HOMOGENEITY {DFA.CANCOR}

Homogeneity of variances and covariances

Description

Produces tests of the homogeneity of variances and covariances.

Usage

HOMOGENEITY(data, groups, variables, verbose)

Arguments

data

A dataframe where the rows are cases & the columns are the variables.

groups

(optional) The name of the groups variable in the dataframe (if there is one)
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.

Value

If "variables" is specified, the analyses will be run on the "variables" in "data". If verbose = TRUE, the displayed output includes descriptive statistics and tests of univariate and multivariate homogeneity.

Bartlett's test compares the variances of k samples. The data must be normally distributed.

The non-parametric Fligner-Killeen test also compares the variances of k samples and it is robust when there are departures from normality.

Box's M test is a multivariate statistical test of the equality of multiple variance-covariance matrices. The test is prone to errors when the sample sizes are small or when the data do not meet model assumptions, especially the assumption of multivariate normality. For large samples, Box's M test may be too strict, indicating heterogeneity when the covariance matrices are not very different.

The returned output is a list with elements

covmatrix

The variance-covariance matrix for each group

Bartlett

Bartlett test of homogeneity of variances (parametric)

Figner_Killeen

Figner-Killeen test of homogeneity of variances (non parametric)

PooledWithinCovarSPSS

the pooled within groups covariance matrix from SPSS

PooledWithinCorrelSPSS

the pooled within groups correlation matrix from SPSS

sscpWithin

the within sums of squares and cross-products matrix

sscpBetween

the between sums of squares and cross-products matrix

BoxLogdets

the log determinants for Box's test

BoxMtest

Box's' test of the equality of covariance matrices

Author(s)

Brian P. O'Connor

References

Box, G. E. P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36 (3-4), 317-346.

Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London Series A 160, 268-282.

Conover, W. J., Johnson, M. E., & Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23, 351-361.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques. Thousand Oaks, CA: SAGE.

Examples

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


# data from Sherry (2006)
HOMOGENEITY(data = data_DFA$Sherry_2006,
            groups = 'Group',
            variables = c('Neuroticism','Extroversion','Openness',
                          'Agreeableness','Conscientiousness'))