NORMALITY: Univariate and multivariate normality
In DFA.CANCOR: Linear Discriminant Function and Canonical Correlation Analysis

View source: R/NORMALITY.R

NORMALITY

R Documentation

Univariate and multivariate normality

Description

Produces tests of univariate and multivariate normality using the MVN package.

Usage

NORMALITY(data, groups, variables, verbose)

Arguments

`data`	A dataframe or numeric matrix where the rows are cases & the columns are the variables.
`groups`	(optional) The name of the groups variable in the dataframe, e.g., groups = 'Group'.
`variables`	(optional) The names of the continuous variables in the dataframe for the analyses, e.g., variables = c('varA', 'varB', 'varC').
`verbose`	Should detailed results be displayed in the console? The options are: TRUE (default) or FALSE.

Details

If "groups" is not specified, the analyses will be run on all of the variables in "data". If "variables" is specified, the analyses will be run on the "variables" in "data". If "groups" is specified, the analyses will be run for every value of "groups". If verbose = TRUE, the displayed output includes descriptive statistics and tests of univariate and multivariate normality.

Value

The returned output is a list with the following elements:

`descriptives`	descriptive statistics, including skewness and kurtosis
`univariate_tests`	the univariate normality tests
`multivariate_tests`	the multivariate normality tests

Author(s)

Brian P. O'Connor

References

Doornik, J. A. & Hansen, H. (2008). An Omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics 70, 927-939.

Henze, N., & Wagner, T. (1997), A new approach to the BHEP tests for multivariate normality. Journal of Multivariate Analysis, 62, 1-23.

Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (3rd. ed.). New Jersey, NJ: Prentice Hall.

Korkmaz, S., Goksuluk, D., Zararsiz, G. (2014). MVN: An R package for assessing multivariate normality. The R Journal, 6(2), 151-162.

Mardia, K. V. (1970), Measures of multivariate skewnees and kurtosis with applications. Biometrika, 57(3), 519-530.

Mardia, K. V. (1974), Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies. Sankhy A, 36, 115-128.

Royston, J. P. (1992). Approximating the Shapiro-Wilk W-Test for non-normality. Statistics and Computing, 2, 117-119.

Shapiro, S., & Wilk, M. (1965). An analysis of variance test for normality. Biometrika, 52, 591611.

Szekely,G. J., & Rizzo, M. L. (2017). The energy of data. Annual Review of Statistics and Its Application 4, 447-79.

Tabachnik, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). New York, NY: Pearson.

Examples

# data that simulate those from De Leo & Wulfert (2013)
NORMALITY(data = na.omit(data_CANCOR$DeLeo_2013[c(
          'Unprotected_Sex','Tobacco_Use','Alcohol_Use','Illicit_Drug_Use',
          'Gambling_Behavior','CIAS_Total','Impulsivity','Social_Interaction_Anxiety',
          'Depression','Social_Support','Intolerance_of_Deviance','Family_Morals',
          'Family_Conflict','Grade_Point_Average')]))


# data from Field et al. (2012)
NORMALITY(data = data_DFA$Field_2012, 
          groups = 'Group', 
          variables = c('Actions','Thoughts'))

# data from Tabachnik & Fidell (2013, p. 589)
NORMALITY(data = na.omit(data_CANCOR$TabFid_2019_small[c('TS','TC','BS','BC')]))

# UCLA dataset
UCLA_CCA_data <- read.csv("https://stats.idre.ucla.edu/stat/data/mmreg.csv")
colnames(UCLA_CCA_data) <- c("LocusControl", "SelfConcept", "Motivation",
                             "read", "write", "math", "science", "female")
summary(UCLA_CCA_data)
NORMALITY(data = na.omit(UCLA_CCA_data[c("LocusControl","SelfConcept","Motivation",
                                         "read","write","math","science")]))

DFA.CANCOR documentation built on June 8, 2025, 11:12 a.m.