Non-parametric ANCOVA

[David Moore-10]

Dear all,

I am wondering if anybody knows how to run a non-parametric version of an
ANCOVA with 3 repeated measures IV's and a continuous covariate?

Best
David

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[Joost van Ginkel]

Dear David,

To my knowledge, nonparametric tests are only available for oneway
problems with two or more groups, such as Wilcoxon's rank sum or rank
sign test or the Kruskall-Wallis test (in case of more than two groups).
These tests are not generalizeable to two- or moreway or ANCOVA
problems, unlike the available parametric tests. If the the distribution
of the dependent variable is severely skewed, consider categorizing or
dichotomizing your dependent variable and perfrom a logistic or ordinal
regression instead.

Best regards,

Joost van Ginkel


Joost R. Van Ginkel, PhD
Leiden University
Faculty of Social and Behavioural Sciences
Data Theory Group
PO Box 9555
2300 RB Leiden
The Netherlands
Tel: [phone]
Fax: [phone]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
David Moore
Sent: 09 November 2009 16:54
To: [hidden email]
Subject: Non-parametric ANCOVA

Dear all,

I am wondering if anybody knows how to run a non-parametric version of
an ANCOVA with 3 repeated measures IV's and a continuous covariate?

Best
David

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[Bruce Weaver]

Ginkel, Joost van wrote

Dear David,

To my knowledge, nonparametric tests are only available for oneway
problems with two or more groups, such as Wilcoxon's rank sum or rank
sign test or the Kruskall-Wallis test (in case of more than two groups).
These tests are not generalizeable to two- or moreway or ANCOVA
problems, unlike the available parametric tests. If the the distribution
of the dependent variable is severely skewed, consider categorizing or
dichotomizing your dependent variable and perfrom a logistic or ordinal
regression instead.

Best regards,

Joost van Ginkel

Alternatively, depending on what your data look like (and sample size), you might be able to simply run the usual parametric model on rank-transformed data.  See Conover's book "Practical Nonparametric Statistics".

[Steve Simon, P.Mean Consulting]

Bruce Weaver wrote:

> Alternatively, depending on what your data look like (and sample size), you
> might be able to simply run the usual parametric model on rank-transformed
> data.  See Conover's book "Practical Nonparametric Statistics".

The rank transform is an interesting idea, but it does not work well for
complex settings. In a two factor ANOVA, for example, it does not
produce a nonparametric (distribution free) test, and it can have very
poor power. I suspect the same problems would occur for ANCOVA.
--
Steve Simon, Standard Disclaimer
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That's actually what I thought, although I wasn't sure of it. I have
never heard of performing two- ore moreway ANOVA or ANCOVA on
rank-transformed data. I thought this only worked well for the oneway
problem, which is equivalent to the Kruskall-Wallis test.

Greetings,

Joost van Ginkel


Joost R. Van Ginkel, PhD
Leiden University
Faculty of Social and Behavioural Sciences
Data Theory Group
PO Box 9555
2300 RB Leiden
The Netherlands
Tel: [phone]
Fax: [phone]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Steve Simon, P.Mean Consulting
Sent: 10 November 2009 16:37
To: [hidden email]
Subject: Re: Non-parametric ANCOVA

Bruce Weaver wrote:

> Alternatively, depending on what your data look like (and sample
> size), you might be able to simply run the usual parametric model on
> rank-transformed data.  See Conover's book "Practical Nonparametric
Statistics".

The rank transform is an interesting idea, but it does not work well for
complex settings. In a two factor ANOVA, for example, it does not
produce a nonparametric (distribution free) test, and it can have very
poor power. I suspect the same problems would occur for ANCOVA.
--
Steve Simon, Standard Disclaimer
The Monthly Mean is celebrating its first anniversary.
Find out more about the newsletter that dares to call itself "average"
at www.pmean.com/news

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[Marta Garcia-Granero]

Steve Simon, P.Mean Consulting wrote:

> Bruce Weaver wrote:
>
>> Alternatively, depending on what your data look like (and sample
>> size), you
>> might be able to simply run the usual parametric model on
>> rank-transformed
>> data.  See Conover's book "Practical Nonparametric Statistics".
>
> The rank transform is an interesting idea, but it does not work well for
> complex settings. In a two factor ANOVA, for example, it does not
> produce a nonparametric (distribution free) test, and it can have very
> poor power. I suspect the same problems would occur for ANCOVA.

Well, the same happens to Kruskal-Wallis (which is also some sort of
ANOVA performed on ranks): it is not a truly distribution free method,
since, like Mann-Whitney's U, it has an assumption: sample distributions
should be similar in spread and shape. If the variable is not normally
distributed, but the cause is non normality is similar in all samples,
then an ANCOVA on ranks should be OK.

I always warn my students against the idea that all nonparametric
methods are absolutely "distribution free". Wilcoxon test needs a
symmetrical distribution, even if it is non normal.

Regards,
Marta GG

(looks like my email is getting SPSS list messages again...).



--
For miscellaneous SPSS related statistical stuff, visit:
http://gjyp.nl/marta/

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[Bruce Weaver]

Steve Simon, P.Mean Consulting wrote

Bruce Weaver wrote:

> Alternatively, depending on what your data look like (and sample size), you
> might be able to simply run the usual parametric model on rank-transformed
> data.  See Conover's book "Practical Nonparametric Statistics".

The rank transform is an interesting idea, but it does not work well for
complex settings. In a two factor ANOVA, for example, it does not
produce a nonparametric (distribution free) test, and it can have very
poor power. I suspect the same problems would occur for ANCOVA.

Here's the section of Conover's book I was thinking of:

"The recommended procedure in experimental designs for which no
nonparametric test exists is to use the usual analysis of variance on the
data and then to use the same procedure on the rank transformed data.  If
the two procedures give nearly identical results the assumptions
underlying the usual analysis of variance are likely to be reasonable and
the regular parametric analysis valid.  When the two procedures give
substantially different results, the experimenter may want to take a
closer look at the data and to look especially for outliers...or very
nonsymmetric distributions." (p. 419)

But Steve and Joost are correct.  In the paragraph before that, Conover says:

"The rank transformation works well in a two-way layout without interaction (see Iman, Hora and Conover, 1984 and Hora and Iman, 1988) where it compares well with the Friedman test, the Quade test, and the parametric F test. However, attempts to apply the rank transformation procedure to test for interaction have met with mixed results, showing that it has good robustness and power by Iman (1974b), Conover and Iman (1976), and Pavur and Nath (1986), but poor robustness and power by Blair, Sawilowsky, and Higgins (1987). A theoretical study by Thompson (1991) shows a flaw in the rank transformation test for interaction showing conclusively that it is not a valid procedure and shouldn't be used. However, Mansouri and Chang (1995) used normal scores instead of ranks and found no problems with the normal scores transformation test for interaction, so the conversion to normal scores might correct the flaw found by Thompson."

I think Marta raises a very good point too, by the way.  

Reference:
Conover W.J. (1999). "Practical Nonparametric Statistics" (3rd Ed.), Wiley.

Cheers,
Bruce

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Hello,

I have a dataset containing the component loadings of a PCA which need to be rotated using Varimax rotation. Does anyone know if there is a way in PASW to apply a Varimax rotation to the dataset directly, rather than carrying it out as a part of PCA?

Best regards,

Joost van Ginkel

Joost R. Van Ginkel, PhD
Leiden University
Faculty of Social and Behavioural Sciences
Data Theory Group
PO Box 9555
2300 RB Leiden
The Netherlands
Tel: [phone]
Fax: [phone]

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[Art Kendall]

FACTOR can read in factor loadings with the /matrix=IN(FAC=file) specification.

if you obtained the loadings with SPSS and the /matrix=out(FAC=file) specification then the file will be correctly formatted.  If you obtained it some other way, see the help for how to format it.  I have sometimes done a FACTOR on any arbitrary data set and used a /matrix=out specification to see how to set up an input file.

Art Kendall
Social Research Consultants

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Hello,

I have a dataset containing the component loadings of a PCA which need to be rotated using Varimax rotation. Does anyone know if there is a way in PASW to apply a Varimax rotation to the dataset directly, rather than carrying it out as a part of PCA?

Best regards,

Joost van Ginkel

Joost R. Van Ginkel, PhD
Leiden University
Faculty of Social and Behavioural Sciences
Data Theory Group
PO Box 9555
2300 RB Leiden
The Netherlands
Tel: [phone]
Fax: [phone]

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