[visionlist] analyzing medians

[Niko Troje]

Hi Todd,

The same happens if you run an ANOVA on d-prime values. The reason is 
that both d-primes and medians are non-linear measures of your raw data. 
The mean of the group means of factor A is the same as the mean of the 
group means of factor B, and both are the same as the overall mean of 
all your data. But of course that is not the case for medians, d-primes, 
and all sorts of other non-linear measures. I always felt uncomfortable 
about this when submitting d-prime values to ANOVA -- even though it 
seems to be common practice to do just that. But I have never seen a 
sound discussion of this issue. I am sure it exists somewhere and maybe 
someone can point it out to us.

Best,

Niko



Todd S. Horowitz wrote:
> I have a puzzle about analyzing RT data. I prefer to use medians 
> rather than means, because I am suspicious of all of the various data 
> trimming procedures. However, medians seem to be creating some 
> problems when I run ANOVAs on the data.
>
> I'm working with some data. Let's say there are 4 factors, A, B, C, 
> and D. However, the critical analyses collapse over the levels of 
> factor D. My collaborator sent me an analysis where she took the ABCD 
> medians, then collapsed by taking the means of those medians across 
> factor D, then running the ANOVA. I decided that was incorrect, and 
> directly computed the ABC medians from the raw data, then ran an 
> ANOVA. The results were subtly different, pushing the 3-way 
> interaction across the p = .05 line. However, it then ocurred to me 
> that the ANOVA does just the same thing as what my collaborator did: 
> the A main effect takes the means of the medians. If I were to 
> directly compute the A medians from the raw data, and run a one-way 
> ANOVA, I would probably get subtly different results from the ANOVA on 
> the ABC medians.
>
> So, what's the correct approach to this analysis? Do I give up and 
> work with means? Always recompute the medians from the raw data for 
> each effect separately? Or is it perfectly OK to just take the mean of 
> medians?
>
> thanks
> Todd
>
>
> Todd S. Horowitz, PhD
> Assistant Professor of Ophthalmology
> Harvard Medical School
> Associate Director
> Visual Attention Lab
> Brigham & Women's Hospital
> 64 Sidney Street, Suite 170 
> Cambridge, MA 02139
> phone:  (617) 768-8813
> fax:    (617) 768-8816
> _http://search.bwh.harvard.edu/_
>
>
> The information in this e-mail is intended only for the person to whom it is
> addressed. If you believe this e-mail was sent to you in error and the e-mail
> contains patient information, please contact the Partners Compliance HelpLine at
> http://www.partners.org/complianceline . If the e-mail was sent to you in error
> but does not contain patient information, please contact the sender and properly
> dispose of the e-mail.
>   
> ------------------------------------------------------------------------
>
> _______________________________________________
> visionlist mailing list
> visionlist at visionscience.com
> http://visionscience.com/mailman/listinfo/visionlist
>   

-- 
-----------------------------------------

Dr. Nikolaus Troje
Professor and Canada Research Chair
in Vision and Behavioural Sciences
Department of Psychology
and School of Computing
Queen's University
Kingston, Ontario, K7L 3N6, CANADA

phone: 613 533-6017
fax:   613 533-2499
email: troje at queensu.ca
www:   http://www.biomotionlab.ca

-----------------------------------------