#### Skewness, Kurtosis, & Kolmogorov-Smirnov

There are basically two ways that a distribution can be
distorted: skewness and kurtosis. Skewness refers to "top heavy" or "bottom
heavy"; (i.e., the tail of the curve). If the longest tail of the curve goes to
the right (the curve is top heavy), it is positively skewed. If it is bottom
heavy (the longest tail of the curve goes to the left), it is negatively skewed.
A value of zero for skewness represents a symmetrical distribution, such as the
normal distribution mentioned above.

Kurtosis refers to how peaked or flat the curve is. A very
flat curve is called "platykurtic" and has a kurtosis of less than three. A very peaked
curve is called "leptokurtic" and has a kurtosis greater than three. A value of
three for kurtosis indicates normal peakedness and the distribution is termed
"mesokurtic".

The Kolmogorov-Smirnov statistic provides a quick check to
determine the degree of normality in the data. The value provides a relative
indication of normality; as the value moves further away from zero, we can be
more certain that the data does not approximate a normal distribution. The distribution is non-normal:

at the .15 level if KS > .775

at the .10 level if KS > .819

at the .05 level if KS > .895

at the .025 level if KS > .955

at the .01 level if KS > 1.035