Voltolini wrote:
>
> Hi,
>
> My doubt is....an outlier can be a LOW data value in the sample (and not
> just the highest) ?
>
> Several text boks dont make this clear !!!
What makes an outlier "an outlier" is your model. If your model accounts
for all the observations, you can't really call any of them an outlier.
If your model adequately accounts for all but one or two unusual
observations, you might regard them as coming from some process other
than that which generated the data you model accounts for, and call them
outliers.
Such "not adequately accounted for" observations may be low
observations, or high
observations, or they may actually turn out be somewhere in the middle
of the range of your data - as I have seen with time series for example,
where in some applications an autoregressive models was a very good
desctiption of a long series, apart from a few outliers in the first
quarter or so of the time period (which did in the end turn out to have
come from a different process, because the protocol wasn't always being
properly followed early on). Two of those "outliers" - in the sense that
the model didn't adequately account for them - turn out to be neither
particularly high or low observations - but they were substantially
higher or lower than expected from the model.
Another case where you might have "outliers" in the middle of your data
is in a regression context, where a generally increasing relationship
shows a tight, gaussian-looking random scatter about the relationship,
but with a couple of relatively low y-values at some of the higher
x-values. The observations themselves may actually be very close to the
mean of the y's, but the model of the relationship makes them "unusual".
A different model - for example, one where the observations come from a
distribution which has the same expectation as a function of x, but
which has a heavier tail to the left around that - might account for all
the data and not find any outliers.
Glen
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