FAQ# 1577 Last Modified 21-February-2010
Skewness quantifies the asymmetry of a distribution of a set of values. GraphPad Prism can compute the skewness as part of the Column Statistics analysis.
How skewness is computed
Understanding how skewness is computed can help you understand what it means. These steps compute the skewness of a distribution of values:
How useful is it to assess skewness? Not very, I think. The numerical value of the skewness does not really answer any of these questions:
The skewness doesn't directly answer any of those questions. Note that the D' Agostino and Pearson omnibus normality test (a choice within Prism's column statistics analysis) is a normality test that combines the skewness with the kurtosis (a measure of how far the shape of the distribution deviates from the bell shape of a Gaussian distribution), and so tries to answer the first question.
The definition of the skewness is part of a mathematical progression. The standard deviation is computed by first summing the squares of he differences each value and the mean. The skewness is computed by first summing the cube of those distances. And the kurtosis is computed by first summing the fourth power of those distances.
While there are good reasons for computing the standard deviation by squaring the deviations, there doesn't appear to be a deeper meaning to summing the cube of the differences between each value and the mean. Since the skewness is computed based on cubes, a value that is twice as far from the mean as another value increases the skewness eight times as much as that other value (because 23=8). I don't see why alternative definitions of skewness where that factor is some other value (4, or 7 or 10 or any other value greater than 1) wouldn't be just as informative and useful.
Multiple definitions of skewness
Skewness has been defined in multiple ways. The method used by Prism (and described above) is the most common method. It is identical to the skew() function in Excel. This value of skewness is often abbreviated g1.
The confidence interval of skewness
Whenever a value is computed from a sample, it helps to compute a confidence interval. In most cases, the confidence interval is computed from a standard error. The standard error of skewness (SES) depends on sample size. Prism does not calculate it, but it can be computed easily by hand using this formula:
The margin of error equals 1.96 times that value, and the confidence interval for the skewness equals the computed skewness plus or minus the margin of error. This table gives the standard error and margin of error for various sample sizes.
|n||SE of skewness||Margin of error|