Donald Burrill wrote:
>
> On Tue, 28 Aug 2001, Dennis Roberts wrote in part:
>
> > however ... the "flagging" of "outliers" is totally arbitrary ... i
> > see no rationale for saying that if a data point is 1.5 IQRs away from
> > some point ... that there is something significant about that
>
> If the data are normally distributed (or even approximately so, what
> seems to be called "empirically distributed" these days), the 3rd
> quartile + 1.5 IQR locates a point 2.0 std. devs. above the mean;
> symmetrically, the 1st quartile minus 1.5 IQR gets you 2.0 SDs below the
> mean. Close enough to the central 95% of the distribution, for the
> precision of the "1.5".
Er, no.
Q1 ~ mu - 2/3 sigma
Q3 ~ mu + 2/3 sigma
1 IQR ~ 4/3 sigma
1.5 IQR ~ 2 sigma
inner fence ~ mu +- 2 2/3 sigma which is about the 0.5 percentile.
The inner fences are selected to give a false positive rate of about 1
in 1000.
I suppose that if we take into account the Unwritten Rule of Antique
Statistics that all data sets have 30 elements, this *does* give
a "p-value" of (1-e)*30*0.001 = 5% <grin>
-Robert Dawson
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