Multiple correlations with pairs of variables and their respective pairs of residual variables

[Jon Peck]

That email appears to belong to one 

Fernando Mazariegos

who may have something to do with SAGE publications.  Of course, it may have been hacked.

On Wed, Sep 9, 2020 at 12:04 PM Rich Ulrich <[hidden email]> wrote:

Folks, 

Possible warning.

I don't know what this means, but I just now received a Reply to

my message here, addressed just to me, which looked innocent,

and contained a Windows Word  .doc document.  I don't have

Word, so I downloaded it.  Norton deleted it, reporting that it is

dangerous. 

The Sender is not a name I recognized, and has not contributed to

this thread under this name, but the context -- quoting my own post

here -- made it believable. "I have made some edits.  Please check."

Sender:

[hidden email]

fmazariegos:  If this was innocent, be informed that I did not read the

file, and that you need to clean your system of a virus.  Or, that your

name or access has been hijacked.

As for me, I have to widen my usual precautions about, "Don't download

something from someone you don't trust."

--

Rich Ulrich

---

From: Rich Ulrich <[hidden email]>
Sent: Wednesday, September 2, 2020 5:23 PM
To: [hidden email] <[hidden email]>; Bruce Weaver <[hidden email]>
Subject: Re: Multiple correlations with pairs of variables and their respective pairs of residual variables

 

Bruce,

It looks to me like your programs provide TWO versions of the test.

A comment in one file says that the Steiger test (which I think of as

the test on variances) outperformed the test by Zou (which I think of as

the test using Fisher's z) in an article comparing them.

I read an article about that comparison, in which variance-better-than-z was

the general conclusion. (Two different articles? I don't know.)  IIRC, there

was also mention that a study's /design/ could make the Zou test more

appropriate.  For this design, comparing the r for (V1,V2) with the r for the

residualized versions, I think "variance" must be more appropriate. The

difference between them will be trivial when the scaling of r is similar to

the scaling of z, i.e., whenever r's are decently small.

However -- if the original outside covariate ("age" in your example), has

little influence, it could be that V1 and V1-adjusted (in the OP's example)

have an r that is close to 1.0.  In that case, tests could differ by non-trivial amounts.

--

Rich Ulrich

---

From: SPSSX(r) Discussion <[hidden email]> on behalf of Bruce Weaver <[hidden email]>
Sent: Wednesday, September 2, 2020 3:58 PM
To: [hidden email] <[hidden email]>
Subject: Re: Multiple correlations with pairs of variables and their respective pairs of residual variables

 

Hi Art.  Please note too that Karl Wuensch and I published an article in 2013
describing all of the common methods for comparing correlations (and
regression coefficients).  I contributed SPSS code, and Karl contributed SAS
code.  You can find the code at the first two links below and the article at
the 3rd:

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch
http://core.ecu.edu/psyc/wuenschk/W&W/W&W-SAS.htm
https://link.springer.com/article/10.3758%2Fs13428-012-0289-7

In 2014, Ray Koopman and I published another article describing a macro to
compute CIs for Pearson correlations.  (I should not say this, as it will
likely cost me some citations, but Jon Peck has since written a nice Python
extension command that you might want to use instead.  It's called STATS
CORRELATIONS, IIRC.)  ;-) 

   https://www.tqmp.org/RegularArticles/vol10-1/p029/p029.pdf
 
https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/rhoci

While we were working on that article, Ray taught me that Fisher's r-to-z
transformation is really the inverse hyperbolic tangent, and the
back-transformation is the hyperbolic tangent.  SPSS does not have those
functions, but Ray showed me that one can get them by using IDF.LOGISTIC()
and CDF.LOGISTIC() functions.  Here are several comment lines from my !rhoCI
macro definition file that describe the basic equations:


* The macro uses the following basic equations.

*  Zr = arctanh[r] <==> r = tanh[Zr]

*  d = z_alpha / sqrt[n-3]

*  t = tanh[d]

*                       tanh[Zr] +- tanh[d]     r +- t
* ci = tanh[Zr +- d] = --------------------- = --------
*                      1 +- tanh[Zr]*tanh[d]   1 +- r*t

* The rightmost term in the last equation works even when r = +1 or -1.

* SPSS has no tanh and arctanh functions. 
* HOWEVER, one can use IDF.LOGISTIC and CDF.LOGISTIC as follows:

*  arctanh[r] = .5*ln((1+r)/(1-r)) = .5*idf.logistic((1+r)/2,0,1)
*  tanh[d] = (exp(2*d)-1)/(exp(2*d)+1) = 2*cdf.logistic(2*d,0,1)-1

* SOURCES:
* http://people.math.sfu.ca/~cbm/aands/page_83.htm (see Equation 4.5.26).
* http://people.math.sfu.ca/~cbm/aands/intro.htm#001 .



Art Kendall wrote
> I do not have access to Psychological methods these days.
> Fisher's Z has been discussed on this list previously.
> In the archives Bruce said
> COMPUTE rprime = 0.5*ln((1+r)/(1-r)).
>
> In 2006 Marta posted macros to compare correlations.
> Search ‘comparing correlations’ in the archives
> If you have the article and you have the formulae in Excel, why not do
> everything directly in SPSS?
>
> Start with the center of what you want, an example 4 by R matrix.  Work
> out
> what you would do.  Then generalize with OMS, Python, or macro.
>
>
>
>
> -----
> Art Kendall
> Social Research Consultants
> --
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-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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