[Rasch] Permissible Transformations

Mike Linacre (RMT) rmt at rasch.org
Thu Mar 19 14:56:09 EST 2009


Anthony:

Ratio scales:  Most zero points (reference points) are chosen for 
convenience.  For instance,

when we make a ratio-scale statement such as "This mountain is twice as 
high as that mountain",  we have chosen sea-level as our zero-point;

when we make a ratio-scale statement such as "This room is twice as hot as 
that room",  we have chosen a room at a comfortable room-temperature as our 
zero-point.

Ratio scales are not invariant against change of zero-point. If "John is 
twice as tall as Jim" is true relative to the floor as zero-point, it is 
not true relative to the center-of-the-Earth as zero-point.

Ratio scales are invariant against changes in interval-level 
measurement-units. "John is twice as tall as Jim" is the same for both 
centimeters and inches.

Hope this helps ....

Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  22:4 Spring 2009
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