Taking a crack at
measuring faultlines
Sherry M.B. Thatcher (University of Arizona)
Katerina Bezrukova (Rutgers University)
Karen A. Jehn (Leiden University)
Academy of Management, New
Orleans, 2004
1
Agenda
• Interactive Exercise
• Why?
– Importance of faultlines vs. other composition measures
• How?
– What we did
• Huh?
– Problems we ran into (and how we fixed them)
• Oh, that!
– Issues that journal reviewers are likely to raise
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2
Interactive exercise
1
2
5
3
4
6
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3
Interactive exercise
• In breaking the group into subgroups, what
characteristics did you look at?
• How homogeneous are the subgroups?
• What assumptions did you make when breaking
the group into subgroups?
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Why?
• Mixed effects of diversity and demography studies
• Focus on more than one attribute at a time
• Takes into account interdependence among
attributes
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How?
From Diversity to Faultlines
Step 1: Picturing what we need to measure
Group A: Strong Faultline
Group B: Weak Faultlines
HWM
HWM
PBF
PBF
HWM
HBF
PBM
PWF
 
 
♂ ♂
H
♀ ♀
P
Educ.
Race
♂ ♂
H
♀ ♀
P
Race
Sex
♂ ♂
H
♀ ♀
P
Educ.
H
H
H
P
P
P
Sex
♂♀ ♂♀
H
P
H
P
♂♀ ♂ ♀
P
♀♀ ♂ ♂
P
H
H
H
P
P
H
H = High school, P = PhD, W = White, B = Black, M = Male, F = Female
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How?
Step 2: Understanding diversity formulas
1 Index of heterogeneity (Blau,
1977; Bantel & Jackson, 1989);
Diversity or entropy index
(Teachman, 1980; Ancona &
Caldwell, 1992).
(1 – SPi2)
s

P
ln
P
i (
i)
i1
Group-level categorical variables.
2 Coefficient of variation (Allison, SD
1978).
x
Group-level interval variables.
3 Relational demography
/individual dissimilarity score
(Tsui & O’Reilly, 1989).
[1/nS(Xi - Xj)2]1/2]
Individual-level categorical and
interval variables.
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How?
Step 3:Creating a faultline strength formula
Faultline strength – Clustering Algorithm based on Euclidean
distance formula (Thatcher, Jehn, & Zanutto, 2003)
 p 2 g
 nk x jk  x j
j 1 k 1
Faug  
g
p 2 nk
  xijk  x j

 j 1 k 1 i1
–
–
–
–
–

)

)
2
2







g 1,2,...S,
xijk = the value of the jth characteristic of the ith member of subgroup k
x•j• = the overall group mean of characteristic j
x•jk = the mean of characteristic j in subgroup k
ngk = the number of members of the kth subgroup (k=1,2) under split g
the faultline strength = the maximum value of Faug over all possible
splits g=1,2,…S.
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Measuring Faultlines
FAULTLINE
STRENGTH/ L & M
None
A
B
A
B
A
A
A
C
B
B
C
Weak
(1 align; 4 ways)
0.463 (strongest split is AC,
BD but AB, CD is also a
strong split)
Weak
(1 align; 3 ways)
0.557 (strongest split is AB,
Strong
(3 align; 2 ways)
0.688 (strongest split is AC,
BD)
Very Strong
(4 align; 1 way)
0.996 (strongest split is AB,
CD)
D
C
C
0
D
C
B
FAU ALGORITHM based on
Euclidean distance formula
D
D
D
CD, but BC, AD is also close)
CODES
gender diff.
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race diff.
age diff.
occupation diff.
9
How?
Revisiting Step 1: Faultline Distance
Faultline distance reflects how far apart the subgroups are from
each other
Group A: Farther Apart
Group B: Closer Together
 
 
Age
Education
Tenure
55
21
Ph.D.
B.A.
22
3
Age
Education
Tenure
Academy of Management, New
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55
30
Ph.D.
M.S.
22
11
10
Faultline Distance (cont’d)
Faultline distance - the Euclidean distance between the two
sets of averages
where centroid (vector of means of each variable) for
subgroup 1 = ( X ., X ., X ., … , X . ),
centroid for subgroup 2 = ( X ., X ., X ., … , X . ).
11
12
13
1P
21
22
23
2P
Group faultline score
Fau = Strength (Faug) x Distance (Dg)
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11
Faultlines Strength and Distance, and Group
Faultlines Scores
Member
Team 1
1
2
3
4
5
Team 2
1
2
3
4
5
Age
65
37
50
36
46
61
34
45
47
37
Race
1
1
1
1
1
2
1
1
2
1
Gender
1
1
0
1
0
1
0
0
1
0
Tenure
26
2
26
4
1
6
10
4
9
1
Function
3
3
3
3
3
1
1
1
1
1
Faultline
Education Strength
Group
Faultline Faultlines
Distance Score
0.8057
2.9334
2.3634
0.8304
2.0265
1.6828
5
7
4
7
7
7
5
5
7
5
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Raw Data
Member
Sex
Age
Race
1
Female
46
1
2
Male
48
1
3
Female
43
2
4
Female
44
1
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Recorded Data
Member
Sex1
Sex2
Age
Race1
Race2
1
0
1
46
1
0
2
1
0
48
1
0
3
0
1
43
0
1
4
0
1
44
1
0
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14
Rescaling Considerations
• Theory driven approach
– to use SME’s judgments to weight
characteristics
• Empirical approach
– to view participants’ responses as a
“true” measure of faultlines
• Statistical approach
– to use standard deviations
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Rescaled Data
Member
1
2
3
4
Rescaled Means
Sex1
0.000
0.707
0.000
0.000
0.177
Sex1= x1
Sex2
0.707
0.000
0.707
0.707
0.530
Age
5.750
6.000
5.375
5.500
5.656
Race1 Race2
0.707
0.000
0.707
0.000
0.000
0.707
0.707
0.000
0.530
0.177
Age= x3
Race2= x5
Sex1= x1
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Subgroup Characteristic Averages
Split (g)
Members
ng
Split #1 (g=1)
Subgroup 1 (k=1)
1
1.000
Subgroup 2 (k=2)
2,3,4
3.000
Split #2 (g=2)
Subgroup 1 (k=1)
2
1.000
Subgroup 2 (k=2)
1,3,4
3.000
Split #3 (g=3)
Subgroup 1 (k=1)
3
1.000
Subgroup 2 (k=2)
1,2,4
3.000
Split #4 (g=4)
Subgroup 1 (k=1)
4
1.000
Subgroup 2 (k=2)
1,2,3
3.000
Split #5 (g=5)
Subgroup 1 (k=1)
1,2
2.000
Subgroup 2 (k=2)
3,4
2.000
Split #6 (g=6)
Subgroup 1 (k=1)
1,3
2.000
Subgroup 2 (k=2)
2,4
2.000
Split #7 (g=7)
Subgroup 1 (k=1)
1,4
2.000
Subgroup 2 (k=2)
2,3
2.000
Subgroup Characteristic Averages
Sex1
Sex2
Age
Race1 Race2
0.000
0.236
0.707
0.471
5.750
5.625
0.707
0.471
0.000
0.236
0.707
0.000
0.000
0.707
6.000
5.542
0.707
0.471
0.000
0.236
0.000
0.236
0.707
0.471
5.375
5.750
0.000
0.707
0.707
0.000
0.000
0.236
0.707
0.471
5.500
5.708
0.707
0.471
0.000
0.236
0.354
0.000
0.354
0.707
5.875
5.438
0.707
0.354
0.000
0.354
0.000
0.354
0.707
0.354
5.563
5.750
0.354
0.707
0.354
0.000
0.000
0.354
0.707
0.354
5.625
5.688
0.707
0.354
0.000
0.354
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Sex1= x1k
Age= x3k
Race1= x4k
17
Between Group Characteristic
Averages
Betw een Group Sum of Squares for Characteristics
Split (g)
Split #1 (g=1)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #2 (g=2)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #3 (g=3)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #4 (g=4)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #5 (g=5)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #6 (g=6)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #7 (g=7)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Members
ng
Sex1
Sex2
Age
Race1
Race2
1
2,3,4
1.000
3.000
0.031
0.010
0.031
0.010
0.009
0.003
0.031
0.010
0.031
0.010
2
1,3,4
1.000
3.000
0.281
0.094
0.281
0.094
0.118
0.039
0.031
0.010
0.031
0.010
3
1,2,4
1.000
3.000
0.031
0.010
0.031
0.010
0.079
0.026
0.281
0.094
0.281
0.094
Sex1=
nkg  x1k  x1 )
2
Age=
4
1,2,3
1.000
3.000
0.031
0.010
0.031
0.010
0.024
0.008
0.031
0.010
0.031
0.010
nkg  x3k  x3 )
1,2
3,4
2.000
2.000
0.062
0.062
0.062
0.062
0.096
0.096
0.062
0.062
0.062
0.062
Race1=
1,3
2,4
2.000
2.000
0.062
0.062
0.062
0.062
0.018
0.018
0.062
0.062
0.062
0.062
1,4
2,3
0.062
0.062
0.002
0.062
2.000
0.062 of Management,
0.062
0.002New 0.062
2.000 Academy
0.062
0.062
Orleans, 2004
2
nkg  x4k  x4 )
18
2
Subgroup and Between SS
Split (g)
Split #1 (g=1)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #2 (g=2)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #3 (g=3)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #4 (g=4)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #5 (g=5)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #6 (g=6)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #7 (g=7)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Subgroup
Total
Between SS Between SS
Members
ng
1
2,3,4
1.000
3.000
0.134
0.045
0.178
2
1,3,4
1.000
3.000
0.743
0.248
0.991
3
1,2,4
1.000
3.000
0.704
0.235
pp=5
6
Subgroup Between SS = nkg  x jk  x j )
2
j 1
0.939
4
1,2,3
1.000
3.000
0.149
0.050
0.199
1,2
3,4
2.000
2.000
0.346
0.346
0.691
1,3
2,4
2.000
2.000
0.268
0.268
0.535
1,4
2,3
2.000
2.000
p 6
2 p=5
Total Between SS= nkg  x jk  x j  )
k 1 j 1
0.252
0.252 of Management,
0.504
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2
Total Sum of Squares and Fau
p 6
2 p=5
Split (g)
Split #1 (g=1)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #2 (g=2)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #3 (g=3)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #4 (g=4)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #5 (g=5)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #6 (g=6)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #7 (g=7)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Members
1
2,3,4
ng
1.000
3.000
2
1,3,4
1.000
3.000
3
1,2,4
1.000
3.000
4
1,2,3
1.000
3.000
Fau-g
Fau g 
0.103
 n  x
k 1 j 1
g
k
 jk
g
pp=5
 6 nk
  x
2
k 1 j 1 i 1
ijk
 x j  )
 x j  )
2
2
0.573
0.543
g
6 nk
2 pp=5
Total Sum of Squares =  xijk  x j  )
2
k 1 j 1 i 1
0.115
Total Sum of Squares
1,2
3,4
2.000
2.000
1,3
2,4
2.000
2.000
(denominator of Fau-g)
0.400
0.309
Fau  max ( Faug )
1.730
g 1,2,...7
excl. 1 pers. split g=5,6,7
1,4
2,3
2.000
2.000
0.291 of Management, New
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Overall Fau=
0.400
20
Distance
Split (g)
Split #1 (g=1)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #2 (g=2)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #3 (g=3)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #4 (g=4)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #5 (g=5)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #6 (g=6)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Split #7 (g=7)
Subgroup 1 (k=1)
Subgroup 2 (k=2)
Members
ng
Distance-g
1
2,3,4
1.000
3.000
0.238
2
1,3,4
1.000
3.000
1.321
3
1,2,4
1.000
3.000
1.251401
4
1,2,3
1.000
3.000
0.2655579
1,2
3,4
2.000
2.000
0.6912553
1,3
2,4
2.000
2.000
0.535005
1,4
2,3
2.000
2.000
D = max (Dg)
excl. 1 pers. split g=5,6,7
Overall Distance=
0.503755
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0.691
21
SAS Faultline Calculation (Version
1.0, July 26, 2004)
1.
WHAT THIS CODE DOES
•
2.
faultline strength and distance for groups of size 3 to 16 (two
sets: incl and excl 1-person subgroups).
WHAT WE ASSUME ABOUT THE DATA
•
•
•
•
3.
a comma-separated data text file (save as .csv file).
dummy variables for categorical vars.
no missing values
group ID variable (groups are numbered from 1 to n)
WHAT WE ASSUME ABOUT THE RESCALING
FACTORS
•
•
rescaling factors must be specified for each variable
rescaling factors must be specified in a comma-separated text
file (save as .csv file).
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SAS Faultline Calculation (Version
1.0, July 26, 2004): Cont’d
4. HOW TO RUN THE CODE
–
–
–
download the SAS code and data files into
C:\Faultline\FL_code\FL_Code_parameters.txt
go to the C:\Faultline\FL_Code directory and double
click on FL_Code_1_0.sas
right click the mouse and select “Submit All”
5. HOW TO MODIFY THE INPUT PARAMETERS
–
–
all user inputs are specified in the file
C:\Faultline\FL_Code\FL_Code_parameters.txt.
keep exact names of files.
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Huh?
Problems we ran into (and how we fixed them)
• Group size
• Number of possible subgroups
• Subgroups of size “1”
• Calculating the overall faultline score
• Measuring faultline distance for
categorical variables
• Rescaling
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Oh That!
Issues that journal reviewers have raised
• Rescaling (influence on results)
– solution: rerun analyses
• Importance of distance component
– solution: explain it better
• Perceptual faultlines = actual faultlines?
– solution: explain to the reviewers that we
didn’t have this data
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Advantages of Fau Measure
• allows continuous and categorical
variables
• unlimited number of variables
• theoretically unlimited group size
• flexible enough to allow for different
rescaling
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Future Research & Work in
Progress
Testing the theory in experimental settings
•
•
Faultlines, coalitions, conflict, group identity and
leadership profiles
Temporal effects of faultlines
Testing the theory in organizational settings
•
Consistency matters! The Effects of Group and
Organizational Culture on the Faultline-Outcomes
Link
Testing the theory in international settings
•
•
Peacekeeping and Ethnopolitical conflict
A quasi-experimental field study in ethnic conflict
zones (i.e., Crimea, Sri Lanka, Burundi and Bosnia)
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Thank you very much
for coming
Any questions?
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