What are permissible transformations?
Permissible transformations are transformations of a scale of measurement that preserve the relevant relationships of the measurement process. Permissible is a technical term; use of this term does not imply that other transformations are prohibited for data analysis any more than use of the term normal for probability distributions implies that other distributions are pathological. If Stevens had used the term mandatory rather than permissible, a lot of confusion might have been avoided. In the example of measuring sticks, changing the unit of measurement (say, from centimeters to inches) multiplies the measurements by a constant factor. This multiplication does not alter the correspondence of the relationships ‘greater than’ and ‘longer than’, nor the correspondence of addition and concatenation. Hence, change of units is a permissible transformation with respect to these relationships.
