[visionlist] analyzing medians

Andrew Leber andrew.leber at unh.edu
Wed Aug 4 17:48:24 GMT 2010

Hi Todd --  Taking the means of medians seems "perfectly okay."   
Consider that you're already using means of medians when reporting  
group-level data.  The reason you and your collaborator saw a subtle  
difference is probably because you don't have an equal number of  
trials per condition in the levels of variable D, thus over- 
representing some levels of D while under-representing others when  
computing a single median (vs. taking the mean of medians).

Andrew B. Leber, Ph.D.
Assistant Professor of Psychology
University of New Hampshire

On Aug 4, 2010, at 12:20 PM, 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
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