Some Common Indices of Group Diversity: Upper Boundaries

Abstract

Workgroup diversity can be conceptualized as variety, separation, or disparity. Thus, the proper operationalization of diversity depends on how a diversity dimension has been defined. Analytically, the minimal diversity must be obtained when there are no differences on an attribute among the members of a group, however maximal diversity has a different shape for each conceptualization of diversity. Previous work on diversity indexes indicated maximum values for variety (e.g., Blau's index and Teachman's index), separation (e.g., standard deviation and mean Euclidean distance), and disparity (e.g., coefficient of variation and the Gini coefficient of concentration), although these maximum values are not valid for all group characteristics (i.e., group size and group size parity) and attribute scales (i.e., number of categories). We demonstrate analytically appropriate upper boundaries for conditional diversity determined by some specific group characteristics, avoiding the bias related to absolute diversity. This will allow applied researchers to make better interpretations regarding the relationship between group diversity and group outcomes.

Multiple diversity concepts and their ethical-epistemic implications

“…In addition, we distinguish concepts from measures of diversity, which we understand as mathematical formulas for quantifying the degree to which a group is diverse. Usually, the relationship between concepts and measures of diversity is one to many: for a given diversity concept, several measures may be reasonably taken to quantify it (McDonald and Dimmick 2003;Solanas et al 2012;Teachman 1980). Since concepts, as opposed to contexts, of diversity have not been clearly distinguished in philosophical literature on diversity among scientists, we review other literatures where they have been, namely, social science and ecology.…”

Does Gender Diversity in the Boardroom Influence Tobin’s Q of Croatian Listed Firms?

“…Diversity as variety conceptualizes categorical differences across the relevant characteristics between group members with variety being commonly measured by both Blau's index and the Shannon-Wiener entropy (Solanas, Selvan, Navarro and Leiva, 2012). Therefore, the authors applied this concept in order to measure diversity of the management and supervisory board.…”

Disparity in organizational research: How should we measure it?

“…Second, as is also shown in Table 1, the maximum disparity score occurs when one member has all the resources and all other members have nothing (Harrison & Klein, 2007;Solanas, Selvam, Navarro, & Leiva, 2012). CV, Gini, Theil, and RMD all meet this property, but SD does not.…”

“…Although CV, Gini, and Theil meet all of the properties of disparity, they all have some weaknesses. First, as is shown in Table 1, the maximum values of CV, Gini, and Theil are ffiffiffiffiffiffiffiffi n−1 p , 1 -1/n, and ln(n), respectively, which all are affected by the unit size (n) (Solanas et al, 2012). For example, for a three-person team, the maximum values of CV, Gini, and Theil are ffiffi ffi 2 p , 2/3, and ln(3), respectively.…”