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

From   Nick Cox <>
Subject   Re: st: RE: Mean test in a Likert Scale
Date   Sat, 1 Sep 2012 17:32:59 +0100

My examples -- miles per gallon, price, weight -- all qualify as ratio scales.

If I understand you correctly, your view is that transformations are
illegitimate in statistics.

Is that right?

How about link functions as in -glm-? Transformed scales on graphs?


On Sat, Sep 1, 2012 at 3:50 PM, Ulrich Kohler <> wrote:
> 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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