psych (version 1.0-97)

mardia: Calculate univariate or multivariate (Mardia's test) skew and kurtosis for a vector, matrix, or data.frame

Description

Find the skew and kurtosis for each variable in a data.frame or matrix. Unlike skew and kurtosis in e1071, this calculates a different skew for each variable or column of a data.frame/matrix. mardia applies Mardia's tests for multivariate skew and kurtosis

Usage

skew(x, na.rm = TRUE)
kurtosi(x, na.rm = TRUE,type=1)
mardia(x,na.rm = TRUE,plot=TRUE)

Arguments

x

A data.frame or matrix

na.rm

how to treat missing data

type

type=1 gives an unbiased estimate of kurtosis, type 2 gives a biased estimate

plot

Plot the expected normal distribution values versus the Mahalanobis distance of the subjects.

Value

• skew
  if input is a matrix or data.frame, skew is a vector of skews
• kurtosi
  if input is a matrix or data.frame, kurtosi is a vector of kurtosi
• bp1
  Mardia's bp1 estimate of multivariate skew
• bp2
  Mardia's bp2 estimate of multivariate kurtosis
• skew
  Mardia's skew statistic
• small.skew
  Mardia's small sample skew statistic
• p.skew
  Probability of skew
• p.small
  Probability of small.skew
• kurtosis
  Mardia's multivariate kurtosis statistic
• p.kurtosis
  Probability of kurtosis statistic
• D
  Mahalanobis distance of cases from centroid

Details

given a matrix or data.frame x, find the skew or kurtosis for each column (for skew and kurtosis) or the multivariate skew and kurtosis in the case of mardia.

As of revision 1.0.93, kurtosi by default gives an unbiased estimate of the kurtosis (DeCarlo, 1997). Prior versions used a different equation which produced a biased estimate. (See the kurtosis function in the e1071 package for the distinction between these two formulae. The default, type 1 is what is called type 2 in e1071. The other is their type 3.) For comparison with previous releases, specifying type = 2 will give the old estimate.

References

L.DeCarlo. 1997) On the meaning and use of kurtosis, Psychological Methods, 2(3):292-307,

K.V. Mardia (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3):pp. 519-30, 1970.

See Also

describe, describe.by, mult.norm in QuantPsyc, Kurt in QuantPsyc

Examples

round(skew(attitude),2)
round(kurtosi(attitude),2)
mardia(attitude)
x <- matrix(rnorm(1000),ncol=10)
describe(x)
mardia(x)