[visionlist] analyzing medians

[Steve Luck]

Hi Todd.  The two ANOVA approaches you described are essentially testing slightly different null hypotheses (one regarding the median across conditions, the other regarding the mean of the medians of the conditions).  As Andy Leber pointed out, taking the mean of the medians has the advantage of weighting each condition equally, irrespective of the number of trials per condition, and that is typically what one wants to do.  In all other respects the two null hypotheses are nearly equivalent, so it doesn't really matter which you choose unless there are different numbers of trials per condition.  The two approaches may differ slightly in the computed p value, but this likely reflects noise rather than anything real.

Steve


On Aug 4, 2010, at 9:20 AM, 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
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