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

 From Ulrich Kohler To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Mean test in a Likert Scale Date Sun, 02 Sep 2012 12:11:01 +0200

```On 01.09.2012 18:32, Nick Cox wrote:
```
```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?

```
No, that is not what I wanted to say. I wanted to say that each scale has a set of transformations that are "allowed" in the sense that they don't change the defining features of the scale (whether its nominal, ordinal, etc.). You can use any transformation that is allowed, but than you should use only those statistics, whose conclusions are robust against that transformations. You can even use transformations that change the scale, but than you should use a statistic
```that is robust against that transformation.

Nick On Sat, Sep 1, 2012 at 3:50 PM, Ulrich Kohler <kohler@wzb.eu> 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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