PROPHET StatGuide: Examples of normal probability plots
 Suspected outlier(s):
For data sampled from a normal
distribution, the XY values in the normality plot
will lie along a hypothetical straight line passing through the
main body of
the XY values. If this is generally true, with
a few points lying off that hypothetical line, those points are likely
outliers, as
with the smallest data value and, perhaps, the largest two
data values in the hypothetical example shown here:

 Skewness to the right:
If both ends of the normality plot bend above
a hypothetical straight line passing through the main body of the
XY values of the probability plot, then
the population distribution
from which the data were sampled may be
skewed to the right.
Here is a hypothetical example of a normal probability plot for
data sampled from a distribution
that is skewed to the right:

 Skewness to the left:
If both ends of the normality plot bend below
a hypothetical straight line passing through the main body of the
XY values of the probability plot, then
the population distribution
from which the data were sampled may be
skewed to the left.
Here is a hypothetical example of a normal probability plot for
data sampled from a distribution
that is skewed to the left:

 Lighttailedness:
If the right (upper) end of the normality plot bends below a hypothetical straight line
passing through the
main body of the XY values of the probability plot,
while the left (lower) end bends above that line (an S curve),
then the population distribution
from which the data were sampled may be
lighttailed.
Here is a hypothetical example of a normal probability plot for
data sampled from a distribution
that is lighttailed:

 Heavytailedness:
If the right (upper) end of the normality plot bends above
a hypothetical straight line passing through the main body of the
XY values of the probability plot, while
the left (lower) end bends below it, then
the population distribution
from which the data were sampled may be
heavytailed.
Here is a hypothetical example of a normal probability plot for
data sampled from a distribution
that is heavytailed:

 Mixtures of normal distributions:
Data may be
sampled
from a mixture of
normal distributions.
Depending on the means and variances of the component normal
distributions, and on the relative proportions of the data
that come from each distribution, a mixture of normal distributions
may produce a variety of normal probability plots.
Here is a hypothetical example of a normal probability plot for
data sampled from a mixture of two normals with the
same mean but different variances:


Such a mixture of normal distributions may be hard to distinguish
from a symmetric, heavytailed
distribution.
Here is a hypothetical example of a normal probability for
data sampled from a mixture of two normals with the
same variance but different means:


Such a mixture of normal distributions may be hard to distinguish
from a lighttailed distribution.
 Truncated normal distributions:
The normal probability plot for data
sampled
from a truncated
normal distribution
will resemble one for data from a skewed
distribution.
Here is a hypothetical example of a normal probability for
data sampled from a normal distribution truncated
at the left:

This may be hard to distinguish from a normal probability plot for a distribution
skewed to the right.
Here is a hypothetical example of a normal probability plot for
data sampled from a normal distribution truncated
at the right:

This may be hard to distinguish from a normal probability plot for a distribution
skewed to the left.
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Last modified: February 20, 1997
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