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

 From Reg Jordan To "statalist@hsphsun2.harvard.edu" Subject Re: st: RE: Mean test in a Likert Scale Date Sat, 1 Sep 2012 20:30:01 -0400

```Can't read your paper. It requires that I purchase a subscription. Do you have a copy you could share?

Reg

On Sep 1, 2012, at 3:48 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:

> of original numerical values of ordinal variables is a very serious
> error, but it has nothing to do with transformation of variables.
>
> To examplify why this is a serious mistake, consider the following
> example taken from Kmenta (1997):
>
> Suppose our dependent variable is the level of wage and our
> independent variable is the level of education with 3 categories: D= 0
> for elementary-school education, D=1 for high school education and D=2
>
> If you run regression between the wage level and D, your implicit
> assumption is that wage difference between D=0 and D=1 is equal to the
> wage difference between D=1 and D=2. This is a wrong and very limited
> assumption.
>
> Moreover, if for some reason you have decided that the scale of D will
> be D= 0 for elementary-school education, D=10 for high school
> education and D=20 for academic education, then the implicit
> assumption becomes that the wage of D=20 is ten time bigger than the
> wage of D=10.  In other words, the ordinal numerical value, which does
> not have any quantitative interpretation, have an impact on the
> regression outcomes. This is the reason we need to use binary
> variables under such circumstances.
>
> To see the correct analysis of questionnaires with ordinal questions,
> you can take a look at my paper published in urban studies:
>
> http://intl-usj.sagepub.com/content/49/11/2479.full
>
>
> On Sat, Sep 1, 2012 at 9:32 AM, Nick Cox <njcoxstata@gmail.com> 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?
>>
>> How about link functions as in -glm-? Transformed scales on graphs?
>>
>> 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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>
>
>
> --
> Dr. Yuval Arbel
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com
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```