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From |
Yuval Arbel <yuval.arbel@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 3 Sep 2012 00:53:42 -0700 |

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 <njcoxstata@gmail.com> 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 <kohler@wzb.eu> 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 <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. >>>> > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ -- Dr. Yuval Arbel School of Business Carmel Academic Center 4 Shaar Palmer Street, Haifa 33031, Israel e-mail1: yuval.arbel@carmel.ac.il e-mail2: yuval.arbel@gmail.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: Mean test in a Likert Scale***From:*Nick Cox <njcoxstata@gmail.com>

**References**:**Re: st: RE: Mean test in a Likert Scale***From:*Ulrich Kohler <kohler@wzb.eu>

**Re: st: RE: Mean test in a Likert Scale***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: RE: Mean test in a Likert Scale***From:*Ulrich Kohler <kohler@wzb.eu>

**Re: st: RE: Mean test in a Likert Scale***From:*Nick Cox <njcoxstata@gmail.com>

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