mardia {psych} | R Documentation |
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
skew(x, na.rm = TRUE) kurtosi(x, na.rm = TRUE,type=1) mardia(x,na.rm = TRUE,plot=TRUE)
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. |
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.
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 |
The mean function supplies means for the columns of a data.frame, but the overall mean for a matrix. Mean will throw a warning for non-numeric data, but colMeans stops with non-numeric data. Thus, the function uses either mean (for data frames) or colMeans (for matrices). This is true for skew and kurtosi as well.
William Revelle
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.
describe
, describe.by
, mult.norm in QuantPsyc, Kurt in QuantPsyc
round(skew(attitude),2) round(kurtosi(attitude),2) mardia(attitude) x <- matrix(rnorm(1000),ncol=10) describe(x) mardia(x)