Re: noob qns on empirical/chebyshev

On Wed, 15 Aug 2007 05:30:54 -0700, s99999999s2003@xxxxxxxxx wrote:

hi
i am a noob in stats so bear with me. for the empirical rule, its
approximated that 95% of observations will fall in plus/minus 2 * std
dev. In one of my investigation, let's say that i arrived at 98%,
which is higher that 95% for k=2, what does it imply about the data
set? should i use the chebyshev approximation instead? by the way,
some stats info: kurtosis and skewness are negative values.
For a second dataset scenario, for k=2,kurtosis=0.9, skew=1.2, i
arrive at 89%, which is less than 95%. what does it mean then? Can i
say that this dataset does not follow normal distribution? should i
use chebyshev inequality instead? thanks

The proportions of data within the +/- 2 s.d. range
is notoriously varying, especially for small samples,
and the count at one end can easily be stuck at zero
because of skewness. That is why 'normative samples'
are pretty poor for looking at extremes, unless the N is
hundreds or thousands.

If you want to *test* whether the distribution is
normal, use a test of normality -- not just *this* eye-balling.

Why do you care about the normality? Normality is
over-rated... are the units subjectively 'interval' to you?
Is there a natural basis for transformation, related to the
nature of the data?

On the other hand, skewness of 1.2 is enough that I would
ask whether transformations are reasonable, if I was headed
toward least-squares analyses.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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