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930813
review-article2020
JOMXXX10.1177/0149206320930813Journal of ManagementBuengeler et al. / LMX Differentiation: A Diversity Lens
Journal of Management
Vol. 47 No. 1, January 2021 260­–287
DOI: https://doi.org/10.1177/0149206320930813
10.1177/0149206320930813
© The Author(s) 2020
Article reuse guidelines:
sagepub.com/journals-permissions
LMX Differentiation and Group Outcomes:
A Framework and Review Drawing on Group
Diversity Insights
Claudia Buengeler
Kiel University and University of Amsterdam
Ronald F. Piccolo
University of Central Florida
Lauren R. Locklear
University of Central Florida
In this review, we address inconsistencies and a lack of clarity in the study of leader-member
exchange (LMX) differentiation and group outcomes. We do so by drawing on another highly visible group dispersion literature in the management domain, group diversity, based on the recognition that LMX quality is a characteristic on which group members vary. Utilizing insights from
Harrison and Klein’s typology of group diversity constructs, we introduce a framework that
specifies the meaning and shape of three variations of differentiated leader-member relationships
in groups and connects each construct with implications in terms of theorizing and measurement.
Specifically, our framework conceptualizes LMX differentiation as LMX separation (dispersion in
LMX relationships as disagreement or opposition regarding an opinion, perception, or position),
LMX variety (dispersion in LMX relationships as distinctiveness in kind, source, or category), and
LMX disparity (dispersion in LMX relationships as inequality in concentration of valued social
assets or resources). We then apply this framework to conduct a systematic review of the LMX
differentiation literature with particular attention to alignment among a study’s descriptions of the
construct, application of theory, expected group outcomes, and construct measurement. Finally,
we offer recommendations for future research and for applying our framework to enhance reliability, validity, and generalizability in studies of LMX differentiation and group outcomes.
Acknowledgment
We would like to thank Corine Boon and Nathan Podsakoff for their helpful comments on an earlier version of the
manuscript. We would also like to thank Christopher O.L.H. Porter and the two anonymous reviewers for the useful
and constructive feedback during the review process.
Supplemental material for this article is available with the manuscript on the JOM website.
Corresponding author: Claudia Buengeler, Kiel University, Institute of Business, Olshausenstrasse 40, 24098 Kiel,
Germany.
E-mail: [email protected]
260
Buengeler et al. / LMX Differentiation: A Diversity Lens   261
Keywords:
leadership; groups/group processes/dynamics; leader-member exchange; teams
An essential assertion in leader-member exchange (LMX) theory (Graen & Uhl-Bien,
1995) is that leaders differentiate among their followers (Yu, Matta, & Cornfield, 2018). For
many years, this phenomenon, known as LMX differentiation (LMXD) (Henderson, Liden,
Glibkowski, & Chaudhry, 2009; Liden, Erdogan, Wayne, & Sparrowe, 2006), was treated as
an inevitable reality of leadership in group settings (Dansereau, Graen, & Haga, 1975;
Erdogan & Bauer, 2010). Empirical examinations, however, have revealed inconsistent and
inconclusive results regarding LMXD’s effects on group outcomes.
Leaders who treat group members differently (i.e., high LMXD) can accommodate distinct
roles, needs, and preferences of followers, or their unique experiences, capabilities, and skills
(e.g., Henderson et al., 2009). Such intentional and strategic differentiation may enable group
members with high-quality relationships (the “in-group”) to optimize their contributions to
group functioning (see Vertical Dyad Linkage Theory [VDL], Dansereau et al., 1975; e.g., Yu
et al., 2018), as apparent in positive effects of LMXD on group outcomes (e.g., Lee & Chae,
2017; Sui, Wang, Kirkman, & Li, 2016). However, recent treatments of LMX at the group
level encourage leaders to maintain similarly positive relationships with all members (i.e., low
LMXD; e.g., newer formulations of LMX theory; Graen & Uhl-Bien, 1995), as LMXD may
incite competition (e.g., Hooper & Martin, 2008), encourage subgroups, compromise cohesion (e.g., Stewart & Johnson, 2009), and reduce fairness perceptions (Nishii & Mayer, 2009).
Recent reviews of the LMXD literature conclude that it is rife with contradictory predictions
and inconsistent results, as reasonable arguments and empirical evidence exist for both the benefits and pitfalls of LMXD in groups (Liden et al., 2006). Attempts to decipher LMXD effects
have included a focus on theoretical underpinnings (e.g., Anand, Vidyarthi, & Park, 2015; Matta
& Van Dyne, 2020), interactions with average levels of LMX (e.g., Martin, Thomas, Legood, &
Dello Russo, 2018), and various outcome categories (e.g., Yu et al., 2018). Though these summaries provide critical insights and constructive recommendations for future research, each has
relied on a traditional, albeit narrow, view of LMXD; one that invokes a simplistic definition of
LMX, focused only on overall relationship quality, and estimates LMXD in terms of degree
only. In our view, there are important implications of this narrow view.
First, most examinations of LMXD have focused only on the degree of variation of LMX
quality without consideration of the concept’s complexity. As Martin et al. (2018) suggested, there is a lack of precision in the definitions and measurements of LMXD. Indeed,
these have been insufficient in recognizing systematic variations of the concept, characterized by distinct shapes as well as nuanced meanings of LMXD in groups. For example,
when leaders differentiate among group members, the resulting shape may reflect two subgroups that are nearly equal in size but differ in terms of quality and intimacy (high vs. low),
one or very few members that are favored over the rest, or a spread of relationships informed
by the unique skills, capabilities, and contributions of group members. Simplistic treatment
of LMXD in groups has limited the concept’s explanatory power and generalizability.
Second, lack of precision may explain why so many different, and conflicting, theoretical
arguments have been invoked, often misaligned with the underlying construct. Researchers have
used a myriad of theories (e.g., equity, Adams, 1965; social identity, Tajfel & Turner, 1986; tournament, Lazear & Rosen, 1981; role system theory, Katz & Kahn, 1978; shared reality, Hardin
& Higgins, 1996) to explain the effects of LMXD on groups. Correspondence between construct
262   Journal of Management / January 2021
definition and theory has not always been clear, which is especially problematic as a construct’s
meaning depends on the theoretical framework in which it is embedded (Peter, 1981).
Finally, imprecise definitions and misalignment in theory application make measurement
choices subject to convention or chance. In general, studies of LMXD rely on a limited set of
perceptual measures of overall relationship quality (e.g., Graen & Uhl-Bien, 1995), aggregated to a conventional set of mathematically related statistical indices (e.g., standard deviation [SD], variance [Var]). Measurement choice is consequential given that different indices
can yield conflicting effects on common outcomes in the same study (Roberson, Sturman, &
Simons, 2007). Measurement choice in general, and in studies of group dispersion in particular, is essentially a choice among alternative definitions of a construct, “rather than a choice
among alternative ways of measuring a single theoretical construct” (Allison, 1978: 865).
To address these concerns, as called for in Martin et al.’s (2018) review, we bridge “traditional barriers” for advancing fields characterized by equivocal findings and a lack of clarity
(Short, 2009: 1312). We draw on insights from Harrison and Klein’s (2007) group diversity
typology, acknowledging that LMX is a characteristic on which group members differ and a
distributional property in groups that can “influence social interactions between members
[and] consequently group-level processes and outcomes” (Roberson, 2019: 71). These insights
include recognition that degree of dispersion alone is insufficient to validly predict the effects
of LMXD on group outcomes. As group dispersion comes in different forms (“types”), with
unique meanings and shapes as well as consequences for groups, predicting whether and why
effects will be positive or negative requires clarifying the type of dispersion first. These
insights allow us to systematically capture and discern, for the first time, the three characteristic types of LMXD (LMX separation, disparity, and variety) by their properly specified
shapes and meanings, theories, group outcome predictions, and measurements. These in turn
serve as a basis for assessing the LMXD literature against a well-established paradigm.
Our review contributes to the literature in three important ways. First, we characterize
LMXD in terms of separation, variety, or disparity within groups, consistent with insights
from Harrison and Klein’s (2007) influential group diversity typology, which then informs
theory application, outcome choice, and operationalization. As such, we are the first to offer
a guiding, prescriptive framework in which construct choice has clear and actionable implications for theorizing and operationalization. Second, we conduct a systematic review of the
literature on LMXD and group outcomes against the background of our framework, which
affords us the ability to make a more substantive, objective evaluation of the literature (e.g.,
the extent to which existing studies achieve alignment in essential study characteristics). We
discern patterns of alignment in the existing empirical literature, projecting misalignment as
one possible cause of inconsistent and inconclusive findings. Finally, we provide detailed
suggestions for representing the varied meanings and shapes of LMXD both conceptually
and methodologically and develop an agenda for further research. We anticipate that precision, consistency, and transparency in choices of study characteristics will yield more reliable, valid, and generalizable results.
Conceptual Building Blocks for Literature Review
LMX Theory
LMX, generally defined as overall relationship quality between a leader and follower, is the
core concept of LMX theory, a relationship-based approach to leader-follower interaction
Buengeler et al. / LMX Differentiation: A Diversity Lens   263
(Graen & Uhl-Bien, 1995; Uhl-Bien, 2006). The quality of one’s relationship with a leader
has meaningful task and social implications for the follower, including differences in status,
attention, autonomy, opportunity, or access to information (Liden et al., 2006). LMX theory
holds that leaders form distinct relationships with each of their followers (Graen & Uhl-Bien,
1995). Leaders might foster relationships characterized by trust, liking, respect, and social
exchange with some subordinates in their workgroups, while maintaining distant relationships with others, realized in transactional exchanges (Liden & Maslyn, 1998). Thus, LMXD,
generally defined as degree of within-group variability in LMX (e.g., Liden et al., 2006), is a
by-product of both leaders and followers choosing to invest in and form distinct relationships
with each other (Yu et al., 2018) and occurs in almost all groups (Erdogan & Bauer, 2010;
Liden & Graen, 1980). LMXD, unlike mean LMX (Anand et al., 2015), is not consistent in
predicting group process, emergent state, and effectiveness outcomes (LePine, Piccolo,
Jackson, Mathieu, & Saul, 2008; Mathieu, Tannenbaum, Donsbach, & Alliger, 2014), the
primary interest in this review.
Group Dispersion
Group composition models “specify the functional relationships among phenomena or constructs at different levels of analysis” (Chan, 1998: 234). Consistent with early characterizations of LMX distinctions in groups (Dansereau et al., 1975), and common definitions (e.g.,
Liden et al., 2006), LMXD, like group diversity, adheres to a dispersion model of group
composition (Chan, 1998). Differences in perceptions of LMX between group members are
used to operationalize LMXD at the group level. For an extended description of group composition models in conjunction with LMXD, see Martin et al. (2018).
An important commonality between group diversity and LMXD is that meaning is contained in the dispersion on the respective attribute of interest in a group. In both fields, there
is recognition that within-group differences in an attribute matter above and beyond its
individual-level (e.g., LMX; Hooper & Martin, 2008) or mean-level effect (e.g., LMX
mean; Yu et al., 2018). After decades of study plagued by a lack of concept clarity and
imprecise theorizing and measurement in the group diversity field (Roberson, 2019), similar to the problems of the LMXD literature, Harrison and Klein (2007) offered more precise
definitions, theories, and measurement of diversity, accelerating development of the group
diversity literature. Here we suggest that the specific group dispersion perspective offered
in Harrison and Klein’s group diversity typology serves as a useful starting point for examining LMXD.
Harrison and Klein’s (2007) Group Diversity Typology
Harrison and Klein (2007: 1200) defined group diversity as “the distribution of differences
among the members of a unit with respect to a common attribute.” Whereas early treatments
of group diversity focused on the attributes of difference (e.g., job-related, deep-level,
demographic; see Roberson, 2019), Harrison and Klein characterized group diversity in
terms of both (1) the attribute on which members in a group vary and (2) the shape or distribution of differences on the attribute in a group. Based on these dimensions, the authors
offered a typology, naming three distinguishable constructs: separation, variety, and disparity. Differences in perceptions, values, beliefs, or opinions reflect separation. Categorical
264   Journal of Management / January 2021
differences in knowledge, education, or competencies reflect variety, and differences in the
concentration of valuable social or task-related assets and resources, such as status, decision-making power, or access to task-related information, indicate disparity.
Explicit and critical discernment of separation, variety, and disparity has not been undertaken in the LMXD literature, though common descriptions of the concept make implicit
reference to these dispersion types. LMXD materializes in different shapes in groups (Martin
et al., 2018) resulting from the formation of LMX relationships with varying levels of intimacy and trust, informed by several distinct source attributes (Erdogan & Bauer, 2010),
which carry different meanings. Studies of LMXD have variously emphasized its distinct
aspects and implications. Some studies describe LMXD in terms of differences in overall
relationship quality and trust (i.e., separation; Guan et al., 2013); others emphasize differential status, autonomy, and access to task-relevant information (i.e., disparity; Boies & Howell,
2006); and some suggest that LMXD reflects members’ unique roles, contributions, capabilities, or knowledge (i.e., variety; Lee & Chae, 2017). Similar to Harrison and Klein (2007),
we characterize LMXD in terms of both source attribute (i.e., the meaning that LMX differences have in a group, referred to as “meaning”) and distribution shape (i.e., the pattern of
LMX differences in a group, referred to as “shape”), mindful of each construct’s role in
understanding LMXD’s impact on group outcomes.
Separation, variety, and disparity suggest fundamentally different interactions among
group members and rely on different theoretical explanations for effects on group outcomes.
Furthermore, each construct requires distinct measurement. Ideally, studies will precisely
characterize the anticipated meaning and shape of dispersion in groups (e.g., separation,
variety, or disparity), then align theories, expected outcomes, and measurements accordingly. In furtherance of that ideal, we use key insights from Harrison and Klein’s (2007)
group diversity typology to offer a guiding framework clarifying the three LMXD constructs (Table 1).
A Framework of LMX Differentiation Constructs
Separation, the composition of differences in “position or opinion among unit members,
primarily of value, belief, or attitude” (Harrison & Klein, 2007: 1203), captures dissimilarity
or disagreement among members in a group. When LMXD denotes separation (LMX separation), there is disagreement among group members, based on divergent perceptions, opinions, or beliefs with respect to LMX (Figure 1). Note that separation is consistent with a key
tenet of the original VDL (Dansereau et al., 1975) and LMX theories (Graen & Uhl-Bien,
1995)—namely, the separation of high- and low-LMX members into an in-group or outgroup. This meaning is reflected in separation’s shape. LMX separation is at its maximum
when there are two equally large subgroups at the two endpoints of the LMX continuum: one
group with high, the other with low LMX quality relationships. LMX separation is at its
minimum when all members share similar perceptions of LMX quality.
Variety, the composition of differences in “kind, source, or category of relevant knowledge or experience among unit members” (Harrison & Klein, 2007: 1203), stresses the
uniqueness of members. LMXD as variety (LMX variety) thus means distinctiveness of LMX
relationships, which reflect members’ unique knowledge, expertise, roles, capabilities, or
contributions. Maximum LMX variety is realized when all group members offer unique contributions as seen in distinct relationships with their leader. When all leader-member
Buengeler et al. / LMX Differentiation: A Diversity Lens   265
Table 1
Framework of LMX Differentiation Constructs, Theories, Predicted Group
Outcomes, and Measurements
Theoretical Rationale
Predicted Group Outcomeb
Measurement
LMX Separation: Dispersion in LMX relationships within a group as disagreement or opposition regarding
an opinion or position.
– Similarity-attractiona;
attraction, selection, and
attritiona
– Social identitya; social,
self-categorizationa
– Balance theory
– Shared reality
–
Morale, cohesiona (−)
Trusta (−)
Relationship conflicta (+)
Social and behavioral
integrationa (−)
– Withdrawala (+)
– Task performancea (−)
– Average deviation (AD)
– Standard deviation (SD)a; SDN;
variance (Var)
– Mean Euclidean distance (MED)a;
MEDN
– rWG(J); r*WG(J); aWG(J)
– Direct measure of LMX
separation
LMX Variety: Dispersion in LMX relationships within a group as distinctiveness in kind, source, or category.
– Information processinga
– Requisite varietya; variation,
selection, and retentiona
– Human and social capitala
– Role theory
– Role clarity/ambiguity
– Role system theory; role
differentiation
–
Coordination (+)
Task conflicta (+)
Creativity, innovationa (+)
Decision qualitya (+)
(Complex) task performancea
(+)
– Blau’s Indexa (Blau); BlauN;
Index of Quality Variation (IQV)a
– Teachman’s (Entropy) Index
(TI)a; TIN
– Direct measure of LMX variety
LMX Disparity: Dispersion in LMX relationships within a group as inequality in concentration of valued
social assets or resources.
–
Social stratificationa
Status and power hierarchya
Social comparison
Tournamenta
Distributive injustice and
inequitya; inequality; relative
deprivationa
– Group-value model of
procedural justice
– Justice climate (−)
– (Quality of) communicationa (−)
– Member inputa (−),
silencea (+)
– Within-group competition (+)
– Interpersonal undermininga (+)
– Resentful deviancea (+)
– Withdrawala (+)
– Coefficient of Variation (CV)a;
CVN
– Gini Coefficient (Gini)a; GiniN
– Social network centralization
– Direct measure of LMX disparity
a. Referred to in Harrison and Klein’s (2007) typology.
b. −/+ = negative/positive association of LMXD construct with predicted group outcome.
relationships are the same, not affected by member’ distinctive contributions to the group,
LMX variety is at its minimum.
Disparity denotes the composition of differences in “proportion of socially valued assets
or resources held among unit members” (Harrison & Klein, 2007: 1203), indicating that
these assets or resources are unequally distributed. LMXD as disparity (LMX disparity)
reflects inequality with respect to LMX, indicative of valued social assets or resources such
as status, attention from the leader, and access to opportunities. In highly disparate groups,
leaders invest in and form high LMX relationships with one or very few group members,
distancing themselves via low LMX with all others. This meaning is reflected in disparity’s
266   Journal of Management / January 2021
Figure 1
Pictorial Representations of the Three LMX Differentiation Constructs
Note:
= leader; = group member. Each figure illustrates the distribution of LMX relationships within groups
at maximum level of LMX separation, LMX variety, and LMX disparity, respectively. High (low) LMX indicates a
group member’s high- (low-)quality LMX relationship with the leader.
asymmetric shape: A large relative proportion of LMX quality is held by only one or very few
group members. Alternatively, when there is no LMX disparity, all group members share
equal LMX relationships with their leader.
Highlighting the various meanings and shapes of LMXD extends our understanding
beyond a simplistic estimate of the degree of dispersion in groups. Consider a group where
each member has formed a unique relationship with the leader based on his or her distinct
role or expertise. While this arrangement would indicate a maximum degree of LMX variety,
the same distribution would suggest a moderate degree of separation and disparity. Similarly,
a maximally disparate group, where only one member has high LMX, could suggest that
LMXD is relatively small if it were examined as separation or variety (Figure 1). Likewise,
a group with two equally large and maximally distant subgroups would suggest high LMX
separation yet only moderate LMXD variety or disparity. As such, LMXD’s degree is valid
only when it is clear which dispersion construct is invoked. In the following section, we
derive implications for the three LMXD constructs in terms of theory application, outcomes,
and measurement.
LMX Separation
Theories. Theories such as similarity-attraction, attraction-selection-attrition, social identity, social categorization, and self-categorization help to explain separation’s negative outcomes for groups (Harrison & Klein, 2007). According to a similarity-attraction perspective,
people prefer working with similar others (Byrne, 1971). Similar perceptions, beliefs, or positions regarding LMX among a group’s members may increase attraction and engender subgroups of similarly minded people. An attraction, selection, and attrition-perspective (ASA;
Schneider, Goldstein, & Smith, 1995) in groups holds that people are attracted to, selected
into, and remain in groups with people similar to themselves. Differing positions in terms
of LMX may decrease attraction and reduce the willingness to remain in the group. According to social categorization and social identity reasoning (Tajfel & Turner, 1986; Turner,
Hogg, Oakes, Reicher, & Wetherell, 1987), people group themselves and others according
to salient categories. Self-concept is partly derived from perceived membership in relevant
Buengeler et al. / LMX Differentiation: A Diversity Lens   267
social groups and their distinctiveness from out-groups. In groups with wide disagreement
regarding LMX, members are likely to categorize themselves and others with similar perceptions regarding LMX into a favored in-group while those with dissimilar perceptions are
categorized as out-group (and often discriminated against).
In addition, balance theory (Heider, 1958) and shared reality theory (Hardin & Higgins,
1996) offer valuable insights into LMX separation’s effects on groups. Balance theory suggests that members of groups need balanced relationships with one another to feel comfortable. When there is LMX separation in a group, the imbalance in LMX should negatively
impact group members’ attitudes and behaviors. Similarly, according to shared reality theory,
when a shared reality is achieved through the process of social verification, this fosters and
regulates social interaction. Subgrouping as apparent in LMX separation may thus impair
social interaction.
Group outcomes. Researchers draw on the outlined theories to argue that groups “whose
members differ markedly on a continuum will experience low cohesion, high conflict, high rates
of withdrawal, and poor performance” (Harrison & Klein, 2007: 1204). Given theoretical predictions of unfavorable social categorization, low attraction, and subgrouping, we thus expect
that LMX separation is negative for groups as apparent in dysfunctional emergent states (e.g.,
relationship conflict, low cohesion and trust), impaired group processes (e.g., low social and
behavioral integration), and low group effectiveness (e.g., withdrawal and low performance).
Measurement. Statistical dispersion indices, following a dispersion composition model
(Chan, 1998), such as SD, Var, Average Deviation (AD), or Mean Euclidean Distance, determine the extent to which there are symmetrical differences in a group (Harrison & Klein,
2007). Consistent with LMX separation, these indices reach their maximum values when
there is a bimodal distribution at or near the endpoints of a scale’s continuum (e.g., at low
and high LMX). In addition, statistical agreement indices such as rWG(j) are used to capture
separation in terms of a lack of consensus (direct-consensus group composition model; Chan,
1998). As r*WG(j) can become negative, it is better suited for assessing strong opposition
(LeBreton & Senter, 2008) consistent with LMX separation than rWG(j), whose lower bound
is constrained to 0 (disagreement), aside from inadmissible negative values. We provide formulas for these indices as well as a suitable alternative, aWG(j), in Table 2 and offer additional
considerations on index choice in Appendix S5 of the online supplement.
Alternatively, researchers may determine LMX separation by averaging group members’
direct assessment of LMXD in a referent-shift consensus model (Chan, 1998), using items
such as “Some members of our group have high-quality relationships with the leader, whereas
other members have low-quality relationships with the leader.” An LMX measure underlying
a separation index could assess broad beliefs, opinions, or perceptions of overall relationship
quality.
LMX Variety
Theories. Requisite variety (Ashby, 1956) and variation, selection, and retention theories
(e.g., Campbell, 1960) explain the importance of variety. Groups can use greater information richness for better choices, plans, or products (e.g., Harrison & Klein, 2007). From
an information-processing perspective (e.g., Hinsz, Tindale, & Vollrath, 1997), groups are
268
J
MED =
 S X2 
J 1 − 2 

σE 


rWG ( J ) =
2
 S X   S X2 
J 1 − 2  +  2 

σE   σE 

 

rWG(J)a
i
Mean Euclidean Distance
∑
aWG ( J ) =
aWG(J)a
S X2
j
J
j =1
σ2E
J
aWG ( j )
r *WG ( J ) = 1 −
j
N
j
j
N
j
i =1
r*WG(J)a
∑
j =1
∑ (X − X )
N
Σ( X i − X ) 2
N
N
σ2 =
Variance
Σ( X i − X ) 2
N
SD =
Standard Deviation
J
M ( j)
ADM ( J )
j =1
∑ AD
=
Formula
Average Deviationa
LMX Separation
Statistical Index
2
N
i =1
N
—
—
—
∑
Σ( X i − X ) 2
q
( X i − X j )2
N −1
N
j =1
N
Σ( X i − X ) 2
q
∑
MED =
σ2N =
SDN =
—
Available Correction for Varying Group Sizes
Table 2
Formulas of Statistical Indices to Assess LMX Differentiation Constructs
Interval
Interval
Interval
Interval
Interval
Interval
Interval
(continued)
Assumed Scale of Measurement
269
k
k
N
j =1
2
N
Xi − X j
i =1
n
X
*
X
i
∑
max ∑ C ( p ) − C ( p )
SDN
X
N
N
j =1
N
—
Interval
Ratio
Ratio
∑ C ( p ) − C ( p ) = the maximum possible sum
n
2 NX ( N − 1)
i =1
∑ ∑
Gini =
CVN =
Nominal
 N 
TI N = TI * 

 N −1 
Nominal
Nominal
Xi − X j
N i ( N i − 1)
∑ N ( N − 1)
Assumed Scale of Measurement
—
BlauN = 1 −
Available Correction for Varying Group Sizes
i =1
X
*
X
i
b Formula from Harrison & Klein, 2007. c Formula from Freeman, 1978.
of differences in point centrality for a graph of n points. Formulas from Biemann & Kearney, 2010 if not indicated otherwise. a Formula from LeBreton & Senter, 2008.
C X ( pi ) = any centrality score of point i. C X ( p* ) = largest value of C X ( pi ) for any point in the network. max
j
Note: AD can also be calculated around the median (ADMd). J = essentially parallel items. X = mean. N = group size. q = unbiased estimator of group size (see
Biemann & Kearney, 2010). Xi = value of subject i, Xj = value of subject j. S X2 = mean of the observed variances for j essentially parallel items. σ E2 = variance expected
when there is complete lack of agreement. i = number of categories. pi = proportion of category i in a group. Max = theoretical maximum. n = number of points.
CX =
i
2N X
n
C X ( p* ) − C X ( pi )

i =1 
i =1
Gini Coefficient
SD
X
i
∑ ∑
Gini =
Social Network Centralizationc
2
i
∑  p *ln ( p )
CV =
TI = −
i =1
Max
i =1
2
i
∑p
1− ∑ p
IQV =
Blau = 1 −
Formula
Coefficient of Variation
LMX Disparity
Teachman’s Index
Index of Quality Variationb
Blau’s Index
LMX Variety
Statistical Index
Table 2 (continued)
270   Journal of Management / January 2021
adaptive information processors in which distinct information, ideas, and cognitive processes
are shared to inform the decision-making process response. LMX variety emphasizes distinctiveness by the unique relationships formed along the members’ expertise, ideas, capabilities,
and cognitive processes, which may benefit the group’s information processing. A human
and social capital view (Adler & Kwon, 2002; Becker, 1964) also suggests that LMX variety
benefits groups. Unique relationships may help members to contribute to group performance
based on their unique knowledge, skills, and abilities (human capital) and their unique networks, relationships, values, shared norms, and identities (social capital).
In addition, theories related to role and resource allocations reflective of group members’
unique strengths, perspectives, and knowledge provide arguments for the advantages of
LMX variety. According to role theory (e.g., Biddle, 1979), individuals hold beliefs for themselves and others based on social position and perform patterned behaviors in line with these
roles. LMX variety may promote role-based behavior in groups because it clarifies rolebased distinctions among group members. In line with role clarity-ambiguity arguments
(e.g., Rizzo, House, & Lirtzman, 1970), the extent to which individuals have a clear understanding of tasks, duties, expectations, and goals related to their work roles matters for effective functioning. Role differentiation theory (e.g., Lewis, 1972) further suggests that an
individual’s role-related knowledge diminishes the likelihood that another role is adopted by
that same individual. Effective functioning of groups and organizations relies on the coordination and culmination of individual work roles (role system theory; Katz & Kahn, 1978).
Distinguishing members through LMX variety inhibits role ambiguity or overlap and encourages role coordination.
Group outcomes. Theories used to explain the positive effects of variety on groups tend
to focus on the availability of distinctive sources of information and their use (Harrison &
Klein, 2007). LMX variety is realized, in part, by a leader’s intentional effort to customize
investments and interactions with members based on their individual needs, motivations,
skills, contributions, and preferences. Accordingly, LMX variety is expected to benefit group
processes such as coordination, emergent states such as healthy task conflict, and group
effectiveness outcomes such as decision quality, creativity, and performance as it leverages
group members’ unique roles, contributions, and capabilities (e.g., Lee & Chae, 2017).
Measurement. Consistent with LMX variety, Teachman’s (1980) Index and Blau’s (1977)
Index capture the degree to which there are qualitative (categorical) differences in a group
(Harrison & Klein, 2007). They are highest when an equal number of members are in each
category (e.g., at each scale anchor of the LMX measure). For a description of using continuous measures in a categorical fashion, see Appendix S5 in the online supplement.
To assess LMX variety directly, items could estimate the extent t