the conditional distribution is different in other ways,
eg, the standard deviation might be different.

   Radford Neal


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Re: ** Stat question

[Henry]

On Sun, 06 Feb 2000 15:41:47 GMT, "Howard S. Hoffman"
<[EMAIL PROTECTED]> wrote:
>(a) If you make a scatterplot of all possible values of U and V you will
>discover that for every value of U the mean value of V is 0.  
>(b) In other >words, the slope of the regression of U on V is zero. 
>(c) This, for me is proof that U and V are independent.

(a) is saying that E(V|U) is independent of U (in this case=0);
(b) is saying that V and U are not linearly correlated
and is a weaker statement than (a)
(c) is not true in this case, given the standard meaning of
independent, even if (a) and (b) are.




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Re: ** Stat question

[Howard S. Hoffman]

If you make a scatterplot of all possible values of U and V you will
discover that for every value of U the mean value of V is 0.  In other
words, the slope of the regression of U on V is zero. This, for me is proof
that U and V are independent.
Howard S Hoffman

Guidi Chan wrote:

> Hello,
>
> I've kinda hit a road block trying to figure out this question, it's a
> pretty basic question but it's been a while since I've taken a stats
> course so perhaps I could get some hints:
>
> Question:
>
> A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
> 1st and 2nd rolls.
>
> U = X1 + X2;  V = X1 - X2.
>
> Show that U and V are NOT independent.
>
> > This is what I have done so far:  I've solved for the mean and
> variance of both U and V.  I've found the covariance of U and V...which
> is  cov(U,V) = var (X1) - var (X2).
>
> I'm basically stuck at trying to show that there not independent.
>
> Any advice?  Thanks in advance!



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Re: ** Stat question

[Donald F. Burrill]

> >> >Guidi Chan wrote:
> >> > > A fair die is rolled 2 times.  X1 and X2 is the # of
> >> > > points showing on 1st and 2nd rolls.
> >> > > U = X1 + X2;  V = X1 - X2.
> >> > > Show that U and V are NOT independent.

This question for some reason puts me in mind of a telephone call that 
was referred to me (I never did find out by whom!) shortly after my 
appointment as lecturer at the then newly-established OISE (The Ontario 
Institute for Studies in Education).  A woman had called asking for 
assistance for her son (a high-school student), whose math teacher had 
set the problem "Show that in cribbage a score of 19 is impossible." 
She was of the opinion that there must be a way to attack the problem 
with algebra (what she said was, "Isn't there a formula or something?", 
in a tone of voice that implied incredibility that the answer might be 
"No"), and was audibly VERY disappointed that my reply was to enumerate 
all possible cases of hands in cribbage (or at least all possible cases 
with scores in the near vicinity of 19). 
I remember noticing at the time that the _son_ had not made the 
call;  I suspected he had more sense.
(Enumerating all hands is not that onerous a task, anyway:  
scores of cribbage hands range from 0 to 29, except 19, in 5 cards, and 
depend only on (1) numbers of pairs of the same denomination, (2) 
sequential runs of 3 or more, (3) combinations of cards whose spots total 
15 [ace=1, face cards = 10], (4) whether 4 of the cards include the jack 
of the same suit as the 5th card.)
-- Don.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  



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Re: ** Stat question

[Henry]

>> >Guidi Chan wrote:
>> > > A fair die is rolled 2 times.  X1 and X2 is the # of
>> > > points showing on 1st and 2nd rolls.
>> > > U = X1 + X2;  V = X1 - X2.
>> > > Show that U and V are NOT independent.

>Herman Rubin wrote:
>> I suggest that, instead, you think about the intuitive
>> meaning of independence, and how it is used.  Objects
>> are independent if information about some of them provides
>> no information about probabilities of events from the
>> others.  It is easy to construct such situations, and
>> even to see the dependence without computing.

On Fri, 28 Jan 2000 13:26:56 -0500, Charles Metz <[EMAIL PROTECTED]>
wrote:
>With all due respect, Herman (and I mean that sincerely, because I
>admire your regular contributions here), I would suggest that this may
>be one situation where intuition isn't the best approach for most
>neophytes, who tend to confuse independence and an absence of
>correlation at the purely intuitive level.

Perhaps intuitive is not quite the right word, but the simple meaning
is what is required here, e.g. if U=12, what could V be? and if U=7?
without working out non-zero probabilities



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Re: ** Stat question

[Charles Metz]

Herman Rubin wrote:
 
> In article <[EMAIL PROTECTED]>,
> Charles Metz  <[EMAIL PROTECTED]> wrote:
> >Guidi Chan wrote:
> 
> > > A fair die is rolled 2 times.  X1 and X2 is the # of
> > > points showing on 1st and 2nd rolls.
> 
> > > U = X1 + X2;  V = X1 - X2.
> 
> > > Show that U and V are NOT independent.
> --snip--
> > > I'm basically stuck at trying to show that there not
> > > independent.
> 
> >Try thinking about the mathematical definition of 
> >"independence" and about the joint distribution of U and V.
> 
> I suggest that, instead, you think about the intuitive
> meaning of independence, and how it is used.  Objects
> are independent if information about some of them provides
> no information about probabilities of events from the
> others.  It is easy to construct such situations, and
> even to see the dependence without computing.

With all due respect, Herman (and I mean that sincerely, because I
admire your regular contributions here), I would suggest that this may
be one situation where intuition isn't the best approach for most
neophytes, who tend to confuse independence and an absence of
correlation at the purely intuitive level.

  Charles Metz


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Re: ** Stat question

[Donald F. Burrill]

On Thu, 27 Jan 2000, Guidi Chan wrote:

> I've kinda hit a road block trying to figure out this question, it's a
> pretty basic question but it's been a while since I've taken a stats
> course so perhaps I could get some hints:
> 
> A fair die is rolled 2 times.  X1 and X2 is the # of points showing on
> 1st and 2nd rolls.
> 
> U = X1 + X2;  V = X1 - X2.
> 
> Show that U and V are NOT independent.

What leads you to suppose that this is a _statistics_ question?

> This is what I have done so far:  I've solved for the mean and
> variance of both U and V.  I've found the covariance of U and V...which 
> is  cov(U,V) = var (X1) - var (X2).

Well, that tells you something.  What relationship exists between var(X1) 
and var(X2)?  (But of course, this only tells you whether or not U and V 
are correlated, not whether they are independent.)

> I'm basically stuck at trying to show that they're not independent.
> Any advice?  Thanks in advance!

If you haven't picked up on the hints offered by Charles Metz and Herman 
Rubin, you might try enumeration.  The sample space is small enough for 
this not to be prohibitive.

 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  



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Re: ** Stat question

[Herman Rubin]

In article <[EMAIL PROTECTED]>,
Charles Metz  <[EMAIL PROTECTED]> wrote:
>Guidi Chan wrote:

> > A fair die is rolled 2 times.  X1 and X2 is the # of 
> > points showing on 1st and 2nd rolls.

> > U = X1 + X2;  V = X1 - X2.

> > Show that U and V are NOT independent.
--snip--
> > I'm basically stuck at trying to show that there not
> > independent.

>Try thinking about the mathematical definition of "independence" and
>about the joint distribution of U and V.

I suggest that, instead, you think about the intuitive
meaning of independence, and how it is used.  Objects
are independent if information about some of them provides
no information about probabilities of events from the
others.  It is easy to construct such situations, and
even to see the dependence without computing.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054   FAX: (765)494-0558


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Re: ** Stat question

[Charles Metz]

Guidi Chan wrote:

 > A fair die is rolled 2 times.  X1 and X2 is the # of 
 > points showing on 1st and 2nd rolls.
 > 
 > U = X1 + X2;  V = X1 - X2.
 > 
 > Show that U and V are NOT independent.
--snip--
 > I'm basically stuck at trying to show that there not
 > independent.

Try thinking about the mathematical definition of "independence" and
about the joint distribution of U and V.

   Charles Metz


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