[visionlist] analyzing medians

[William McIlhagga]

To: "Todd S. Horowitz" <toddh at search.bwh.harvard.edu>

There are a few things you might consider.

First, ANOVA tests (i.e. F tests) tend to be highly robust against
devaitions from normality, so it may be quite safe to feed RTs into
the ANOVA and not worry too much.

Second, there is some research on robust ANOVAs, but it doesn't seem
too well developed. One suggestion is to do a rank-transform on the
data and then do an ANOVA on the ranks. This would be fine I guess if
the ranks were more normal than the original data, but for RTs I don't
think that's the case.

Third, if one analysis gives a p value slightly less than 0.05, and
another gives a p value slightly more than 0.05, the analyses really
have reached the same conclusion, and you have been skewered by the
0.05 convention (but you knew that already). Journals should really
just ask for the p value, or the effect size with a CI.

I'd probably advise a bit of mild outlier elimination (say trim 5% off
the top and bottom) followed by a plain vanilla ANOVA. The loss of 10%
of the data is not a _big_ deal, but it does make subsequent
normal-assumption analyses more robust (and together with the inherent
robustness of ANOVA, things should be fine).

Hope that helps.


On 4 August 2010 17:20, Todd S. Horowitz <toddh at search.bwh.harvard.edu> 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/
>
>
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--
Dr. William McIlhagga
Bradford School of Optometry & Vision Science,
Bradford University
Great Horton Road
Bradford BD7 1DP
UK

Room G23, Richmond tel. (44) (1274) 235957



-- 
Dr. William McIlhagga
Bradford School of Optometry & Vision Science,
Bradford University
Great Horton Road
Bradford BD7 1DP
UK

Room G23, Richmond tel. (44) (1274) 235957