unless you had a table comparable to the z table for area under the normal
distribution ... for EACH different level of skewness ... an exact answer
is not possible in a way that would be explainable
here is one example that may help to give some approximate idea as to what
might happen though
.
.:::.
.:::::.
.:::::::.
.:::::::::.
.:::::::::::.
:::::::::::::::
. .....:::::::::::::::::::..... .
+---------+---------+---------+---------+---------+-------C1
the above is a norm. distribution of z scores ... where 1/2 the data are
above 0 and 1/2 are below
:
:.
.::.
::::.
:::::.
::::::::.
::::::::::::................. ... .
+---------+---------+---------+---------+---------+-------C2
-5.0 -2.5 0.0 2.5 5.0 7.5
here is a set of z score data that is radically + skewed ... and even
though it has 0 as its mean, 50% of the area is NOT above the mean of 0 ...
note the median is down at about -.3 ... so, there is LESS than 50% above
the mean of 0 ...
this means that for z scores above 0 ... there is not as much area beyond
(to the right) ... as you would expect if the distribution had been normal ...
so, we can have some approximate idea of what might happen but the exact
amount of this clearly depends on how much skew you have
MTB > desc c1 c2
Descriptive Statistics: C1, C2
Variable N Mean Median TrMean StDev SE Mean
C1 10000 0.0008 0.0185 0.0029 1.0008 0.0100
C2 10000 0.0000 -0.3098 -0.1117 1.0000 0.0100
Variable Minimum Maximum Q1 Q3
C1 -3.9468 3.9996 -0.6811 0.6754
C2 -0.9946 8.0984 -0.7127 0.3921
At 07:27 AM 1/30/02 -0800, Melady Preece wrote:
>A student wants to know how one can calculate the area under the curve for
>skewed distributions. Can someone give me an answer about when a
>distribution is too skewed to use the z table?
>
>Melady
_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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