# [Rasch] Dimensionality and Correlation

Andrew Kyngdon akyngdon at lexile.com
Fri Nov 14 17:01:04 EST 2008

```"...though,  that in relevant cases, the measurement itself must be conjoint;
whereas the description in terms of correlations presupposes the
properties can be measured separately then correlated."

Could not agree with you there more mate!

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: Fri 14-Nov-08 2:22 PM
To: rasch at acer.edu.au
Subject: RE: [Rasch] Dimensionality and Correlation

Precisely Andrew. A complementary way of saying the same thing is that
there may be a correlation between a quantitative property A and
another quantitative property B that is produced in an experiment for
a *fixed level* of a property C.

The structure of many physical definitions and laws implies, though,
that in relevant cases, the measurement itself must be conjoint;
whereas the description in terms of correlations presupposes the
properties can be measured separately then correlated. As an example,
you cannot measure the mass of an object without a force and,
symmetrically, you cannot measure a force without using an object with
mass. Acceleration, in some form, is the experimental outcome. Force
and mass are measured conjointly -- so I agrue at least, and I
maintain that Poincaré made this point in 'Science and Hypothesis'.

Steve

Quoting Andrew Kyngdon <akyngdon at lexile.com>:

> Anthony,
>
> Those were not my words, they were Steve Humphry's. I was merely
> supporting them.
>
> Steve was making the point that in the social sciences, the
> calculation of correlation coefficients has largely supplanted
> experimental investigation of relationships between quantitative
> attributes. There is nothing wrong in calculating correlations and
> they may indeed reveal interesting things from time to time. But
> they are limited.
>
> The investigation of "trade off" relations is one avenue through
> which a relationship between two attributes can be ascertained. If
> the behaviour of the trade offs is consistent with that entailed by
> the theory of conjoint measurement, then a relationship is
> discovered without any resort being made to correlation coefficients.
>
> Cheers,
>
> Andrew
>
> 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 Anthony James
> Sent: Fri 14-Nov-08 12:53 AM
> To: rasch at acer.edu.au
> Subject: RE: [Rasch] Dimensionality and Correlation
>
>
>
>
> 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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