The Use and Misuse of the Coefficient of Variation

[Pages:10]The Use and Misuse of the Coefficient of Variation in Organizational Demography Research?

Jesper B. S?rensen

Sloan School of Management Massachusetts Institute of Technology

E52-581 50 Memorial Drive Cambridge, MA 02142 Email: sorensen@mit.edu Voice: (617) 253-7945 Fax: (617) 253-2660

Author Biographical Sketch Jesper B. S?rensen is Associate Professor of Strategic Management at the Sloan School of Management, Massachusetts Institute of Technology. His current research examines how the movement of individuals between organizations affects a variety of outcomes, including firm performance and patterns of entrepreneurship. Other research adopts a longitudinal perspective to understand the effects of organizational demography on individual and group outcomes. Recent publications include "Changes in Group Composition and Turnover: A Longitudinal Study" (American Sociological Review, 2000) and "Aging, Obsolescence and Organizational Innovation" (with Toby Stuart, Administrative Science Quarterly, 2000).

Abstract Demographic heterogeneity is a central theoretical construct in organizational demography research. The most commonly used measure of demographic heterogeneity is the coefficient of variation. I critically evaluate the rationale for using this measure and show that the use of the coefficient of variation raises a number of methodological and interpretive problems. Empirical analyses of turnover suggest that using the coefficient of variation may lead to incorrect conclusions about the effects of demographic heterogeneity.

In recent years, organizational sociology has witnessed a rapid growth in research in the field of organizational demography. Studies in this research tradition relate the demographic composition of groups and organizations to a variety of organizational outcomes. The organizational demography research program represents a promising and powerful structural approach to understanding organizational behavior (Pfeffer 1983). Its strongest appeal lies in being able to link individual and organizational attributes in a simple manner. Research in this tradition covers an impressively wide range of organizational outcomes, including turnover (e.g., O'Reilly, Caldwell and Barnett 1989; S?rensen 2000), social integration (e.g., Smith et al. 1994), firm performance (e.g., Pegels, Song and Yang 2000), strategic behavior (Hambrick, Cho and Chen 1996), and diversification (Wiersema and Bantel 1992).

Organizational demographers focus primarily on the consequences of demographic heterogeneity in groups. Depending on a researcher's substantive interests, such heterogeneity can occur along a number of social dimensions, including race, sex, education and organizational or group tenure. While there is some disagreement about the mechanisms linking group heterogeneity to group outcomes, the most commonly posited intervening construct is social integration (Carroll and Harrison 1998). Drawing on either the logic of social identity theory (Tajfel and Turner 1986) or the similarity/attraction paradigm (Berscheid and Walster 1978), organizational demographers expect that demographic heterogeneity lowers social integration and attachment in groups (Williams and O'Reilly 1998). This leads to the expectation, for example, that group heterogeneity will increase turnover rates (e.g., Wagner, Pfeffer and O'Reilly 1984).

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A large proportion of the organizational demography research conducted to date suffers from a methodological shortcoming. This weakness lies in the measurement of demographic heterogeneity (the central theoretical construct) with the coefficient of variation. As with other theoretical constructs, demographic heterogeneity can be measured in a wide variety of ways. Given its central theoretical role, it is important that organizational demographers take particular care in measuring group heterogeneity, so that the measurement strategy at a minimum does not lead to spurious conclusions. In this paper, I review and assess the adequacy of the coefficient of variation, the de facto standard among organizational demographers for measuring group heterogeneity. (The coefficient of variation is defined as the standard deviation of a variable divided by its mean.)

Organizational demographers use the coefficient of variation because they wish to standardize their heterogeneity measure to improve comparability across organizations. However, this standardization comes at a minimum price of interpretive ambiguity. In some cases, using the coefficient of variation may lead to incorrect conclusions about empirical phenomena. Moreover, this standardization is often unnecessary and can be achieved -- with less ambiguity -- through other means. As I will demonstrate, the coefficient of variation therefore should be used with care, if at all.

The coefficient of variation is widely used in organizational demography research. Its use can be traced back to some of the first empirical studies following Pfeffer's (1983) foundational article. Wagner, Pfeffer and O'Reilly (1984), for example, used the coefficient of variation (in addition to a Euclidean distance measure) in tenure to predict executive turnover among a sample of Fortune 500 firms. As an indication of how standardized this practice is,

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consider the subfield of organizational demography that focuses on the organizational consequences of heterogeneity in the tenure distribution. Carroll and Harrison (1998) review twenty-one such studies. Of these twenty-one studies, sixteen use the coefficient of variation in tenure as their measure of heterogeneity. The coefficient of variation is also commonly used in other areas of organizational demography research where demographic characteristics are measured using continuous variables (e.g., years of education). For example, Pelled, Eisenhardt and Xin (1999) examine how age diversity affects conflict using the coefficient of variation in age; Knight et al. (1999) investigate how the coefficient of variation on age, tenure and education affect strategic consensus in top management teams.

The remainder of this paper is organized as follows. I first discuss arguments in favor of the coefficient of variation as a measure of demographic dispersion, focusing on Allison's (1978) oft-cited article on measures of inequality and its relevance to organizational demography research. I then discuss a number of technical and substantive shortcomings associated with the coefficient of variation in the context of organizational demography. I conclude with an empirical example using data on turnover among television station managers in the United States.

The Case for the Coefficient of Variation Because organizational demographers are interested in how variation between group

members (along some demographic dimension) affects group outcomes, a natural measure of heterogeneity for continuous variables is the variance. For example, the heterogeneity of a group's tenure distribution can be measured by the variance about the mean level of tenure ?, or

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E(x-?)2. A characteristic of the variance (or equivalently the standard deviation) is that it is sensitive to the scale on which the variables are measured: if all values are multiplied by a constant c, the variance will increase by a factor of c as well. When making cross-unit comparisons, this scale dependence may -- if the differences in scale between units are not substantively meaningful -- lead to spurious differences in heterogeneity between units. One solution to this problem is to use the coefficient of variation, which is defined as the standard deviation divided by the mean. Since the scaling factor c would enter into both the numerator and the denominator, the coefficient of variation is scale insensitive.

For many organizational demographers, this scale invariance is the reason for preferring the coefficient of variation to the standard deviation as a measure of group heterogeneity. Although not all researchers explain their choice of the coefficient of variation (e.g., Smith et al. 1994; Harrison 1998; Pelled, Eisenhardt and Xin 1999), those who do point to this scale invariance as a desirable characteristic (e.g., O'Reilly, Caldwell and Barnett 1989: 25). Wiersema and Bantel (1993: 495), for example, use the coefficient of variation "because of its scale invariant properties, as compared to the standard deviation or variance."

However, organizational demographers rarely make clear why they desire a scaleinvariant measure. A clue may be found in the most common citation used to justify the use of the coefficient of variation: Paul Allison's 1978 article of measures of income inequality (a large share of the articles cited above cite Allison's article). Allison's article is a careful examination of the properties of a number of common measures of inequality, including the coefficient of variation, Theil's index and the Gini coefficient. Allison's principal concern is to compare different methods for assessing relative levels of social inequality (particularly income

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inequality) between social units. He presents three primary arguments in favor of using a scale invariant measure of inequality, such as the coefficient of variation. First, the measured level of inequality should not change in response to a change in the units of measurement. In the case of cross-national comparisons of income inequality, for example, the desirability of a scaleinvariant measure is clear: "inequality of income should not depend on whether income is measured in dollars or yen" (Allison 1978: 866). Second, scale-invariance is desirable if one wishes to compare inequality across different quantities, such as energy consumption and income, that are measured on different scales. Finally, Allison favors scale-invariant measures because the ones he considers generally "respond in an intuitively appealing manner when a positive constant is added to everyone's score; specifically, they decline." (Allison 1978: 867). For example, a standard deviation in income of $10,000 dollars indicates a high degree of inequality if the mean income is $20,000. However, if everyone's income is increased by $1 million, the standard deviation remains constant but one may wish to conclude that the level of inequality has declined.

Can we use the same reasons to justify a scale-invariant measure such as the coefficient of variation in organizational demography research? Consider each of Allison's reasons in turn:

Insensitivity to changes in units of measurement: This argument seems largely irrelevant to organizational demography research, since demographers usually compare distributions measured on the same scale. For example, organizations or groups are compared in terms of the tenure of their employees. In fact, unlike the currencies used in measuring income inequality, researchers typically set the measurement scale and can therefore avoid differences in scale across observation units. One might argue in response that the "social meaning" of tenure or

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