[Rasch] Dimensionality and Correlation

Anthony James luckyantonio2003 at yahoo.com
Fri Nov 14 00:53:40 EST 2008


Andrew, 
Your reply is interesting and raises new questions. What are these
 "experiments that are required to understand relationships between quantitative properties"?
Cheers
Anthony

--- On Tue, 11/11/08, Andrew Kyngdon <akyngdon at lexile.com> wrote:

> From: Andrew Kyngdon <akyngdon at lexile.com>
> Subject: RE: [Rasch] Dimensionality and Correlation
> To: "Stephen Humphry" <shumphry at cyllene.uwa.edu.au>, rasch at acer.edu.au
> Date: Tuesday, November 11, 2008, 4:12 PM
> Also in my view, a lot of people try to use correlations 
> as a substitute for experiments that are required to
> understand 
> relationships between quantitative properties.
> 
> Hear, hear!
>  
> Dr Andrew Kyngdon
> Director of Pacific Rim Operations
> MetaMetrics, Inc.
> P.O. Box 754 North Sydney NSW 2059 Australia
> Phone: 0401768090 (Int. +61401768090)
> Email: akyngdon at lexile.com 
> Web: www.lexile.com <http://www.lexile.com/>  
> Lexile Teacher's Lounge:
> http://lexile-teachers.blogspot.com/ 
> 
> ________________________________
> 
> From: rasch-bounces at acer.edu.au on behalf of Stephen
> Humphry
> Sent: Sat 08-Nov-08 7:46 PM
> To: rasch at acer.edu.au
> Subject: Re: [Rasch] Dimensionality and Correlation
> 
> 
> 
> 
> Hi Anthony. In my view there's a lot of confusion
> surrounding this in 
> the social sciences.
> 
> Think of volume and mass. If the densities of a set of
> objects is 
> uniform (e.g. they're all made of uranium), then the
> correlation 
> between measurements of their mass and volume will be near
> 1.
> 
> Does that make mass and volume the same quantitative
> property? Clearly not.
> 
> Suppose on the other hand, objects are made of a range of
> substances 
> -- styrofoam, rubbers, metals (even gases). Then
> measurements of mass 
> and volume will not be highly correlated and may have a
> very low 
> correlation.
> 
> It is possible to have a perfect correlation between two
> sets of 
> measurements yet for those measurements to be of different
> kinds of 
> quantities (dimensions).
> 
> So if two sets of measurements (i) are genuinely
> measurements and (ii) 
> have a low correlation, then they must be different kinds
> of 
> quantities (dimensions).
> 
> On the other hand, though, the fact two sets of
> measurements has a 
> high (even perfect) correlation is not sufficient to
> demonstrate there 
> is only one kind of quantity (kind of dimension). In my
> view it's 
> theoretically instructive to consider whether it is
> conceivable that 
> levels of two properties could be uncorrelated among any
> group of 
> individuals under any conditions. It's an experimental
> question 
> whether there are conditions under which two things are not
> 
> correlated. Also in my view, a lot of people try to use
> correlations 
> as a substitute for experiments that are required to
> understand 
> relationships between quantitative properties.
> 
> I also personally think the word unidimensionality is bit
> frought with 
> traps. Hope that helps.
> 
> Steve Humphry
> 
> 
> Quoting Anthony James <luckyantonio2003 at yahoo.com>:
> 
> > Dear all,
> > I have difficulty understanding the difference between
>  
> > dimensionality and correlation. I have seen several
> times in the  
> > literature that people talk about correlated
> dimensions and  
> > uncorrelated dimensions. I was always under the
> impression that if  
> > two dimensions are correlated then they are not two
> separate  
> > dimensions. They are one. But apparently, this is not
> true and there 
> >  can be two separate, and at the same time, correlated
> dimensions. 
> > Is  that right? I'd be grateful for any comments
> on the relationship 
> >  between correlation and dimensionality. Apparantly
> corrlation  
> > doesn't have much to do with unidimensionality.
> > Cheers
> > Anthony
> >  
> >
> >
> >
> 
> 
> 
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