Basic Analyses > DESCRIPTIVE Command

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