# [Rasch] Permissible Transformations

Stephen Humphry stephen.humphry at uwa.edu.au
Thu Mar 19 16:34:08 EST 2009

```I forgot to include the couple of references that summarise and use the
metrological conventions of 'quantity calculus'. Here they are ...

Allisy, A. (1980). Physical Quantities. In A.F. Milone & P. Giacomo (Eds.),
Proceedings of the International School of Physics 'Enrico Fermi' Course
LXVIII, Metrology and Fundamental Constants (pp. 14-17).  Amsterdam:
North-Holland.

Emerson, W.H. (2008). On Quantity Calculus and Units of Measurement.
Metrologia, 45, 134-138.

_____

From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Anthony James
Sent: Thursday, 19 March 2009 1:15 AM
To: rasch at acer.edu.au
Subject: [Rasch] Permissible Transformations

Dear folks,

It is said that linear transformations in the from of X' = a + bX are
permissible for interval scales. What does this mean? If we multiply a set
of numbers by a constant and add them with another constant we will get a
new different set. What properties does this new set have and how is it
related to the first set that makes it a linear transformation?

Why isn't multiplication permissible? Isn't multiplication a linear
transformation where the additive component is zero? So it must be a linear
transformation? (or probably zero isn't allowed to be the multiplicative
component). When a scale in linearly transformed the distances between the
objects are increased 'a' times the distances in the first scales.

I don't understand how interval and ratio scales are different in relation
to permissible transformations. I'd be thankful for comments.

Cheers

Anthony

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