[Rasch] Permissible Transformations

Swank, Paul R Paul.R.Swank at uth.tmc.edu
Thu Mar 19 08:33:55 EST 2009

You can add a costant to a interval scale but not to a ratio scale because it changes the absolute zero. You can multiply either by a constant.

Dr. Paul R. Swank
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From: rasch-bounces at acer.edu.au
To: rasch at acer.edu.au
Sent: Wed Mar 18 11:14:22 2009
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.

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