[Rasch] Units of measurement in the social sciences

Stephen Humphry stephen.humphry at uwa.edu.au
Tue Oct 23 15:41:42 EST 2007

Hi Andrew.
It is indeed theoretically possible to measure in an infinite number of
units, each having a different size, provided the attribute has the
necessary structure. Nevertheless, to measure in any particular unit
requires deliberate and careful construction of the instrument and use of
the instrument under controlled conditions. The unit in terms of which
measurements are expressed can be arbitrarily chosen, but you cannot gain
precision that does not exist given the instrument and conditions. The unit
in terms of which measurments are obtained depends upon empirical features
of the instrument and, more generally, the observational frame of reference.
On this, Andrich (2003) made a distinction between the arbitrary and natural
unit and showed that precision is inversely proportional to the size of the
unit and that precision is reflected in the theoretical distribution of
repeated measurements. The unit plays a genuinely non-arbitrary role.
This is consistent with the SI system of units, and with the definition of
the Lexile you have just given. The definitions of all base SI units make
reference to empirical conditions. Another interesting point is that the
definitions of all SI units, base and derived, make reference to other kinds
of quantities. For example, the kelvin is a fraction of the triple point of
water, the definition of which involves pressure. There is one exception,
the kg. However, even the definition of the kg originally involved volume.
The universality with which a unit can be defined depends upon these
features of the definitions.
I agree the selection of a unit of measurement certainly doesn't bestow
ontological privelege on that unit over others. I also agree there is
nothing special about the unit in terms of which measurements are expressed.
However, I think there is something unique, ontologically, about the unit in
terms of which measurements are actually made because it is not possible to
gain (or lose) precision that does not exist given the instrument and more
generally the observational frame of reference.
Great discussion.
Andrich, D. (2003). On the distribution of measurements in units that are
not arbitrary. Social Science Information, 42, 557-589.



From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Andrew Kyngdon
Sent: Tuesday, 23 October 2007 5:06 AM
To: rasch at acer.edu.au
Subject: RE: [Rasch] Units of measurement in the social sciences

My two cents.


If an attribute possesses additive structure, then it is theoretically
possible it can be measured with an infinite number of types of units. The
prime example of this is length which can be measured using cubits,
millimetres, Planck lengths, feet, inches, kilometres or light years. This
is because measurement involves not just a unit and a magnitude, but a
conception of additivity (Michell, 1993) or symmetry (Luce, 2001) of the
attribute. An infinite number of compositional relations exist for
quantitative attributes, all of which satisfy the formal requirements for
additive structure (Michell, 1993).


Not all units are useful for all measurement purposes (e.g. Planck lengths
or lightyears when you are measuring your waistline). The unit of
measurement in the Lexile reading scale is defined as 1/1000th of the
difference in comprehensibility between basal primer texts and Grolier's
(1986) Encyclopaedia (Stenner, 1986). As an interval scale, it has to be
unique up to linear transformations (i.e. y = m(x) + b). We add a constant
to theoretical logit measures of text difficulty, multiply this sum (x) by
another constant (m), then add another constant (b) to this product to
obtain the Lexile scale (for person reading ability in Lexiles the same
equation is used except empirical Rasch person logit measures are
substituted for the theoretical text logits). The unit is arbitrary as it is
in thermometry, where the unit of the Celsius scale, for example, is defined
as 1/100th of the difference in temperature between the boiling and freezing
points of water at sea level. In both situations other equally valid scales
are possible with different units. The selection of one unit of measurement
does not bestow ontological privilege on it over the other possible units
(Michell, 1993). There is really nothing special about units in and of








Luce, R.D. (2001) Conditions equivalent to unit representations of ordered
relational structures. Journal of Mathematical Psychology, 45, 81-98.


Michell, J. (1993). Numbers, ratios and structural relations. Australasian
Journal of Philosophy, 71, 325-332.


Stenner, A.J. (1996) Measuring reading comprehension with the Lexile
framework. Paper presented to the California Comparability Symposium
(available at www.lexile.com <http://www.lexile.com/> ). 




From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Anthony James
Sent: Sunday, October 21, 2007 2:25 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Units of measurement in the social sciences


regarding my question I found something which seems relevent:


Anthony James <luckyantonio2003 at yahoo.com> wrote:

Dear folks,

Another dumb question...

I'll be grateful for any comments.

When we are talking about "units of measurement" in the physical sciences we
are talking about some tangible things. (I avoide the word "concrete"
because I know you don't like it in this context and argue that all measures
are abstractions). However, I mean kilo or meter , for example, are
understandable attributes that have a concerete existence. A "sample meter"
,i.e., a rod of 1 meter can be aligned with any object and count the number
of alignments. Or we can put some potatos on the pan of a scale and put
enough weaights on the other pan until the beam is balanced. 


1. How does the Rasch model make this "sample meter" or the one-kilo weight
to compare the performance of the students against?

2. Whose performance  is considered as the unit and how is it constructed?

3. What's the defenition of a logit?






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