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Re: st: RE: Mean test in a Likert Scale


From   Ulrich Kohler <kohler@wzb.eu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Mean test in a Likert Scale
Date   Sat, 01 Sep 2012 16:50:20 +0200

Am Samstag, den 01.09.2012, 02:16 +0100 schrieb Nick Cox:
> But this objection is so strong that it rules out taking out means in
> most circumstances, not just for ordinal scales.
> 
> It's clearly true that mean of transform is not transform of mean
> unless that transform is a linear function. The same argument would
> imply that means are invalid for measured variables (e.g. means of
> miles per gallon, weight, price in the auto data) because they are not
> equivariant under transformation. Both theory and practice tell us
> that means, geometric means, harmonic means, etc. can all make some
> sense for many measured variables. Poisson regression and generalised
> linear models all hinge on this.

Sorry but I disaggree here. For an intervall scale a transformation such
as the one that I used in my example are not allowed because it would
obvioulsy distroy the equal distance characteristic of subsequent
values. For an intervall scale only linear transformations are allowed
and therfore substantive conclusions taken from the mean are robust for
arbitrary _allowed_ transformation of the intervall scale. 

> There's also a big difference of viewpoint here. Measurement theory
> loves these arguments about arbitrary order-preserving
> transformations, but I don't think they make much sense to scientists
> who actually do measurements.


But I don't think we -- that is me and you -- disaggree here. In way
that's what I wanted to say when I said that an ordinal scale could be
taken as kind of an "conventional" absolute scale in some instances. 



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