skewness: Test for Skewness
In SciencePo: Political Behaviour Analysis Tool

Description Usage Arguments Details Value Author(s) References See Also Examples

Three types to perform the skewness test, see details below.

1	skewness(x, na.rm = TRUE, type = 2)

`x`	A numeric vector containing the values whose skewness is to be computed.
`na.rm`	A logical value indicating whether NA values should be stripped before the computation proceeds.
`type`	An integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below.

The skewness is a measure of symmetry distribution. Intuitively, negative skewness (g_1 < 0) indicates that the mean of the data distribution is less than the median, and the data distribution is left-skewed. Positive skewness (g_1 > 0) indicates that the mean of the data values is larger than the median, and the data distribution is right-skewed. Values of g_1 near zero indicate a symmetric distribution. The skewness function will ignore missing values in ‘x’ for its computation purpose. There are several methods to compute skewness, Joanes and Gill (1998) discuss three of the most traditional methods. According to them, type 3 performs better in non-normal population distribution, whereas in normal-like population distribution type 2 fits better the data. Such difference between the two formulae tend to disappear in large samples.

Type 1: g_1 = m_3 / m_2^(3/2).

Type 2: G_1 = g_1 * sqrt(n(n-1)) / (n-2).

Type 3: b_1 = m_3 / s^3 = g_1 ((n-1)/n)^(3/2).

An object of the same type as x.

Daniel Marcelino

Joanes, D. N. and C. A. Gill. (1998) Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189. http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/abstract

detail.

skewness(c(100,200,300), type = 2)

skewness(c(100,200,300), type = 1)

skewness(c(100,200,300), type = 3)


w<-sample(4,10, TRUE)

x <- sample(10, 1000, replace=TRUE, prob=w)

skewness(x, type=2)

skewness(x, type=3)


detail(x)