skewness function

Calculate skewness

Skewness is a summary of the symmetry of a distribution's probability density function. In a Normal distribution, the skewness is 0, indicating symmetry about the expected value.

skewness(x, na.rm = TRUE, unbiased = TRUE)

Arguments

• x: A numeric variable (vector)
• na.rm: default TRUE. Should missing data be removed?
• unbiased: default TRUE. Should the denominator of the variance estimate be divided by N-1?

Returns

A scalar value or NA

Details

If na.rm = FALSE and there are missing values, the mean and variance are undefined and this function returns NA.

The skewness may be calculated with the small-sample bias-corrected estimate of the standard deviation. It appears somewhat controversial whether this is necessary, hence the argument unbiased is provided. Set unbiased = FALSE if it is desired to have the one recommended by NIST, for example. According to the US NIST, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm, skewness is defined as the mean of cubed deviations divided by the cube of the standard deviation.

mean((x - mean(x))^3) skewness = ___________________ sd(x)^3

where sd(x) is calculated with the denominator N, rather than N-1. This is the Fisher-Pearson coefficient of skewness, they claim. The unbiased variant uses the standard deviation divisor (N-1) to bias-correct the standard deviation.

Author(s)

Paul Johnson pauljohn@ku.edu