Re: MAD() on small data sets

[Søren Hauberg]

Hi and sorry about the late reply

tor, 01 04 2010 kl. 08:18 -0800, skrev CdeMills:
> For instance, consider the sequence [496 286 292]; the median is 292, the
> absolute differences are 
> [ 204 6 0]; std is 116 and median is 6. What I would achieve is to spot 496
> as suspicious and get as robust median of the sequence 289. An operator
> where this effect is milder is 
> tmp = abs(x-median(x))
> tmp=tmp(find(tmp)) % remove zero diffs
> mad = median(tmp)
> 
> This way, the result on the previous sequence is median([204 6])] whose
> result is 99, closer to 116, which permits to detect that one of the
> difference is much bigger than the other. 
> 
> Thus it make sense, from a statistical point of view, to remove points equal
> to the median from the sequence before estimating the mad ?

To be honest I do not follow your logic here. I don't see why 'mad'
should discard data; wouldn't that be against the standard definition of
the 'mad' operator?

Also, it is worth noticing that both Octave and Matlab gives the same
result (92) for your demonstration data.

Søren