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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   Sun, 2 Sep 2012 11:23:00 +0100

The original question was posed by Leonor Saravia: here is the link
again for anyone interested.

Yuval is _not_ here returning to the original question, which was
about response variables on a Likert scale. My own line on this is
that despite what people say, t tests often work well, but watch out.

Yuval is criticising the use of an ordinal predictor treated
numerically in regression. I imagine widespread agreement with Yuval's
point, which is elementary. The only good justification for doing that
is if the relationship is linear in practice, which is unlikely to be
true of Yuval's kind of example. But again that is true of any

I want to stress that this problem is a different target.

The details of the Kmenta (1997) reference are missing.

For my part, I am shy of claiming "the correct analysis" of anything.
I've seen too many cases where smart people have come up with
different good analyses which each have merits. I think there are many
incorrect analyses around -- meaning analyses that can be argued to be
incorrect -- but the asymmetry is important.


On Sat, Sep 1, 2012 at 8:48 PM, Yuval Arbel <> wrote:
> David, if we return to your original question, I believe that the use
> 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
> for academic education.
> 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:
> On Sat, Sep 1, 2012 at 9:32 AM, 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?
>> How about link functions as in -glm-? Transformed scales on graphs?
>> 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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