Re: Assessing credibility of a q-q plot by presence of outliers
- From: "Reef Fish" <large_nassua_grouper@xxxxxxxxx>
- Date: 27 Oct 2006 18:46:05 -0700
Aleik wrote:
What proportion of a data set should significantly betray a particular
distribution in order to reject the hypothesis that this is the correct
distribution (i.e. how many points in a data set of n=100, say, should
lie significantly away from the diagonal line in a q-q plot)?
By the very way you asked your question, I can tell you definitively
that's the WRONG question to ask!
The idea behind q-q plot is that you EYE can detect many
departures that are systematic, while the maximum departure is
small.
An example of that might be a q-q plot of 100 points in which
the first 30 are below the diagonal line, the next 40 are above,
and the next 40 are below again. Or the reverse.
That would be a very definite departure from the reference
distribution no matter how small the departures are.
Kolmogorov-Smirnov is a test-statistics that examines the
MAXIMUM departure and ignores the rest -- which is why it
is so ineffective.
In short there are so many SYSTEMATIC departures that are
readily seen by EYE that cannot be captured by an analytical
TEST STATISTIC that it remains the most effective way of
judging an empirical distribution and its agreement or
departure from a theoretical distribution.
I have a q-q plot that seems to have all the hallmarks of a correct
fit, but there are data points in upper quantiles that don't fit the
line. Are there any web references on this topic?
It's much more than a question of "fit". In fact the scale is not
uniform. Departure that looks larger at the upper (or lower)
quantiles may be just those quantile scales are distorted to
make the reference quantiles a diagonal straight line for
VISUAL comparison purposes because the human eye is
terribly ineffective in judging the departure of curvature from
one curve to another curve.
There may be web references that talks about how to EYE
such a plot as I describe here, but I don't know of any. Others
may.
Thanks for any help you can give.
Trust your own EYES.
That is why the visual test is sometimes referred to as the
"interocular traumatic test". suggested by Berkson
(see Edwards, Lindman & Savage,. 1963),
-- Reef Fish Bob.
.
- References:
- Prev by Date: kurtosis
- Next by Date: Re: Testing for normality
- Previous by thread: Assessing credibility of a q-q plot by presence of outliers
- Next by thread: kurtosis
- Index(es):
Relevant Pages
|
