HDTenEightyP/NetNews huggingface dataset:
From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Newsgroups: sci.math.stat
Subject: Re: Fwd: Standard Deviation.
Date: 17 Aug 92 17:19:09 GMT
Reply-To: thompson@atlas.socsci.umn.edu
Organization: University of Minnesota

news@massey.ac.nz (USENET News System) writes:

>In article <1992Aug16.212245.27577@mailhost.ocs.mq.edu.au>, wskelly@laurel.ocs.mq.edu.au (William Skelly) writes:
>> 
>> This and other posting indicate that there is a relationship between
>> sample size and and estimated variance (of the population) which is
>> positive and always an underestimate.  What is the limit, or point
>> at which an increasing sample size no longer improve the estimate
>> of populations variance?
>> 
>When the sample size is equal to the population size (never for an
>infinite population).

Not necessarily true.  It depends on the sample design.  Suppose that
we have a finite population of size N and we draw _with_replacement_ a
sample of size n using independent draws.  Then the bias from using
the "n" denominator is (minus)

          <population variance> / n

and this is true for _any_ n, including n = N, or even n = 2N.

>> Can this be tested by taking samples of sample 

>Yes but we can work out the theory so it isn't necessary.

>> (the later sample
>> being elevated to the status of population)?
>> 

Perhaps we can work out the theory for the bias, but this is not so
clear when we consider other features of the distribution of the
estimate.  See the related questions about the bias of the usual
SD estimate in this thread for an example.

The intuition in the original comment was right on!

In fact the procedure of taking samples from the original sample,
"elevating" the original sample to the status of population is
_exactly_ the definition of (a particular variety of) bootstrap
resampling.  See for example the book _The_Bootstrap_and_Edgeworth_
_Expansion_, by Peter Hall (Springer-Verlag, 1992), which provides
many references and examples.

It is shown in the bootstrap literature that for certain purposes
(e.g. constructing statistical tests when the sample is drawn from a
non-normal population) the bootstrap procedure can outperform
(sometimes significantly) the traditional procedures.

So, for example, if the reason you are estimating a variance is to put
its square root in the denomenator of a t-statistic, then boostrapping
_may_ be the way to go (unless you really believe in the normality of
your population).  For this application, you really aren't interested
in whether or not your estimate of the variance is biased, and so the
n vs. n-1 debate is irrelevant.  In fact, the bootstrap based test
procedure will lead to the same test whether you choose n _or_ n-1, an
invariance property that I find appealing.

T. Scott Thompson              thompson@atlas.socsci.umn.edu
Dept. of Economics
University of Minnesota
Newsgroups: sci.math.stat
From: mortenaa@Lise.Unit.NO (Morten Aagaard)
Subject: SYSTAT FOR WINDOWS 
Keywords: systat
Organization: Norwegian Institute of Technology
Date: Sat, 22 Aug 92 13:06:50 GMT

There is a demo for Systat for Windows, would someone please
upload it to:

"ftp.cica.indiana.edu" in "pub/pc/win3/uploads"

Thank you.
From: hougen@uirvlh.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math.stat
Subject: Re: Standard Deviation.
Date: 19 Aug 92 18:36:18 GMT
Article-I.D.: roundup.l95552INNa4h
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: uirvlh.csl.uiuc.edu

wskelly@laurel.ocs.mq.edu.au (William Skelly) writes:

*>In article <WVENABLE.92Aug18180002@algona.stats.adelaide.edu.au> wvenable@algona.stats.adelaide.edu.au (Bill Venables) writes:

*>*> and (b) the degrees of freedom,
*>*>which is the dimension of the residual space.  This latter number is
*>*>sometimes n-1, but more often n-p where p is somewhat larger than 1.  These
*>*>two quantities, *separately*, are what you need for virtually all
*>*>inferential procedures, like testing and confidence intervals.  Whether you
*>*>divide one by the other to give an estimate of the variance is up to you.
*>*>Incidently, if you do, it turns out to be unbiased, but "so what?", really

*>Bang on!  Yes, I think I see light.  This concept "degrees of freedom"
*>is probably a much more confusing concept.  Made even more confusing to
*>non-statistians, because a lot of us are thinking "n" sample size...
*>i.e. the number of observations we have, rather than the more abstract
*>(right term?) concepts of sample or residual "space."

Before people get too confused, just let me add my two cents worth.
The number of "degrees of freedom" in a problem represents the amount
of information in the data and is generally equal to the number of
samples.  Intuitively, as statistics are computed using the data, the
independent information in the data is gradually "used up" and the
number of degrees of freedom is reduced.  The information is not
actually lost, but the statistics that have been computed contain some
of the information so that the amount of independent information left
in the data is reduced.

Consider the example of calculating the sample variance.  To calculate
the variance, one must first calculate the sample mean.  Calculating
the mean uses up one degree of freedom.  This can be seen by noting
that if one knew the mean and the values of n - 1 samples, one could
infer the value of the remaining sample.  Therefore, there are only n
- 1 independent "pieces" of information left in the data.  Similarly,
when one calculates the quantities used in an analysis of variance or
some other more complex statistical procedure, one may think of p
degrees of freedom being assigned to treatments, b to blocks, 1 or 2
to computing various means, etc., with the total always adding up to
the number of samples, n.

Darrell
From: whart@cs.ucsd.edu (Bill Hart)
Newsgroups: sci.math.stat
Subject: Generating a set of random bits
Date: 18 Aug 92 22:46:06 GMT

I have an application for which I need to generate a random 'vector' of 
bits of length N.  I have looked at stuff in Numerical Recipies for
generating a random sequence of bits, but it remains unclear whether
such a generator would be appropriate for generating a random
vector of bits.

I need/want to have the distribution of vectors remain 'random'.  Right
now I'm generating a random float in [0,1> and testing to see
if it is less than 0.5 or not.  This works, but I'm sure there is
a better way of doing this.

Any ideas or pointers?

--Bill
From: mokaba@binah.cc.brandeis.edu
Newsgroups: sci.math.stat
Subject: sample size and Maximulikelihood  estimates in LISREL
Date: 18 Aug 92 15:23:55 GMT
Reply-To: mokaba@binah.cc.brandeis.edu
Organization: Brandeis University

could somebody explain in English what the true effect of sample size
is on maximulikelihood estimates.  I have been playing around with 
LISREL and have a little problem conceptualizing the effect of sample
size on the estimates I get using maximumlikelihood estimators.  Are the
effects comming in becuase of the effect of sample size on the standard
error of estimates or is there something I am too dense to see. 
I have also learn that the problem with large sample in LISREL is that they
lead to even small effect being significant... or something like that..
Furthermore, is a sample of 103 good enough for a full model estimation.
i.e running the Mesurement equations at the same time as the Structural 
model.  

My Q-Plot has a tangent of less than 1 (angle less than 45 degrees) would 
this respond to increase in sample size?...

Thanks for answering this question ... e-mail welcome.
Mokaba
From: celms@vim.brl.mil (Dr. Aivars Celmins )
Newsgroups: sci.math.stat
Subject: Re: Parameter Covariance Matrix in Nonlinear Regression
Date: 19 Aug 92 14:15:42 GMT
Organization: U.S. Army Ballistic Research Laboratory, APG, MD.

In article <muzic.713536981@ds2.uh.cwru.edu> muzic@ds2.uh.cwru.edu (Ray Muzic) writes:
>I have 2 references that give different answers.  I believe one of the
>answers is restricted to the case of a model that is linear in the
>parameters.  However, I seem to recall that for a nonlinear model, an
>approximation that the model is linear about the optimum point is often
>employed.  Does this mean the covariance of the parameter estimates may be
>estimated assuming the model is linear about the operating point?
>

  The suggested linearization produces an approximation to the parameter
  covariance matrix that is less than first order accurate.  A true
  first order approximation contains second order derivatives of the
  model function.  For a derivation and discussion of the corresponding
  formula see

   A. Celmins, Least-Squares Optimization with Implicit Model Functions, in
   "Mathematical Programming with Data Perturbations II", Anthony V. Fiacco,
   Ed., Marcel Dekker, 1983, pp. 131-152.

  The covariance computation is discussed on pp. 136-138.
 
  Aivars Celmins
  
Newsgroups: sci.math.stat
From: choup@bionette.cgrb.orst.edu (Ping Chou)
Subject: Answers to 'quiz of the day'
Organization: Biological Computing Consortium, OSU, Corvallis, OR.
Distribution: usa
Date: Thu, 20 Aug 1992 04:44:42 GMT

The 'quiz of the day' got answered on the same and the following days. Many
thanks to those of you who responded (so quickly). As for those who asked for
a summary (and beyond), here it is:

(The quiz, rephrased)

Let P and Q are independent variates of Normal distribution of mean=0 and
standard deviation= Sp and Sq, respectively. Let R=P/Q.
What is the distribution of R?

(The answer)

R will follow Cauchy distribution. The normalized density function is

f(R) = (Sr/_pi_)/(R^2+Sr^2),

where Sr=Sp/Sq and _pi_= 3.1415926535897932..., and

INTEGRATE(from a to b)[f(R) dR] = (1/_pi_)*arctan(R/Sr)|(from a to b).

(The note)

1. Cauchy distribution is the same as Lorentzian distribution. Or may be not,
   but I have done some NMR (sorry, it's Nuclear Magnetic Resonance) spectra
   analysis, by using Lorentzian band to decompose NMR spectra. Both
   distribution have the same density function.
2. The parameter Sr in f(R) is analog to standard deviation in Normal
   distribution. Sr is the half width at half height of the peak.
3. Let P'=P/Sp, Q'=Q/Sq (which imply Sp'=Sq'=1) and R'=P'/Q', then Sr'=1.

(The most-cited reference)

Advanced Theory of Statistics, originally by Sir Maurice Kendall
5th ed., Vol. I, 'Distribution Theory', by Alan Stuart and J. Keith Ord
(Vol. II also contains many useful stuffs)

(The beyond)

The following table contains accumulated probability of R in 8 intervals,
(-inf,-10), (-10,-1), (-1,-0.1), (-0.1,0), (0,0.1), (0.1,1), (1,10), (10,+inf)
from three simulations. Data in each column of 'SIMULATE' are obtained from
10^7 R's, and those of 'INTEGRATE' are calculated according to the integral
expression above.

Accumulated probability of Cauchy distribution of R=P/Q, Sr=Sp/Sq
==============================================================================
         Sp=1, Sq=2, Sr=0.5      Sp=1, Sq=1, Sr=1        Sp=2, Sq=1, Sr=2

         SIMULATE  INTEGRATE     SIMULATE  INTEGRATE     SIMULATE  INTEGRATE
==============================================================================
-inf
         0.016107  0.015902      0.031650  0.031726      0.062803  0.062833
-10.0
         0.131533  0.131681      0.218344  0.218274      0.289752  0.289583
 -1.0
         0.289553  0.289583      0.218205  0.218274      0.131613  0.131681
 -0.1
         0.062802  0.062833      0.031769  0.031726      0.015813  0.015902
  0
         0.062824  0.062833      0.031660  0.031726      0.016073  0.015902
 +0.1
         0.289866  0.289583      0.218351  0.218274      0.131529  0.131681
 +1.0
         0.131609  0.131681      0.218253  0.218274      0.289616  0.289583
+10.0
         0.015706  0.015902      0.031768  0.031726      0.062801  0.062833
+inf
==============================================================================

Ping

PS. By the time I'm ready to post this, 9 more responses come in with more
    suggestions, hints, references, answers and requests. You boys and girls
    are really beautiful. Thanks again.
From: dr3u+@andrew.cmu.edu (Daniel Read)
Newsgroups: sci.math.stat
Subject: Fwd: Standard Deviation.
Date: 14 Aug 92 22:11:41 GMT
Organization: Engineering and Public Policy, Carnegie Mellon, Pittsburgh, PA

---------- Forwarded message begins here ----------

Can someone explain why calculating the Standard Deviation (SD),
for small samples, with (n-1) in the denominator is better than
doing so with (n) in the denominator?  I'm sure that there's
a perfectly good reason for doing so.  But we, lowly engineers
aren't usually told the reason.  Thanks now, for your response later.;-)

RESPONSE (and my own query):

The variance increases as a function of sample size.  That is, a small
sample will systematically underestimate the population variance (if we
estimate the population variance with denominator N-1).  Using this
reduced denominator therefore has the effect of increasing the variance
estimate.

My question:  why does a small sample underestimate the population variance?  

daniel read
Newsgroups: sci.math.stat
From: ted@dgbt.doc.ca (Ted Grusec)
Subject: Re: HELP - WITHIN-S ANOVA
Organization: The Communications Research Centre
Date: Sun, 23 Aug 92 06:29:51 GMT

In article <1992Aug22.214340.10028@ucsu.Colorado.EDU> mcclella@yertle.Colorado.EDU (Gary McClelland) writes:
>ted@dgbt.doc.ca (Ted Grusec) writes:
>
>>My CSS:Statistica (Statsoft) program will not analyze a 2 X 10 X 13
>>within-subject design. It indicates a 252 dependent variable limit,
>>while this experiment has 260.  All of this despite a recent update
>>to release 3.1 which I got just days ago,
>
>>Is there any commercial package that will do "large" within-subject
>>designs? Can someone share experiences, make recommendations?
>
>No sympathy from me.  With such large within-subject designs the key
>sphericity and homogeneity assumptions are almost surely violated.
>No one should be doing such large within-s analyses.  It is much better
>to think of the much smaller degree-of-freedom questions you really want
>to ask of your 260 data values for each subject.  Then, any standard
>regression program can be used to answer those specific questions.
>For details, see
>
>Judd, C.M., & McClelland, G.H. (1989).  Data Analysis: A Model Comparison
>   Approach.  HBJ  (see especially Chapter 14)
>
Thanks. But I should point out that, in real world applications of
experimental design, people sometimes want answers to explicit
questions that lead you into designs that, whether you like it or not,
result in violations of theoretical assumptions.  Also, some questions
are pressing - important decisions need to made and there are narrow
time limits.  All of this was true in my case.  Having done (and now,
thanks to |Stat having analyzed) the experiment, it only now is
obvious which levels of which factors proved uninformative. But there
is no time to rerun this extremely expensive experiment. For better or
worse, the decisions, based on the experiment, have been made.

For many years, I taught experimental design and stat. Having long
since left academia, I am sometimes tempted to offer a course which
would sprinkle some "real world" constraints into design applications.
It's something, I'm afraid, many academics are unaware of, as I too
was unconscious of when I was in that situation.

-- 
==========================================================================
Ted Grusec    Communications Research Centre    (Govt. of Canada, DOC)
 3701 Carling Ave., Ottawa, Ont.K2H 8S2, CANADA  Internet: ted@dgbt.doc.ca
  Compuserve: 73607,1576  (613) 998 2762   Fax (613) 993 8657
From: mcclella@yertle.Colorado.EDU (Gary McClelland)
Newsgroups: sci.math.stat
Subject: Re: HELP - WITHIN-S ANOVA
Date: 22 Aug 92 21:43:40 GMT
Organization: University of Colorado, Boulder

ted@dgbt.doc.ca (Ted Grusec) writes:

>My CSS:Statistica (Statsoft) program will not analyze a 2 X 10 X 13
>within-subject design. It indicates a 252 dependent variable limit,
>while this experiment has 260.  All of this despite a recent update
>to release 3.1 which I got just days ago,

>Is there any commercial package that will do "large" within-subject
>designs? Can someone share experiences, make recommendations?

No sympathy from me.  With such large within-subject designs the key
sphericity and homogeneity assumptions are almost surely violated.
No one should be doing such large within-s analyses.  It is much better
to think of the much smaller degree-of-freedom questions you really want
to ask of your 260 data values for each subject.  Then, any standard
regression program can be used to answer those specific questions.
For details, see

Judd, C.M., & McClelland, G.H. (1989).  Data Analysis: A Model Comparison
   Approach.  HBJ  (see especially Chapter 14)

gary mcclelland
univ of colorado
mcclella@yertle.colorado.edu
Newsgroups: sci.math.stat
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: Fwd: Standard Deviation.
Organization: The Ohio State University
Date: Fri, 14 Aug 1992 23:19:16 GMT



In article <seX2yRq00Uh785H2EB@andrew.cmu.edu> Daniel Read <dr3u+@andrew.cmu.ed
u> writes:
>---------- Forwarded message begins here ----------
>
>Can someone explain why calculating the Standard Deviation (SD),
>for small samples, with (n-1) in the denominator is better than
>doing so with (n) in the denominator?  I'm sure that there's
>a perfectly good reason for doing so.  But we, lowly engineers
>aren't usually told the reason.  Thanks now, for your response later.;-)
>
>RESPONSE (and my own query):
>
>The variance increases as a function of sample size.  That is, a small
>sample will systematically underestimate the population variance (if we
>estimate the population variance with denominator N-1).  Using this
>reduced denominator therefore has the effect of increasing the variance
>estimate.
>
>My question:  why does a small sample underestimate the population variance?
>
>daniel read

I'm not certain what "underestimate" means here: if you are speaking of
bias (bias being the difference between the estimand and the expected
value of the estimator), then

        ---  _        _
        \   | X - Xbar |2
T =     /   |_        _|
        ---
       ------------------
               n

will "underestimate" the population variance *for any sample size n*.
T will always have a negative bias *regardless of how large a sample is
used to compute T*.

More intuitively, if we take a very sample, we are less likely to get
extreme values and so our notion of what the population variance is (note
that I am not proposing some particular estimator) will be unrealistic.
For instance, I give an exam to two students. Their scores are 67 and
71. I think, "Gee, there's not a lot of variability in these scores."
But then 8 more students take the exam:
     60 78  100 38  50 88  99 39

and it now is clear there *is* more variability in these scores.

But let me reiterate that T will *always* have a negative bias for the
population variance whatever the sample size is

Robert George
(speaking  only for myself)
From: inlowm@cpva.saic.com
Newsgroups: sci.math.stat
Subject: Re: Powell's Min. w/ Brent's mod. wanted
Date: 12 Aug 92 20:42:10 GMT
Organization: Science Applications Int'l Corp./San Diego

See "Numerical Recipes" by Press (? -- three other authors).
There is a fortran version and a c version.  If you use the
c version be careful -- I have a friend who claims there are
some bugs in it.

Mark Inlow
SAIC
(619) 546-6978
inlowm@jupiter.saic.com
Newsgroups: sci.math.stat
From: KSZ@VM.NRC.CA
Subject: What is "bootstrap method"?
Organization: National Research Council
Date: Fri, 14 Aug 92 11:58:32 EDT

The title says it all. Does anybody know what the "bootstrap method" is?
 
 
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 KAIJUN S. ZHAN                          || (613) 990 - 0734 (voice)
 Internet:ksz@vm.nrc.ca                  ||
 Internet:kzhan@sgi1.mathstat.uoguelph.ca|| "Three generates everything".
 Internet:gilwf16@vm.uoguelph.ca         ||
 Bitnet:ksz@nrcvm01                      ||      -- Lao Zhi
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From: sljbr@cc.usu.edu
Newsgroups: sci.math.stat
Subject: e-mail of Dr.Wang Min-Chiang wanted!!!!!
Date: 12 Aug 92 18:51:41 MDT
Organization: Utah State University

hi!, i want the e-mail address of dr.Wang Min-Chiang, Prof. Dept. of Management
Systems,
Washington State Univ., Pullman.
could someone help me..

thanx in advance

balaji rajagopalan,
utah water research laboratory,
utah state univ.,
logan, utah,
UT - 84321-8200.
sljbr@cc.usu.edu or rbala@kernel.uwrl.usu.edu
From: sutton@lamar.ColoState.EDU (Rich Sutton)
Newsgroups: sci.math.stat
Subject: Looking for Cox & Hinkley's Theoretical Statistics
Summary: out of print, want to buy
Date: 20 Aug 92 23:17:36 GMT
Followup-To: sci.math.stat
Distribution: usa
Organization: Colorado State University, Fort Collins, CO  80523

I just called a local bookstore to order Cox & Hinkley's
Theoretical Statistics (ISBN 0 412 161605) and Problems
and Solutions in Theoretical Statistics (ISBN 0 412 15370 X).
The clerk told me they are out-of-print.

A) Would anyone have unmarked copies of these they wish to sell?
B) Could anyone suggest a good bookstore for hard-to-find or out-
of-print statistics books?

Thank You,
Rich Sutton
From: rizzo@cbnewsf.cb.att.com (anthony.r.rizzo)
Newsgroups: sci.math.stat
Subject: Re: Inference
Date: 20 Aug 92 14:18:07 GMT
Organization: AT&T

In article <1992Aug19.124712.305@ginger.hnrc.tufts.edu> jerry@ginger.hnrc.tufts.edu (Jerry Dallal) writes:
>In article <1992Aug18.214711.6657@mailhost.ocs.mq.edu.au>, wskelly@laurel.ocs.mq.edu.au (William Skelly) writes:
>> I am not sure I follow you.  From my applications I only want to test
>> some null-hypothesis (perhaps a narrow application...but very useful!).
>> Generally I want to know if two samples are from the same population.
>> Isn't this just asking whether or not the two sample means are close?
>> 
>
>Heck, *NO*!!!
>
>Suppose you have two safety devices.  Both are inexpensve to manufacture,
>install, and replace, compared to the consequences of their failure.  
>One has failure times that follow a
>normal distribution with a mean of 10 years and a standard deviation of 1 day.
>The other has failure times that follow a
>normal distribution with a mean of 10 years and a standard deviation of 
>3 years.  I hope you wouldn't be indifferent in choosing a 
>device to use when your test of significance fails to reject the null
>hypothesis of equal population means.

Thank you very much for this TRULY FINE example and explanation!
I just finished reading about sample characteristicts versus
population characteristics; I understood the material; but the cement
hadn't quite cured yet.  Thanks to your example, the material is now
fully cured and safe for use. ;-)

Tony Rizzo                  There's no shortage of engineers.
att.com!homxc!rizzo         There's only a shortage of engineering.
Newsgroups: sci.math.stat