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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   Mon, 3 Sep 2012 10:01:42 +0100

(Those confused by continuity here should know that Yuval is in fact
replying to a different post of mine, which you can find at

Thanks for the reference and the quotations.

What bites for an ordinal predictor bites also for a numeric
(interval/ratio, or cardinal if you wish) predictor. Such a strict
line (and such a straight face) from Kmenta that you must "know a
priori" that any predictor enters linearly raise the question of what
scope there is for learning from the data or for using purely
empirical approximations.

Econometricians' practice seems almost invariably looser than that --
and a good thing too -- although the idea that an analysis is correct
or incorrect, and no shades of grey, still seems pervasive.


On Mon, Sep 3, 2012 at 8:53 AM, Yuval Arbel <> wrote:
> Regarding Nick's question, the exact reference of Kmenta (1997) is:
> Jan Kmenta (1997): Elements of Econometrics, Second Edition, Chapter 11.
> The particular example is taken from page 464. On the second sentence
> of the first paragraph the author says that:
> "It would be incorrect to use one variable with three values say, 0
> for B.A., 1 for M.A. and 2 for a Ph.D."
> Then he explains formally why it is wrong:
> "That is, by using one variable with values 0, 1 or 2 (or any three
> equidistant values) we are in fact assuming that the difference
> between the salary of a Ph.D. and an M.A. is the same as that between
> the salary of M.A. and B.A. Unless we know a priori this is the case,
> we are not justified in making such an assumption."
> On Sun, Sep 2, 2012 at 3:35 AM, Nick Cox <> wrote:
>> Thanks for the clarification. I am not sure whether that leaves our
>> positions as essentially similar despite apparent differences, or the
>> opposite.
>> How far researchers are willing to use transformations is strikingly
>> variable between, and even within, fields of statistical science.
>> Nick
>> On Sun, Sep 2, 2012 at 11:11 AM, Ulrich Kohler <> wrote:
>>> 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 <> 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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