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Here's a message that I found in another newsgroup that folks here may 
find useful.
-- 
Steven J. Pierce
Master's Student in Experimental Psychology
Mississippi State University
E-Mail: sjp2@ra.msstate.edu
WWW: http://www2.msstate.edu/~sjp2/index.html
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Subject: WWW: Meta-Analysis Page
Date: 23 Nov 1996 20:20:53 -0500
From: "Larry C. Lyons" 
Organization: Monumental Network Systems
Newsgroups: sci.psychology.research,sci.psychology.msic,sci.psychology.announce,sci.psychology.personality,scie.psychology.psychotherapy,sci.psychology.theory
I have recently posted a set of Web pages devoted to Meta-analysis.  They
describe how to use statistical procedures to accumulate results of
independent studies that examine related research areas.  Topic areas
include converting individual study statistics to a common metric,
correcting for sampling error, measurement error and range restriction.
Finally I also include a step by step guide for conducting a
meta-analysis.
Comments, suggestions for improvement, and contributions to the pages are
welcomed.
The url is:
  http://www.mnsinc.com/solomon/MetaAnalysis.html
Best Regards,
Larry Lyons                  | email:     solomon@mnsinc.com
                             | Home Page: www.mnsinc.com/solomon
                             |
My opinions alone, no one else will take responsibility for them!
========================================================
Life is Complex. It has both real and imaginary parts.
========================================================
--------------4F62701A2DBF--

Shu-Fai Cheung  wrote:
> The following issue have been posted several days before by other, but I
> saw no response to it.  I think it is an interesting issue and would like
> raise the issue again for discussion:
> 
> Suppose researcher A wants to test a theory asserting that whether Y 
> occurs is influened by X1 bu not by X2.  A logistic regression anaylsis
> is conducted, and find coeff. of X2 non-significant.  Assuming X1 and X2
> are not correlated, researcher A accepts a final model that has X2 dropped
> and only includes X1 as the predictor.
> 
> This sounds reasonable.
> 
> Now another case.  Suppose researcher A has a study with three different
> groups.  The theory being tested asserts that Gp1 and Gp2 differ in the
> probability of Y's occurence, while Gp1 and Gp2 on average do not differ
> from Gp3 on that probability.  (Assume that Gp1, Gp2 and Gp3 represent
> three different experimental treatment.)  Dummy variables are created and
> then logistic regression is conducted:
In general creating a parsimonious model by reducing the number of
parameters is a good thing. The model is easier to interpret and the
parameters are more robust. The reduced model must be substantively
meaningful though, but that would be the case for this problem. A number
of reduced models have been designed for square tables such as father to
son occupational mobility. See the chapter on loglinear models in the
SPSS advanced statistics manual for examples.
The reduced model should also be designed a priori as is the case here
rather than on a basis of the results. Doing so can lead to the problem
of 'capitializing on chance' where your reduced model is customized to
fit the sample data, but has no relationship to the processes in the
population.
> 
>         D1    D2
> Gp1  -0.50  -.33
> Gp2   0.50  -.33
> Gp3    .00  0.66
> 
> Suppose D2 is non-significant.  Is the researcher justified to drop D2
> in the final model and include D1 as the only predictor?
> 
These dummies use the repeated contrast (I think) so D1 indicates the
difference between Gp1 and Gp2 and D2 indicates the difference between
Gp2 and Gp3. Dropping D2 will therefore not test your hypothesis
correctly: it doesn't take the relationship between Gp1 and Gp3 into
consideration. To test the hypothesis above you would have to create a
special contrast like this:
  /contrast(GP)=special(1     -1   0  /* comparison of GP1 and GP2
                        -.5  -.5   1) /* GP3 vs the mean of GP1 and GP2
The preferred way of testing your hypothesis would be to run LOGISTIC
with both parameters for GP and with GP(1) only and use a likelihood
ratio test for the difference between the two models. The Wald statistic
for the significance of GP(2) is too small, especially if the parameter
has a larger absolute value.
> (Some may think that logistic regression is not the only method and certainly
> is not the simplest method in this case.  I still choose this case
> because it, I think, is easier for me to present the problem.)
> 
These methods apply in principle to any model with categorical
independent variables and linear predictors, including loglinear, anova,
logistic, Cox regression models. If you have a dichotomous dependent
variable then logistic regression is the way to go.
I wrote a set of SAS macros for creating a design matrix with different
types of contrasts. This could then be used in PROC GENMOD, the SAS
procedure for Generalized Linear Models (which includes the above models
except for Cox regression). Anyone interested in these macros can find
them at .
> Thanks for any opinion.
John Hendrickx
Department of Sociology, University of Nijmegen, The Netherlands.

In article <3297AF2F.41C67EA6@ifp.uiuc.edu>,
Igor Kozintsev   wrote:
>Hello,
>The following distribution is called Generalized Gaussian
>and is widely used in image processing:
>\begin{equation}
>f_{X}(x)=\left[\frac{\nu \eta (\nu ,\sigma )}{2\Gamma (1 / \nu)}\right]
>\exp (-[\eta (\nu ,\sigma ) |x|]^\nu ),
>\end{equation}
>where
>\begin{equation}
>\eta = \eta(\nu ,\sigma ) = {\sigma}^{-1}
>\left[\frac{\Gamma (3/\nu )}{\Gamma (1/\nu)}\right]^{1/2}.
>\end{equation}
>(sorry for this latex code)
>I need to generate random numbers for this distribution
>and evaluate first three moments of the distribution (conditioned 
>on variable to be in some interval) on the computer.
To begin with, I suggest that we simplify the expressions,
by not evaluating all constants.  As I do not write LaTeX,
I will use the simpler "newsgroup TeX"
	f(x) = A exp(-B |x|^\nu),
where B is chosen to get the right variance, and A to make it
a probability distribution.
As for computing the moments of a truncated distribution, unless
\nu is a rational number with very small numerator, it is going to
involve numerous computations of incomplete gammas.
As for generating random variable from this distribution, acceptance-
rejection methods ignore the A anyhow.  For \nu at least 1, the 
logarithm of the density is concave, and so the methods for that
can be used.  Otherwise, I suggest that |x|^\nu = |y|, with the
appropriate sign attached, and that the appropriate \Gamma distribution
be simulated.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

In article <32977892.4EE@students.wisc.edu>, Tatsuo Ochiai
 wrote:
> 
> Suppose X ~ N(mu, sigma^2). Then, what is the formula for
> 
>      E[X|X=>X^*] : Expected value of X given X is greater than or
> equal      to some fixed number X^*
Let Z = (X-mu)/sigma.
Then E[X|X=>X^*] = mu + sigma*E[Z|X=>X^*]
= E[Z|Z=>Z^*] where Z^* = (X^*-mu)/sigma.
The latter can be integrated easily.
E[Z|Z=>Z^*] = 1/sqrt(2pi) integral(Z^*,oo, z exp(-z^2 /2) dz)
= 1/sqrt(2pi) [-exp(-z^2 /2)](Z^*,oo)
= 1/sqrt(2pi) [1 - exp(-Z^*^2 /2)].
Of course you can work in terms of X, but the above
is a little easier.
Terry Moore, Statistics Department, Massey University, New Zealand.
Imagine a person with a gift of ridicule [He might say] First that a
negative quantity has no logarithm; secondly that a negative quantity has
no square root; thirdly that the first non-existent is to the second as the
circumference of a circle is to the diameter. Augustus de Morgan

In article , T.Moore@massey.ac.nz
(Terry Moore) wrote:
> 
> In article <32977892.4EE@students.wisc.edu>, Tatsuo Ochiai
>  wrote:
> > 
> > Suppose X ~ N(mu, sigma^2). Then, what is the formula for
> > 
> >      E[X|X=>X^*] : Expected value of X given X is greater than or
> > equal      to some fixed number X^*
> 
> Let Z = (X-mu)/sigma.
> Then E[X|X=>X^*] = mu + sigma*E[Z|X=>X^*]
> = E[Z|Z=>Z^*] where Z^* = (X^*-mu)/sigma.
> 
> The latter can be integrated easily.
> E[Z|Z=>Z^*] = 1/sqrt(2pi) integral(Z^*,oo, z exp(-z^2 /2) dz)
> = 1/sqrt(2pi) [-exp(-z^2 /2)](Z^*,oo)
> = 1/sqrt(2pi) [1 - exp(-Z^*^2 /2)].
Sorry, I forgot to divide by P(Z=>Z^*) which is best
looked up in tables as there is no closed form formula.
Terry Moore, Statistics Department, Massey University, New Zealand.
Imagine a person with a gift of ridicule [He might say] First that a
negative quantity has no logarithm; secondly that a negative quantity has
no square root; thirdly that the first non-existent is to the second as the
circumference of a circle is to the diameter. Augustus de Morgan

Mike Tennant (tennant@mh.uk.sbphrd.com) wrote:
: Hi,
: 	I'm trying to find a way of binning frequency data into a number of
: bins (either predetermined or using some measure of bin 'density' to
: determine the number), and then calculating some stats on the bins (eg
: width, hight, density etc). Does anybody know whether this is possible
: using SAS, as I have access to that program.
: The data I have is measured angles (0-360 degrees) along x and frequency
: of occurance along y.
: 
Yes, this certainly can be done in SAS.  If the bins are predetermined,
then write in a DATA step something like:
   If 0 le ANGLE lt 15 then BIN = 1;
   else if 15 le ANGLE lt 30 then BIN = 2;    etc.
If the bin boundaries are to be determined by the data, first compute the
quantiles of the ANGLEs (e.g. PROC UNIVARIATE), then merge these back onto
the dataset.  The BINs can be formed as above with the quantiles replacing
0, 15, 30, etc. 
-- 
Michael P. Cohen                       home phone   202-232-4651
1615 Q Street NW #T-1                  office phone 202-219-1917
Washington, DC 20009-6331              office fax   202-219-2061
mcohen@cpcug.org

LINDA J. FELCH (lfelch@welchlink.welch.jhu.edu) wrote:
: We are using the Holm's modified Bonferroni procedure to correct for 
: multiple comparisons. Recently a journal editor asked us for exact 
: p-values associated with the tests for which we had done the correction.
: 
: We have exact p-values from the uncorrected tests. Using an unmodified 
: Bonferroni procedure, it seems that one can multiply the uncorrected 
: p-value by the number of comparisons to obtain a corrected exact p-value. 
: The Holm's procedure, and others like it, use a shifting criteria of 
: statistical significance which is based on the number of comparisons left 
: to be considered. Is there a way to obtain exact p-values for this procedure?
This notion of "exact p-value"  (a funny term for this idea) seems to
assume that the corrected p-value  depends only on the uncorrected p-value
and the number of comparisons.  This would not be true for procedures
other than the Bonferroni.  We could still compute something if we knew
what the journal editor wanted us to hold constant.
By the way, the Bonferroni procedure is based on an inequality.  The
"exact p-values" are not exact; they are conservative.
-- 
Michael P. Cohen                       home phone   202-232-4651
1615 Q Street NW #T-1                  office phone 202-219-1917
Washington, DC 20009-6331              office fax   202-219-2061
mcohen@cpcug.org

http://www.mcs.com/%7Ejcr/junkemail.html has all sorts of interesting info
about junk e-mail, including an explanation of why adding your name to a
list (like www.zerojunkmail.com) is not likely to have the desired effect.
    Karl L. Wuensch, Dept. of Psychology, East Carolina Univ.
    Greenville, NC  27858-4353, phone 919-328-4102, fax 919-328-6283
    Bitnet Address: PSWUENSC@ECUVM1
    Internet Address:  PSWUENSC@ECUVM.CIS.ECU.EDU

On 19 Nov 1996, LINDA J. FELCH wrote:
> We have exact p-values from the uncorrected tests. Using an unmodified 
> Bonferroni procedure, it seems that one can multiply the uncorrected 
> p-value by the number of comparisons to obtain a corrected exact p-value. 
> The Holm's procedure, and others like it, use a shifting criteria of 
> statistical significance which is based on the number of comparisons left 
> to be considered. Is there a way to obtain exact p-values for this procedure?
Yes, and despite what a previous reply suggested it is unique  -- 
the p-values are perfectly well-defined as the lowest overall alpha at which 
one would reject the respective hypotheses using Holm's method.
The p-values for this and the slightly more powerful methods of Hochberg 
and Hommel are described in Wright S.P. "Adjusted p-values for simultaneous 
inference", Biometrics (1992) 1005-1013. Hommel's method is complicated, 
the other two are simple.
If there are k tests the procedure is to first multiply the smallest by 
k, the second-smallest by k-1, the third-smallest by k-2 and so on.  This 
gives a set of numbers which need not be in the same order as the 
original p-values.  To fix this, we increase these numbers where 
necessary to retain the original order.  More precisely, suppose p_1 is 
the largest original p-value and p_k the smallest.
First compute r_i=i*p_i
Then compute adjusted p-values qi as
q_k=r_k
q_(k-1)=max(r_(k-1),q_k)
and in general
q_i= max(r_i, q_(i+1))
If any q_i is greater than 1 set it to 1.
For Hochberg's procedure the same r_i are used but adjusted p-values q_i are 
defined as 
q_1=r_1
q_2=min(q_1,r_2)
...
q_i=min(q_(i-1),r_i)
so that the adjusted p-values must be less than 1 and can be no greater 
than the Holm p-values.
thomas lumley
UW biostatistics