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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

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

Date |
Sat, 1 Sep 2012 17:03:57 -0400 |

And what would be wrong with just using some form of ordinal or multinomial regression? Cam > Date: Sat, 1 Sep 2012 12:48:20 -0700 > Subject: Re: st: RE: Mean test in a Likert Scale > From: yuval.arbel@gmail.com > To: statalist@hsphsun2.harvard.edu > > 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: > > 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. > >> > >> > >> > >> * > >> * 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/ > > * > > * 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/ * * 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/

**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:*Yuval Arbel <yuval.arbel@gmail.com>

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