m.euclidean.dist: Diversity as separation: mean Euclidean distance

In DLEIVA/diversity: Diversity indexes for organizational research

Description

This function computes mean Euclidean distance for quantifying diversity as separation.

Usage

  m.euclidean.dist(X, min, max, method = c("biemann", "harrison"))

Arguments

X	A numeric vector with group data.
min	The minimum value for the random variable.
max	The maximum value for the random variable.
method	String vector. 2 possible values: "biemann" and "harrison"

Details

Mean Euclidean distance (MED) is defined as the square root of the mean squared differences between the ith member and all others in the group. The minimum value is zero and the maximum value depends on the parity of the group size. m.euclideand.dist provides statistic value computed by means of the empirical data, theoretical maximum value and normalized value. In order to compute statistic, the function uses the formula provided by Harrison and Klein (2007):

	MED = {{∑\limits_{i = 1}^n {√ {∑\limits_{j = 1}^n {≤ft( {x_i - x_j } \right)^2 } /n} } } \over n} .

The function also includes the formula proposed by Biemann and Kearney (2010):

	MED = {{∑\limits_{i = 1}^n {∑\limits_{j = 1}^n {{{√ {≤ft( {x_i - x_j } \right)^2 } } \over {n - 1}}} } } \over n} .

Value

The function returns a list of class deviation with following components:

call	Function call.
method	Method used for computing MED.
data	Original data vector.
min	Minimum value for the random variable.
max	Maximum value for the random variable.
med	Mean Euclidean distance.
med.max	Maximum value of mean Euclidean distance.
med.norm	Normalized value of mean Euclidean distance.

Author(s)

Antonio Solanas, Rejina M. Selvam, Jose Navarro and David Leiva.

References

Biemann, T., & Kearney, E. (2010). Size does matter: How varying group sizes in a sample affect the most common measures of group diversity, Organizational Research Methods, 3, 582-599.

Harrison, D. A., & Klein, K. J. (2007). What's the difference? Diversity constructs as separation, variety, or disparity in organizations. Academy of Management Review, 32, 1199-1228.

Solanas, A., Selvam, R. M., Navarro, J., & Leiva, D. (2010). On the measurement of diversity in organizations. Unpublished manuscript.

Examples

g.3 <- c(1,1,9)
m.euclidean.dist(g.3,1,9,'b')
m.euclidean.dist(g.3,1,9,'h')

g.4 <- c(2,4,5,6)
m.euclidean.dist(g.4,1,9,'biem')
m.euclidean.dist(g.4,1,9,'har')

g.5 <- c(rep(1,2),rep(9,3))
m.euclidean.dist(g.5,1,9,method='biemann')
m.euclidean.dist(g.5,1,9,method='harrison')

g.10 <- c(rep(1,4),rep(9,5),2)
m.euclidean.dist(g.10,1,9,'biemann')
m.euclidean.dist(g.10,1,9,'harrison')

DLEIVA/diversity documentation built on May 10, 2019, 1:14 a.m.