Running Head: EVEN- AND ODD-SIZED GROUPS
Getting Even vs. Being the Odd One Out:
Conflict and Cohesion in Even- and Odd-Sized Groups
Tanya Menon
And
Kath Philips
Electronic copy available at: http://ssrn.com/abstract=1298497
Even- and odd-sized groups
Abstract
Contrary to people’s intuitive theories about even and odd numbers and groups, this paper argues
that odd-sized groups are often more harmonious than even-sized groups. Study 1 found that
people view even numbers more favorably than odd numbers and predict that even-sized groups
are more peaceful than odd-sized groups. However, Study 2 found that three- and four-person
groups without conflict did not differ, but three-person groups with coalitions (two vs. one)
produced more positive relationships than four-person groups with coalitions (both two vs. two and
three vs. one). Finally, Study 3 involved a natural experiment at Harvard University, and found that
White freshmen assigned to odd-sized rooming groups (three or five persons) maintained
relationships with White roommates more than did White freshman assigned to even-sized rooming
groups (four or six persons), but these patterns did not emerge when Whites roomed with Asians
and Blacks. We suggest that a group’s even or odd size is an important situational variable that
affects its coalitional structure, conflict management, and cohesion.
Electronic copy available at: http://ssrn.com/abstract=1298497
1
Even- and odd-sized groups
Everyone knows that two heads are better than one. We also know that two’s company and
three’s a crowd. We try our best to remain “even keeled” when we are “at odds” with someone.
We seek friends and lovers with whom we are “two peas in a pod,” and we laugh at the “odd
couples” we encounter.
Although even and odd are simply mathematical concepts, these common idioms reveal
that even numbers carry positive connotations and odd numbers carry negative connotations
(Hines, 1990; Nishiyama, 2006). Their very definitions reflect these undertones: The word even is
synonymous with “balanced, stable, placid, and calm” (even, n.d.), whereas the word odd means
“awkward, irregular, peculiar, strange, bizarre, eccentric, and incomplete” (odd, n.d.). Given that
people associate even numbers with harmony and odd numbers with conflict, it seems intuitive that
social interactions that involve even- or odd-sized groups should reflect these patterns too, and that
even-sized groups should experience more harmony than odd-sized groups.
In contrast to conventional wisdom that two’s company and three’s a crowd, this paper
argues that very often, three’s company, and four’s a crowd. We explore how even- and odd-sized
small groups differ and propose that odd-sized groups are often more harmonious than even-sized
groups. Our key premise is that even or odd size often affects (a) whether a small group can
harness majority influence and (b) how it chooses to use that power. Specifically, odd-sized groups
often fracture into a majority and a minority, which enables the majority to influence dissenters
(Asch, 1951; Cialdini, 2001; Hastie & Kameda, 2005; Wittenbaum, Merry, & Stasser, 1996). By
contrast, even-sized groups experience tension because they often divide along balanced lines (e.g.,
two versus two in four-person groups; Murnighan, 1978; Shears, 1967), which prevents them from
applying majority influence to resolve conflicts (Frank & Anderson, 1971). Majority influence
should enable odd-sized groups to cohere more than even-sized groups. We suggest that this is
especially true when group members are socially or demographically homogeneous, because
people tend to conform within homogenous (versus diverse) groups (Abrams, Wetherell, Cochrane,
Hogg, & Turner, 1990; Phillips & Loyd, 2006).
Second, we posit that coalitional structure shapes how groups use majority influence.
Specifically, majorities within odd and even groups may differ in how they apply their influence.
Unlike even groups, in odd-sized groups, a single-person can determine the majority (e.g. two
people versus one or three people versus two). When a single individual’s opinion can change the
group’s balance, the majority must use influence subtly. However, when the majority possesses a
more comfortable margin (e.g. three versus one or four versus two in even groups), they silence
dissenters more aggressively.
Electronic copy available at: http://ssrn.com/abstract=1298497
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Even- and odd-sized groups
Even and Odd: Intuitive Predictions Versus Real Interaction
Intuitive theories about even and odd numbers and groups are important because they can
affect how people form groups and how they interact within them. Next, we examine people’s
actual behavior within even- and odd-sized groups, and propose that these experiences diverge
from people’s predictions.
Intuitive Theories about Even and Odd
Intuitive theories about even- and odd-sized groups perhaps derive from preferences for
and greater perceptual fluency with even rather than odd numbers (Hines, 1990). In English, the
word even is a linguistically “unmarked” adjective, i.e., it is the default. Thus, people use it more
frequently than the word odd (100 per million to 38 per million; Greenberg, 1966; Thorndike &
Lorge, as cited in Hines, 1990). Further, negative prefixes attach to the word even (e.g. uneven) but
not the word odd (unodd does not make sense; Hines, 1990; Zimmer, 1964). In addition to greater
linguistic and cognitive accessibility of even numbers, at least in the West, people may view even
numbers more favorably than odd numbers because they convey symmetry and balance
(Nishiyama, 2006).1
Both academic and lay theories associate balance with positive social relationships. Just as
early political theorists equated the “balance of power” with stability in foreign policy (Hume,
1752/1985), American government employs “checks and balances” to prevent a tyrannical autocrat
from dominating the system (Montesquieu, 1748/1949). Likewise, ordinary people often seek
intrapersonal balance (i.e., consistent cognitions without dissonance; Festinger, 1957) and
interpersonal balance (Heider, 1958) and symmetry (i.e., having congruent social relationships;
Newcomb, 1953). Given a linguistic and cultural heritage that treats evenness preferentially, an
intellectual heritage that equates balance with stability and peace, and innate psychological
preferences for balanced cognitions and relationships, we hypothesize that Americans will view
even numbers more favorably than odd numbers, and that they will expect even-sized groups to
exhibit more positive dynamics than odd-sized groups.
Relationships in Even- and Odd-Sized Groups
People might predict that even-sized groups experience more positive relationships than
odd-sized groups, but are these expectations accurate? To answer this question, we draw from
classic social psychological research, which has frequently examined group size (Cummings,
Huber, & Arendt, 1974). Although group size is “perhaps the least ambiguous and most precisely
measurable characteristic of small groups” (O’Dell, 1968: p. 75), critics have characterized group
size research as unsystematic (Hackman & Vidmar, 1970; Thomas & Fink, 1963) and yielding
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Even- and odd-sized groups
little consensus (Frank & Anderson, 1971, p. 135). For instance, whereas some researchers
celebrated six-person groups because they fostered good communication (Ziller, 1957), inspired
solidarity (Bales & Borgatta, 1955), and promoted effective leadership (Bass & Norton, 1951);
others noted that five-person groups were neither too small nor too large (Slater, 1958), and that
four- and five-person groups experienced high member satisfaction (Hackman & Vidmar, 1970).
On the other hand, researchers found that dyads were tense (Bales & Borgatta, 1955; Hackman &
Vidmar, 1970; O’Dell, 1968), and that four-person groups experienced conflict (Bales & Borgatta,
1955).
In the hundreds of group size studies, although we did not locate a single study that
featured the even/odd effect as the focal topic, a few investigators noticed that even- and odd-sized
groups differed. For instance, Frank and Anderson (1971) found that people in odd-sized groups
(three or five persons) considered their interactions more “warm, pleasant, cooperative, and not
serious…and less antagonistic” (p. 147) than those within even-sized groups (two or eight
members). They argued that odd groups resolve conflict because they split into a majority and
minority, whereas even groups stalemate. Similarly, Bales and Borgatta’s (1955) study of two- to
seven-person groups suggested that odd-sized groups function more smoothly, although their
sample only contained four groups of each size, and their design involved various confounds and
statistical errors (see O’Dell, 1968, for a critique). Finally, Maier (1972) found, contrary to his
initial predictions, that triads were more harmonious than four-person groups. These studies offered
tantalizing evidence that even- and odd-sized groups might differ.
Despite this initial interest in group size, current research shows little interest in the topic.
Indeed, group size is so irrelevant that various paradigms exclusively employ a single group size
(often three-person groups) for methodological convenience (see Murnighan, 1978 and Phillips,
Mannix, Neale, & Gruenfeld, 2004 for a discussion). When we surveyed dissertations over the past
20 years, we found only one small-groups dissertation that featured the term group size in its title.2
One reason that group size research has declined is that, as in much small-groups research,
empirical results have outpaced theory-building (Levine & Moreland, 1998). For instance, because
prior researchers noted even/odd differences tangentially, they posited a mechanism on a post hoc
basis (majority influence), and did not examine it in depth. The current paper further examines the
questions of who is subject to majority influence, how it is exercised, and how coalitional structure
shapes its usage.
Stability from Imbalance in Dyads and Triads
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Even- and odd-sized groups
George Simmel’s comparisons between dyads and triads revealed theoretical processes that
could account for the fundamental instability of even-sized groups. Individuals in a dyad are:
Confronted only by one another and not by a collectivity…[The triad is] the simplest
structure in which the group as a whole can achieve domination over its component
members; …the triad can impose its will upon one member through the formation of a
coalition between the two others. It is a distinct sociological entity (Coser, 1971: p. 186-187).
Thus, although social psychology often maligns the majority tendency to dominate minorities
(Asch, 1951; see Peterson & Nemeth, 1996 for an exception), one potentially beneficial
consequence is that majority influence enables groups to resolve disputes and achieve coherence.
In addition to majority influence, mediation is another mechanism that enables a triad to
cohere even if two parties clash (Belliveau & Stolte, 1977; Burt, 1992; Carnevale & Pruitt, 1992;
Conlon, Carnevale, & Murnighan, 1994). While a dyad disintegrates if one person leaves it, a
mediator, as Simmel (1950) noted, produces “psychological unity which resides in group life… he
can carry and direct the very movement of the whole group if the antagonism of the other two tends
to paralyze their forces” (p.152).3 Through majority influence and mediation, imbalance moves
triads forward, whereas balance paralyzes dyads.
Beyond the Triad: Odd versus Even Groups
This research moves from dyads and triads to even- and odd-sized groups more generally,
and hypothesizes that whereas balance destabilizes even-sized groups, majority influence stabilizes
odd-sized groups and encourages them to cohere. Moreover, majorities within odd-sized groups
enact their power in a more benign and tolerant way. Odd groups often contain narrow majorities
(e.g., two versus one or three versus two) which imply that coalitions can be fluid. If a single
individual changes allegiances, the majority can easily become the minority. Given their tenuous
status, majorities must be sensitive to the minority’s interests and opinions. Because the majority
in odd-sized groups gives more consideration to minority viewpoints, we hypothesize that this
increases cohesiveness.
Overview
To test the hypothesis that odd-sized groups possess several features that create greater
stability and cohesion than even-sized groups, we designed three studies that involved multiple
methods (survey, laboratory experiment, and natural experiment); groups in various contexts
(MBA and undergraduate discussion groups, undergraduate roommates); and different tasks (short
term discussion groups, long term living arrangements over a year).
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Even- and odd-sized groups
Studies 2 and 3 moved from people’s predictions about groups to their actual experiences in
groups. Study 2 compared three- and four-person groups and manipulated their coalition structure.
We did not expect differences to emerge between 3- and 4- person groups when no one disagreed.
However, we predicted that the coalitions within four- person groups would impair cohesion more
than those within three-person groups. Balanced 2-2 coalitions would lack access to a simple
conflict resolution strategy (majority influence). Additionally, odd-sized groups enable narrow
majorities (two versus one, three versus two) which encourages the majority to influence without
dominating minorities (as in 3-1 groups).
Finally, Study 3 considered a natural experiment at Harvard University, where the
administration assigns first-year students to rooming groups of one to six persons. We examined
how initial freshman group size affected a pair’s likelihood of staying together in their second year.
We predicted that Whites assigned to odd-sized rooming groups (three or five persons) would
maintain their relationships with their White roommates more than Whites assigned to even-sized
rooming groups (four or six persons). Additionally, we predicted that these patterns would be
mitigated among diverse pairs (Whites with Asian and Black roommates) because majority
influence declines in diverse versus than homogeneous settings (Abrams, Wetherell, Cochrane,
Hogg, & Turner, 1990; Phillips & Loyd, 2006).
Key Research Assumptions
We next identify our key assumptions. In addition to revealing crucial moderators, the
conditions described here highlight the challenges of developing a general even/odd theory.
Small Groups. Given that small and large groups differ in their structure and behavior
(Levine & Moreland, 1998; Simmel, 1950), this research focuses on small groups only. For
instance, a majority’s presence can be less salient in a large group (e.g. 25 vs. 26 people), and more
complex coalitions can emerge, which might mitigate odd-even effects.
Equal Status. We assumed that group members have roughly equal status. If certain people
hold leadership positions, veto power (Murnighan & Roth, 1980; Murnighan & Szwajkowski ,
1979), or status based on expertise, personality, tenure, or attractiveness (Ridgeway, 1991), they
exert disproportionate influence on group decision making (Thomas-Hunt & Phillips, 2003), and
can impose conformity without majority influence, so that odd-even size becomes less relevant.
Issue Structure. Just as political systems often fracture into two parties (Duverger, 1972),
people in small groups also often split into two camps. When issues are dichotomous, odd-sized
groups always fracture into a majority and minority. When issues are multi-sided, even/odd
dynamics are more complex than the processes we have considered here. Similarly, some groups
6
Even- and odd-sized groups
use decision making rules other than a majority rule (e.g. a 2/3 approval). These variations in issue
structure and decision making procedure may shift the relevant fault lines (Lau & Murnighan,
2005), such that even/odd size ceases to tap pivotal dynamics.
Function. Although we examined groups in various settings (freshman roommates, decision
making groups), we did not directly examine whether group function moderates odd-even effects.
Given that people may hold different expectations about conformity and conflict in social- and
task-focused groups, even/odd effects might vary based on group purpose.
Study 1. Intuitive Theories About Odd and Even Numbers
We first examined people’s intuitive theories about even and odd numbers and groups. We
predicted that people view even numbers more favorably than odd ones, and further, extend these
impressions to groups.
Method
Participants
We surveyed 34 American students from the University of Chicago (55.8% male, 39.5%
female, and 2 participants failed to report their gender). Their average age was 20.74 years.
Procedure
Participants viewed even and odd number sequences and rated their first impressions using
a 7-point scale (1 = negative, 4 = neutral, 7 = positive). We counterbalanced these sequences such
that some participants saw the odd sequence first and others saw the even sequence first. The
instructions and number sequences were as follows:
Please list your first impressions about this sequence of numbers:
2
4
6
8
10
12
14
16
Please list your first impressions about this sequence of numbers:
3
5
7
9
11
13
15
17
Next, participants read the following vignette:
At work, you are assembling a committee to make an important forecast about the
company’s strategic position. Obviously, the committee can either be composed of an even
(4, 6, 8) or odd (3, 5, 7) number of individuals. We’d like to ask you a few questions about
your predictions about being in a group with an even or odd number of people.
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Even- and odd-sized groups
We asked participants whether they believed that even- and odd-sized groups function a)
similarly or b) differently (they circled either a or b). They then read a list of group characteristics:
peaceful, argumentative, experience positive relationships, resolve conflict productively, develop
coalitions, result in exclusion, and use the majority rule to resolve conflicts. Finally, we asked
whether they preferred to participate within even-sized or odd-sized groups. They circled either the
word even or the word odd to indicate their choices.
Results
Participants preferred even numbers (M = 4.85, SD = .99) to odd numbers (M = 3.97, SD =
1.14), F(1, 32) = 7.30, p = .01. People’s preferences for even numbers extended to even-sized
groups. Among the participants, 85.3% expected even- and odd-sized groups to function
differently, t(33) = -5.73, p < .01. Specifically, 73.5% assumed that even-sized groups had more
positive relationships, t(33) = 3.06, p < .01, and 67.6% assumed that they were more peaceful, t(67)
= 2.17, p < .05. On the other hand, 67.6% expected odd-sized groups to experience more conflict,
t(33) = -2.17, p < .05; 76.5% assumed that they involved more exclusion, t(33) = -3.56, p < .01;
and 88.2% assumed that they used the majority rule more, t(33) = -6.82, p < .01. With regard to
coalitions, 73.5% expected that coalitions were more prevalent within even-sized groups, t(33) =
3.06, p < .01. People preferred to participate within even-sized and odd-sized groups equally
(55.9% preferred odd-sized groups), t(33) = -.68, p = .23.
Discussion
Study 1 assessed people’s intuitive theories about even and odd numbers. As predicted,
people favored even sequences over odd sequences. Further, people assumed that even-sized
groups were more peaceful and positive and experienced less conflict and exclusion than odd-sized
groups. On the other hand, people preferred even- and odd-sized groups equally, perhaps because
of the group’s tasks (i.e., it was a decision making group in which quick, efficient decisions would
be favorable).
These intuitive preferences for even groups may arise from culturally-derived positive
associations with evenness, rather than from their analysis of social relationships. In the next
study, we examine how people actually experience social relationships within odd and even groups.
Study 2: Manipulating Coalitions in Three- and Four-Person Groups
To simplify the empirical context, Study 2 examines only three- and four-person groups.
We seek to directly test the conflict resolution mechanisms that people within even and odd-sized
groups use. First, we expect no differences between three- and four-person groups when they
8
Even- and odd-sized groups
experience no conflict, and thus suggest that even/odd effects derive, not from group size per se,
but from coalitional structure and conflict resolution processes.
Additionally, this study compares unbalanced three-person coalitions (two versus one) with
both balanced (two versus two) and unbalanced (three versus one) four-person coalitions. We argue
that regardless of whether four-person groups experience a balanced or unbalanced distribution of
opinions, they are likely to experience the group as more conflict-ridden and less cohesive than
three-person groups. When even groups split into balanced forces, they face unresolvable conflict
and instability. Furthermore, we predicted that moderately unbalanced groups (two vs one) would
use subtle social pressure and that extremely unbalanced groups (three vs one) would aggressively
silence dissenters.
We experimentally manipulated the group’s coalitional structure based on participants’
initial opinions about a discussion topic. Thus, we created five conditions: (a) three-person group,
members all agree; (b) three-person group, two people agree and one disagrees; (c) four-person
group, members all agree; (d) four-person group, three people agree and one disagrees; and (e)
four-person group, two agree and two disagree. In sum, our theory relies on coalitional structure, so
we did not expect three- and four-person groups to differ when all members agreed. We
hypothesized that three-person groups (two vs. one coalitions) would evoke more positive
relationships than four-person groups both when four-person groups were balanced (two vs. two)
and when they were extremely unbalanced (three vs. one).
Method
Participants
The participants included 189 students from Northwestern University (50% male). Of
these, 94 were MBA students who participated in a class exercise, and 95 were undergraduates who
participated in the lab and were paid $10. We excluded 14 MBA student participants because they
failed to complete the pretest or because of experimenter error in creating group assignments. We
pooled these data because participants in the groups did not vary.
Procedure
All participants read the Carter Racing case (Brittain & Sitkin, 1988), in which they
assumed the role of an automobile racing team deciding whether to race (and potentially win a
large endorsement) or not race (because of the risk of a potentially disastrous engine failure).
Although participants tend to select the risky option (racing), the correct choice, based on the data,
is to not race. (Indeed, the failure rates come from the data that NASA scientists viewed before
they decided to launch the doomed Challenger space shuttle.) Participants made a race/no race
9
Even- and odd-sized groups
decision and then answered a brief pretest which assessed their confidence about their decision
using the following questions:
How confident are you about your decision to race or not to race? This question was scaled
from 0 percent to 100 percent in 10 percentage increments (0=0% not at all confident, 11=100%
completely confident)
Assume you have $250 at your disposal, how much of it would you be willing to bet that
you have made the right decision? This question response was scaled from $0 to $250 in $25
increments (0= $0, 11=$250)
Do you expect the other members of the class to agree with your decision? (1= not at all to
7=very much)
Do you feel you have all the information you need to make this decision? (1=not at all,
7=very much)
Next, we randomly assigned participants into three- and four-person groups that varied in their
coalition structure. As mentioned before, our design contained five alternative coalitional
structures: (a) three-person group, members all agree (n = 12); (b) three-person group, two people
agree and one disagrees (n = 11); (c) four-person group, members all agree (n = 8); (d) four-person
group, three people agree and one disagrees (n = 9); and (e) four-person group, two agree and two
disagree (n = 8). Given that most participants in this exercise elect to race, we always assigned
nonracers to the minority. After we assigned the participants to groups and before they discussed
the case, participants completed another survey in which they rated how well they knew each group
member, rated how close they felt towards each member, and predicted their group’s dynamics.
They predicted the extent to which each of the following outcomes was likely (All items used a 9point scale in which 1 = not at all and 9 = completely):
To be difficult to resolve disagreements with the other people with whom you have been
assigned to discuss this situation.
That some of the people you have been assigned to work with have difficult personalities.
To be difficult to coordinate interactions in a group of this size.
Finally, participants discussed the decision for 20 minutes within their small groups,
submitted a group decision to the experimenter, and then completed a final survey. Varimax factor
analysis revealed two factors that tapped group process:
Group cohesion (Alpha = .88). The items included were as follows: We were a cohesive
group; We felt comfortable working together; I felt strong ties with this group; I identified with this
group; and I feel good about the group.
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Even- and odd-sized groups
Satisfaction with group decision making (Alpha = .72). The items included were as follows:
I am satisfied with our decision-making process; The majority of people in the group agreed with
my view; We had enough time to discuss the case; I am satisfied with our final decision.
Next we asked participants about their groups’ conflict-resolution techniques. We asked
participants whether the group was characterized by each of the following:
Mediators/leaders (Alpha = .64). The items included were as follows: One person tended
to play the role of a mediator to resolve our disagreements; One person acted as a leader who
facilitated our discussion.
Majority rule: The item was worded as follows: We used the majority rule to solve our
disagreements.
Feeling excluded (alpha=.74). The items included were as follows: I sometimes felt
excluded; I felt like a useless group member; Some of the people I was assigned to work with had
difficult personalities; I often simply went along with the others even if I didn’t agree with them.
Avoiding exclusion. The item was worded as follows: I felt badly if one person seemed
excluded from the group.
Finally we debriefed all participants and paid the undergraduates.
Results
Given the multi-level data, (individuals who were nested within discussion groups), we
used hierarchical linear modeling (HLM). We included individual-level variables (e.g. group
process ratings), group level characteristics (e.g. group size, coalition structure), and interactions
between individual and group characteristics (for examples and discussions of similar analyses, see
Kreft & de Leeuw, 1998; Wilk & Moynihan, 2005).
Differences Between Racers and Nonracers
Among the participants, 137 elected to race and only 39 chose not to race. Racers and
nonracers did not vary in their initial confidence, F(1, 141) = 1.45, n.s.; in the amount they bet that
their decision was accurate, F(1, 142) = .15, n.s.; or in whether they expected that others would
agree with them, F(1, 142) = 1.11, n.s. However, nonracers were more likely than racers to believe
that they had all the information necessary to make an accurate decision, F(1, 142) = 7.50, p < .01
(See Table 1a).
Differences Between Three- and Four-Person Groups
Next, we examined participants’ responses after we assigned them to groups but prior to
their actual interaction within those groups. Using HLM to control for the group, we found that
participants who expected to interact in three-person groups did not differ from those who expected
11
Even- and odd-sized groups
to interact in four-person groups. They did not differ in how well they knew their fellow group
members, B = -.15, t(52) = -.72, n.s.; or in how close they felt to them, B = .04, t(51) = .08, n.s.
(See Table 1b)..
Additionally, in contrast to Study 1 in which we highlighted a group’s oddness versus
evenness, participants we assigned to three- and four-person groups expected their groups to
operate similarly. Thus, participants we assigned to three- and four-person groups expected
disagreements to be equally difficult to resolve, B
some people to have difficult personalities, B
= .24, t(52) = .90, n.s.; they equally expected
= .14, t(52) = .55, n.s.; and they equally expected
that interactions would be difficult to coordinate in a group of their particular size, B
= .26, t(52)
= -1.33, n.s.
Differences Following Group Discussion in Three- and Four-Person Groups
Finally, we examined outcomes following the group discussion and introduce coalition
structure as a manipulated factor. As predicted, the group’s coalitional structure shaped its
subsequent cohesion (See Table 1c). Specifically, participants in both two vs. two and three vs.
one groups reported lower cohesion than participants in two vs. one groups (two vs. two: B = -.74,
t(43) = -2.44, p < .05; three vs. one: B = -1.12, t(43) = -.3.60, p <= .01), but they did not differ
from one another B = -.38, t(43) = -1.05, n.s.
Likewise, compared to participants in two vs. one coalitions, participants in four-person
groups rated their group processes more negatively (three vs. one: B = -1.00, t(43) = -2.37, p <=
.05; two vs. two: B = -1.15, t(43) = -2.65, p = .01). Three vs. one and two vs. two groups did not
differ from one another: B = .15, t(43) = .35, n.s.
One alternative explanation for these results is that they are simply due to group size.
Perhaps four-person groups were more difficult to manage than three-person groups. However,
four vs. none and three vs. none groups did not differ from one another with respect to cohesion, B
= -.15, t (43) = -.41, n.s., or from two vs. one groups (four vs. none: B = -.41, t (43) = -1.36, n.s.;
three vs. none: B = -.56, t(43) = -1.66, n.s.) and satisfaction with group process, (three vs. none: B =
.72, t(43) = 1.77, p < .10, and four vs. none: B = .25, t(43) = .59, n.s.). This suggests that coalition
structure within these groups, rather than simply group size, mattered.
A second possibility is that disgruntled minority participants drove these findings.
Therefore, we excluded minorities and examined racers only. Even the racers in the two vs. two
and three vs. one groups identified with the groups less (three vs. one:
< .01; two vs. two: B
B = -1.21, t(43) = -3.96, p
= -.74, t(43) = -2.79, p < .01) and were more dissatisfied with the group’s
12
Even- and odd-sized groups
decision making process (three vs. one:
B = -.78, t(43) = -1.98, p = .05; two vs. two: B
13
= -1.48,
t(43) = -3.49, p < .01) than majority racers in two vs. one groups.
Another indicator of group cohesion is whether participants’ individual opinions conformed
to the group’s decision following the discussion. We coded whether a group was united (i.e., if
each individual’s private opinion conformed to the group’s opinion) or whether it contained private
dissenters (i.e., individuals who remained unpersuaded by the group’s opinion). As expected, there
was greater unity in two vs. one groups (nine united groups vs. two with private dissenters),
compared to two vs. two groups (three united groups vs. five with private dissenters), χ 2(1, N = 19)
= 3.91, p < .05; and three vs. one groups (two united groups vs. seven with private dissenters), χ 2
(1, N = 20) = 7.10, p < .01.
Note that our hypotheses did not predict that three-person groups would be more accurate
than four-person groups. Thus, although two vs. one groups reported greater conformity and
satisfaction, they did not differ from three vs. one and two vs. two groups in their racing decision, χ
2
(2, N = 28) = 3.24, n.s.
Dispute Resolution Mechanisms
We next assessed whether group processes varied within three- and four-person groups.
Two vs. one and three vs. one groups used a leader/mediator to resolve disputes equally, (three vs.
one: B
= .05, t(43) = .09, n.s.; two vs. two: B = .32, t(43) = .57, n.s.). However, participants in
three vs. one groups used the majority rule more than did two vs. one participants, B = 1.63, t(43) =
2.20, p < .05.
Whereas the three vs. one groups explicitly used the majority rule to silence dissenters,
people in two vs. one coalitions used majority influence in a more subtle manner (Rico, SanchezManzanares, Gil, & Gibson, 2008). Thus, participants in three vs. one groups felt more excluded
than participants in two vs. one groups, B = .69, t(43) = 2.55, p = .01. Compared to nonracers in
two vs. one groups, nonracers in three vs. one groups were more dissatisfied with the decision
making process (two vs. one: M = 6.65, SD = 1.25; three vs. one: M = 4.86, SD = 2.08, F(1, 17) =
5.31, p < .05) and felt marginally more excluded than dissenters in two vs. one groups (two vs. one:
M = 1.55, SD = .62; three vs. one: M = 3.06, SD = 2.25, F(1, 17) = 4.15, p < .10). Because a lone
dissenter seems especially unreasonable in a three vs. one group, participants felt less bad about
excluding that person,
B = -1.61, t(43) = -2.44, p < .05.
Discussion
Study 2 suggests that an even/odd effect arises from unique coalitional structures, which
can shape how conflict emerges and how people resolve it. Given that dispute resolution is
Even- and odd-sized groups
unnecessary when all participants agree, we did not expect or find that three- and four-person
groups differ when people shared a common viewpoint. However, when people disagreed, threeperson groups (two vs. one) reported greater cohesion and more positive relationships than fourperson groups (both three vs. one and two vs. two groups).
Participants resolved disputes differently within these coalitional structures. In contrast to
the four-person groups, people in two vs. one groups did not silence dissenters via the majority rule
or exclusion and instead reported that they felt especially bad if they excluded others. As a result,
they gained conformity through subtle (rather than explicit) coordination (Rico et. al, 2008) and
maintained cohesion, both publicly and privately.
In addition to finding negative effects with respect to balance (two vs. two groups were
more hostile than two vs. one groups), we also found that imbalance evoked hostility under specific
circumstances (three vs. one groups were also more hostile than two vs. one groups, Mannix, 1993;
O’Leary & Mortensen, 2005). Whereas balance leads to coalition formation and polarization
(Murnighan, 1978), extreme imbalance (e.g. a single resistant dissenter) also disrupts harmony in
an otherwise unanimous group. When facing a large majority, a lone dissenter seems especially
wrong and unreasonable.
Further, such dissenters undermine the group’s ability to form a powerful unanimous front
to external constituents (Pfeffer, 1992). Consider an occasion when the Supreme Court faced an
eight vs. one situation and Chief Justice Warren persuaded the lone dissenter: “Stan, you’re all by
yourself on this now. You’ve got to decide whether it’s really the best thing for the country”
(Schwartz, 1993, p. 298). Thus, within an extremely imbalanced group, an overly aggressive
majority might feel especially justified in its right to exclude and undermine minorities. These
differences between two vs. one and three vs. one groups highlight the need for more nuanced
theories about tokens (e. g., Ely, 1994; Levine & Moreland, 1998) and majority/minority
relationships (Levine & Thompson, 1996).
Note that participants initially expected that three- and four-person groups would not differ.
In contrast to Study 1, which indicates that people’s expectations about even/odd groups differ,
Study 2 did not highlight group size or ask about it directly. Further, we surveyed people before
they realized that they were in the majority or the minority, so numerical issues were less salient
(Kanter, 1977). As such, although a group’s even/odd size crucially shapes group processes, this
issue can recede into the background when people intuitively understand groups and how they
operate.
14
Even- and odd-sized groups
Finally, whereas much research has compared dyads and triads as the building blocks of
social relationships (Caplow, 1968; Simmel, 1950), we propose that three- and four-person groups
offer a fruitful starting point for thinking about group structure and conflict. Although three- and
four-person groups enable us to understand structures and processes within even- and odd-sized
groups, a key question is how patterns within these groups generalize to larger groups, and whether
an even/odd effect emerges. Additionally, we move from a laboratory experiment to a natural
experiment that examines people in real groups.
Study 3. Roommates at Harvard University: A Natural Experiment
We examined a unique natural experiment at Harvard University in which students made
meaningful decisions about their living arrangements. The university administration assigns
freshmen to roommate groups that vary in size. In their second year, students select their own
roommates. We can thus examine how group size affects cohesion. Further, we can examine how
ethnic diversity shapes odd-even effect.
Research Context
Before incoming Harvard freshmen arrive on campus, they answer questions about their
habits (e.g. neatness, studiousness, smoking) and interests (e.g. sports, music). The university uses
this information to match students in freshmen dormitory rooms with between one and six persons.
The administration attempts to match compatible personalities and also integrates students
ethnically. Given that the freshman distribution maximizes diversity, and given that the
administration attempts to ensure basic compatibility between roommates, these assignments are
not perfectly randomized. However, it is unlikely that students request an odd or even number of
roommates. According to the Harvard Dean of Freshman, Thomas Dingman, students rarely report
preferences or aversions to roommates based on ethnicity, and the housing assignment process does
not accommodate such requests (Dingman, personal communication).
In the sophomore year, students choose blocking groups of up to 20 persons and move into
one of 13 “houses” where sophomores, juniors, and seniors live together, in contrast to the 16
dorms, which house only freshmen. Students list their top four choices and participate in a lottery
to determine whether they receive their preferred house with theor preferred group. Roommate
choice indicates interpersonal relationships. We infer that a relationship was relatively positive
when students decide to maintain it, because people who choose to stay together ensure that they
remain in close contact for the next three years. By contrast, when people decide not to live
together in the second year, they tend to live in separate houses, and this reduces their likelihood of
dining together or even seeing each other regularly, especially if they live at opposite ends of the
15
Even- and odd-sized groups
campus. This makes it reasonable to infer that people who chose not to room together often
experienced negative or neutral rather than positive relationships.
Creating the Dataset
To create the dataset, we used the freshman phone directory and the annual house yearbook
entries to arrange students from Harvard’s class of 1995 into their freshman and sophomore rooms.
We recorded each freshman roommate pair as a case, and coded whether they remained in the same
dorm in the second year or lived in different dorms. We next coded ethnic information (i.e., was the
pair White-White; White-Asian; Asian-Black; etc.). We coded ethnic information based upon the
students’ appearance in photographs and on their names as reported in the freshman and house
yearbooks.4
Limitations
Given the indirect route necessary to collect data, limitations arise in two specific areas: the
coding of dorm placement and the coding of ethnicity. Specifically, because the university keeps
information such as student ethnicity and roommate selection private, we had to make inferences
based on the available data.
Coding Dorm Rooms
We had no direct access to students’ choices. We simply examined whether the students
lived in the same or different dorms as sophomores. If they were not in the same second year dorm,
we inferred that they chose to separate. However, if they chose to separate, there was a 1 in 13
chance that the housing lottery randomly assigned them to the same dorm. Because such processes
are due to chance, they should not affect even- and odd-sized groups systematically.
Coding Ethnicity
Second, without access to university records, we coded ethnicity using students’ yearbook
photos. Thus, if people appeared Black or White in their photographs although they were of mixed
descent, they were coded according to their appearance for the purposes of this study. Additionally,
given the relatively limited representation of minorities in the sample, our categories lumped many
groups together (e. g., Black included American, Caribbean, and African; Asian included
American, Korean, Chinese, Japanese, etc.). Finally, we categorized people as mixed or “other” if
we couldn’t clearly identify their ethnicity. An independent coder validated the first author’s
perceptions of the students' physical appearance, with high inter-rater reliabilities (Whites: 87%;
Asians: 97%; and Blacks: 86%).
Results
16
Even- and odd-sized groups
Given the multi-level data (i.e., individuals are nested within rooming groups), we again
used HLM to control for the group-level effects. We included controls for gender, freshman room
size, and odd-even size, and included an interaction between odd-even size and whether roommates
shared the same or different ethnicity. The dependent variable was dichotomous (do roommate
pairs stay or break), so we used binomial logit.
We found an interaction between odd-even room size and whether roommates were same
or different race, B = -.52, t(1561) = -2.06, p < .05. Specifically, we found an odd-even main effect
among White-White pairs, whereby they stayed together more in odd-sized groups (three and five
persons) than in even-sized groups (two, four, and six persons; Figure 1 represents this zig-zag
pattern). Although White pairs in two- and three-person groups did not differ in their likelihood of
staying together, B = -.14, t(108) = -.36, n.s., White pairs in three- to six-person groups differed.
White pairs in three-person groups stayed together more than Whites in four-person groups, B = .63, t(210) = -2.42, p < .05; Whites in four-person groups stayed together less often than Whites in
five-person groups, B = -.73, t(176) = -2.11, p < .05; and Whites in five-person groups stayed
together more than Whites in six-person groups, B = -.70, t(51) = -1.98, p = .05. Gender, B = -.14,
t(411) = -.82, n.s., and freshman room size, B = -.82, t(411) = -.82, n.s., were nonsignificant.
By contrast, we did not find odd-even effects between Whites and their Black and Asian
roommates, B = -.15, t(268) = -.65, n.s. This could occur because people feel uncomfortable both
when ingroup members exclude them and when they exclude fellow ingroup members. As a result,
whereas people expect ingroup members to conform, they expect minorities (who are already
outsiders due to their ethnicity) to disagree with ingroup members (Phillips, 2003; Phillips et. al.,
2004). This mitigates majority influence among diverse pairs and reduces odd/even effects.5
Discussion
Whereas most groups research employs laboratory experiments (see Moreland, Hogg, &
Hains, 1994 for a discussion), this study found that people in real even- and odd-sized groups
differed in their relationships. In contrast to intuitive predictions, Whites in odd-sized groups
maintained their roommate ties more often. We propose that this occurs because odd-sized groups
can readily employ majority influence to resolve conflicts. Consistent with this mechanism, the
effect pertains to same-ethnicity roommate pairs. Because congruence implies that similar people
should agree and dissimilar people should disagree (Phillips, 2003; Heider, 1958), the majority’s
power to influence a dissenting minority declines among diverse people, and even-odd effects
disappear.
General Discussion
17
Even- and odd-sized groups
A common challenge to social relations is that groups polarize along fault lines (Lau &
Murnighan, 2005). Civil wars between ethnic subgroups fracture countries such as Iraq and the
former Yugoslavia; “Red” and “Blue” states in the United States hold fundamentally incompatible
values and lifestyles; and governing institutions such as Congress stall due to political conflict. At a
micro level, top management teams (Hambrick, 1994; Peterson et. al., 1998), work teams (Lau &
Murnighan, 2005; O’Reilly, Williams, & Barsade, 1998; Pelled, 1996), judges (Sunstein, Schkade,
Ellman, & Sawicki, 2006), juries (Davis, Kerr, Atkin, Holt, & Meek, 1975; Guarnaschelli,
McKelvey, & Palfrey, 2000; Hastie, Penrod, & Pennington, 1983; Saks, 1977), and families
(Caplow, 1968; Grusky, Bonacich, & Webster, 1995) also divide along fault lines. This paper
examines how small groups fracture in distinctive ways due to a seemingly inconsequential factor:
their even or odd size.
As such, this research connects classic studies on group size with recent themes such as
diversity (Williams & O’Reilly, 1998) and demographic fault lines (Lau & Murnighan, 2005;
Pfeffer, 1983). While early research examined group size without considering coalition structure
and diversity as moderators, and recent research treats group size as fundamentally uninteresting
and unimportant, the current research asserts that a group’s odd or even size is a crucial situational
feature that shapes its decision making, coalition structure, and cohesion.
In three studies that used multiple methods, we examined two issues: people’s predictions
about even- and odd-sized groups and the actual cohesion within these groups. We found that
people held more positive attitudes towards even than odd numbers and further predicted that
people in even-sized groups experienced more positive social relationships (Study 1).
Studies 2 and 3 examined people’s actual experiences in these groups. Study 2 found that
three- and four-person groups did not differ when all parties agreed, but they differed when they
fractured into coalitions. Four-person groups (both two vs. two and three vs. one coalitions)
experienced more hostile group relationships than three-person groups (two vs. one coalitions).
Both balance (e. g., two vs. two coalitions, which cause unresolvable conflict) and extreme
imbalance (e.g., three vs. one coalitions, which lead majorities to unilaterally exercise power)
undermine positive group relationships (Mannix, 1993; O’Leary & Mortensen, 2005). In a natural
experiment at Harvard University (Study 3), first-year students assigned to odd-sized roommate
groups stayed with roommates more often than those who were assigned to even-sized roommate
groups, and ethnic homogeneity moderated this effect. We argue that these differences do not arise
from group size per se but from coalitional structure. In sum, these studies systematically replicate
18
Even- and odd-sized groups
even/odd effects that appeared occasionally and tangentially decades ago in the group size
literature, and examine their underlying mechanisms.
Limitations
Although our evidence indicates that even- and odd-sized groups exhibit critical
differences, as mentioned previously, a parsimonious even/odd theory may be elusive given that
group size (Simmel, 1950), member status (Thomas-Hunt & Phillips, 2002), issue structure, and
salient decision rules (Hastie & Kameda, 2005) likely all moderate the effect.
Second, this research emphasizes the ways that groups resolve conflict once they fracture,
rather than how they tend to fracture in the first place. Thus, we manipulated disagreement in Study
2, and, in Study 3, we assumed that roommate groups experience disagreement when they live in
close quarters for one year. For instance, Murnighan (1978) cited several studies indicating that
tetrads tend to split in two vs. two groups (Shears, 1967; Willis, 1962) rather than three vs. one
coalitions. Further research should consider how triads, tetrads, and larger groups naturally split
into particular coalitional structures.
Next, although we considered group heterogeneity, we did not directly manipulate social
identity and categorization (Tajfel & Turner, 1986). If we prime people to identify with a group,
this should heighten even-odd effects; by contrast, if we prime within-group distinctions (race,
gender, interests) we expect even/odd effects to weaken. Although Study 2 manipulated
heterogeneity through opinions and Study 3 examined ethnic heterogeneity that naturally occurred
within groups, further research should experimentally manipulate the group’s salience as an
overarching identity and within-group categories (Gaertner & Dovidio, 2000).
On a related note, our research has not considered cross-cultural differences. On one hand,
odd/even effects might decrease within consensus-building, collectivistic cultures, because their
strong norms encourage conflict avoidance and compromise (Morris, et. al., 1998), which imply
that collectivistic groups fracture less often, regardless of whether a group is even- or odd-sized.
However, once collectivistic groups fracture, even/odd effects can be more pronounced. People
who are especially concerned about exclusion (e.g., two vs. one groups) may readily come in line.
Further, if groups fracture into evenly matched coalitions (e.g. two vs. two), collectivists might
view the rival coalition as an outgroup and avoid them more (Leung, 1987).
Implications
Expectations Versus Preferences
Study 1 reveals that our results for real groups (Studies 2-3) are counterintuitive. People
like even numbers and predict that even-sized groups experience more positive relationships. Just
19
Even- and odd-sized groups
as marketers tend to sell products in even numbers (e.g. chairs, dishes, eggs, and baked goods),
people may compose social groups in even numbers, because they associate them with balance and
harmony. Further, people could feel apprehensive when they enter odd-sized groups. For instance,
when we presented this research at a conference, one professor observed that her daughter, an
entering college freshman, worried because the university had assigned her to a three-person dorm
room.
Expectations also affect how people explain and resolve conflict. If people in even-sized
groups expect smooth relationships, conflict is especially upsetting. By contrast, if people in oddsized groups expect conflict, they may emphasize situational rather than personalistic attributions
(“It’s not easy being a threesome”), which make conflict more easily resolvable (Morris, Larrick, &
Su, 1999).
Finally, people’s expectations affect coalitional strategies. If people assume that balance
benefits groups, they might join the weaker powers to create a countervailing force rather than
bandwagoning, i.e., joining stronger parties to dominate weaker parties (Walt, 1987). Although
people predict that balance leads to positive outcomes, the current research suggests that they may
instead prefer interactions within unbalanced coalitions.
Shared Cognition
Contrary to people’s expectations (Study 1), we found that even-sized (four-person) groups
used the majority rule more than odd-sized (three-person) groups (Study 2). Whereas even-sized
groups engage in explicit coordination via communication to enforce agreement (e.g., directly
invoking the majority rule), odd-sized teams engage in implicit coordination (e.g., subtly inducing
conformity through majority influence; Rico et. al., 2008).
Because odd-sized groups achieve cohesion through implicit rather than explicit
coordination, they may form transactive memory systems more rapidly, i.e., they come to share
cognitive processes, such as encoding, storing, and retrieving information (Hollingshead, 1998;
Levine, Resnick, & Higgins, 1993; Moreland, Argote, & Krishnan, 1996; Wegner, 1987). On other
hand, people in even-sized groups may form transactive memory systems within subgroups.
Because they do not acknowledge that rivals possess valuable knowledge (Menon & Pfeffer, 2003;
Menon, Thompson, & Choi, 2006), they may replicate that knowledge rather than create shared
memory systems
Finally, further research might examine the patterns of transactive memory errors that
even- and odd-sized groups develop. For instance, people in odd-sized groups may display false
consensus (Ross, Greene, & House, 1977), and assume that their peers agree with their viewpoints.
20
Even- and odd-sized groups
By contrast, people in even-sized groups may exhibit a “false dissent” effect and assume that rival
group members disagree.
Designing and Forming Effective Groups
Given that group harmony facilitates some tasks (e.g., implementation) whereas debate and
disagreement facilitate other tasks (e.g., creativity and brainstorming; Janis, 1982; Peterson &
Nemeth, 1996; Sutton & Hargadon, 1996; Swaab, Phillips, Diermeier & Medvec, 2008), further
research might compare performance differences between even- and odd-sized groups. Ultimately,
such research would enable people to selectively deploy even- or odd-sized groups for appropriate
tasks. Further, this simple group characteristic helps people predict the distinct group dysfunctions
within even- and odd-sized groups. Specifically, disruptive coalitions within even-sized groups can
inhibit cooperation and collaboration (Jehn & Mannix, 2001); while odd-sized groups suffer from
conformity and groupthink (Janis, 1982). Perhaps odd-sized groups benefit from different
organizational “repairs” (Heath, Larrick, & Klayman, 1998) such as the use of a devil’s advocate
(Janis, 1982), while even-sized groups benefit from other strategies (e.g., assigning an expert or
leader to help resolve disputes).
Finally, in contrast to traditional group interventions such as discussing conflicts directly or
enhancing morale through team-building activities, changes in group size offer a relatively simple
and subtle means to shift group behavior (Moreland, Levine, Wingert, 1996). For instance,
although research has emphasized the challenges that newcomers face (Choi & Levine, 2004;
Gruenfeld, Martarona, & Fan, 2000; Levine & Moreland, 1991), adding a newcomer to a
deadlocked four-person group also turns it into a five-person group, and encourages conflict
resolution through majority influence. Conversely, if a group relies on majority influence too
readily, removing or adding a member can alter its numerical context and increase debate.
Conclusion
This research extends Simmel’s (1950) theories about dyads and triads to tetrads and small
groups more generally. Our key point is that sometimes a group essentially operates as a polarized
dyad, and other times it coheres as a stable, unified entity. A simple quantitative feature of the
group—odd or even size—powerfully shapes which dynamic emerges. Indeed, precisely because
no one wants to be the odd one out, people in odd-sized groups may conform, agree, and achieve
stability, while people in even-sized groups are often at odds.
21
Even- and odd-sized groups
End Notes
1
According to Nishiyama (2006), these preferences arise from cultural factors. The Chinese, for
example, hold negative connotations about even numbers, perhaps because yin-yang theories
associate odd numbers with masculinity (yang) and even numbers with femininity (yin). In
Japanese, “The number 2 means to divide (or to part, separate); 4 is associated with death; and 6,
as in the word rokudenashi, means good for nothing” (p. 479). Likewise, a monetary gift of $101
(vs. $100) appears strange to Americans, but Indians traditionally offer monetary gifts in odd sums.
Whereas Americans celebrate the “Sweet 16” birthday or a “debutante” ball at age 18, Latin
cultures mark the 15th birthday (quinceanera), and Japanese celebrate the 3-5-7 festival to mark a
child’s odd birthdays.
2
Three other dissertations included the term group size, but they were not small group research.
Two concerned class size in education and one concerned mental institutions.
3
A broker can also be a partisan who connects these parties for personal profit (Burt, 1992;
Simmel, 1950)
4
We examined Whites, Asians, and Blacks in this analysis because these were the largest minority
groups. Hispanics, East Indians, Middle Easterners, and mixed race participants were excluded
because they lacked critical numbers in this dataset.
5
One possibility is that odd-sized groups may be generally more stable than even-sized groups. To
test this, we examined whether odd-sized groups were more likely than even-sized groups to stay
together in their entirety. We analyzed the data at the group level and cross-tabulated group size
and group outcome (entire group stayed together, group disbanded). Two-person groups stayed
together in their entirety more than three-person groups (two-person: 57 groups stayed, 71
disbanded; three-person: 30 groups stayed, 75 disbanded), χ 2 (1, N = 233) = 6.28, p = .01. Threeperson groups stayed together more than four-person groups, (four-person: 17 groups stayed, 145
disbanded) χ 2 (1, N = 267) = 14.35, p < .01; and five-person groups stayed together more than did
six-person groups, (five-person: 7 groups stayed, 28 disbanded; six-person: 0 groups stayed, 18
disbanded), χ 2 (1, N = 53) = 4.15, p < .05. These effects could simply reflect the unsurprising
effects of group size, given that larger groups have more linkages to maintain. However, fiveperson groups were more likely to stay together as a whole than four-person groups, though this
trend missed significance, χ 2 (1, N = 197) = 2.43, p = .12.
22
Even- and odd-sized groups
Study 2 Means
Table 1a: Pretest Characteristics of Racers and Nonracers
Pretest Scores
Racers
Variable
Initial confidence
Amount of bet
Expected
agreement
Adequate
information
Nonracers
M
8.16
7.32
4.49
SD
1.71
2.54
1.27
M
7.68
7.11
4.21
SD
2.47
3.11
1.17
3.41
1.44
2.57
1.55
Table 1b: Three-person and Four-person Groups Prior to Interaction
Group assignment
Three-Person Groups
Four-Person Groups
Variable
M
SD
M
SD
Relationships to group members
Knew group
1.67
1.26
1.52
.86
members well
Closeness
3.35
2.22
3.40
2.17
Predicted difficulty of…
Resolving group
3.14
1.76
3.38
1.76
disagreements
Personalities
2.31
1.66
2.45
1.54
within the group
1.92
1.14
2.19
1.39
Coordinating
interactions
within a group of
their size
Table 1c: Comparison of Cohesion Scores by Coalitional Structure (Study 4)
Cohesion scores
Coalition structure
M
SD
three vs. none
6.78
1.40
two vs. one
7.33
1.10
four vs. none
6.91
1.24
three vs. one
6.21
1.32
two vs. two
6.59
1.27
23
Even- and odd-sized groups
Figure 1
Percentage of first year White-White and White-Minority pairs who stayed together in the second
year.
60
50
40
30
20
10
0
white-white pairs
white-minority pairs
2 person 3 person 4 person 5 person 6 person
groups groups groups groups groups
24
Even- and odd-sized groups
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