[Warning: This isn't really a statistics question. I'm taking a punt that one of the others interested in psychometrics around here might know the answer to this ]

I've working again on my off-again on-again attempt to provide a guide to the whole controversy of admissable statistics.

Something's troubling me in representationalist measurement theory (i.e. the theory that measurement is about representing empirically observable relations amongst objects).

Specifically I'm wondering about the exact requirements for an interval scale. Obviously we need to make some kind of observations with respect to the

But do we need only to make observations of the type:

1) The difference between A and B is noticeably greater than the difference between B and C

or do we need to be able observe

2) The difference between A and B is twice the difference between B and C?

It seems to me that if we only need to make observations of type (1), then some non-linear transformations would preserve the information we have about the empirical relations (whereas the permissable transformations for an interval scale are theoretically limited to linear transformations [

Any takers? Sorry for brevity; I can flesh this out if people unfamiliar with the area are nevertheless interested.

I've working again on my off-again on-again attempt to provide a guide to the whole controversy of admissable statistics.

Something's troubling me in representationalist measurement theory (i.e. the theory that measurement is about representing empirically observable relations amongst objects).

Specifically I'm wondering about the exact requirements for an interval scale. Obviously we need to make some kind of observations with respect to the

*differences*between objects. That's what distinguishes an ordinal from an interval scale.But do we need only to make observations of the type:

1) The difference between A and B is noticeably greater than the difference between B and C

or do we need to be able observe

*ratios*of differences, e.g.2) The difference between A and B is twice the difference between B and C?

It seems to me that if we only need to make observations of type (1), then some non-linear transformations would preserve the information we have about the empirical relations (whereas the permissable transformations for an interval scale are theoretically limited to linear transformations [

*edit to clarify: by linear transformation I mean x' = ax + b, where x could be a vector but a and b are constant*s]).Any takers? Sorry for brevity; I can flesh this out if people unfamiliar with the area are nevertheless interested.

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