academy of management, new orleans, 2004 1 taking a crack at measuring faultlines sherry m.b....

Academy of Management, New Orleans, 2004

1

Taking a crack at measuring faultlines

Sherry M.B. Thatcher (University of Arizona)

Katerina Bezrukova (Rutgers University)

Karen A. Jehn (Leiden University)


2

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


3

Interactive exercise

11

22

66

55

44

33


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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?


5

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

♀♀P♂♂H

♂♂H ♂♂H

♂♂H ♂♂H

♀♀P

♀♀P♀♀P

♀♀P♀♀P

Educ.

Race

Sex

♂♂P♀♀P♂♂H ♀♀H

♂♂P♀♀P ♂♂H♀♀H

♂♂P ♀♀P♂♂H♀♀H

Educ.

Race

Sex

Group A: Strong Faultline Group B: Weak Faultlines

♂♂H

H = High school, P = PhD, W = White, B = Black, M = Male, F = Female

HWMHWMPBFPBF

HWMHBFPBMPWF


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How? Step 2: Understanding diversity formulas

3

2

1

[1/n(Xi - Xj)2]1/2]

Individual-level categorical and interval variables.

Relational demography /individual dissimilarity score (Tsui & O’Reilly, 1989).

SD

Group-level interval variables.

Coefficient of variation (Allison, 1978).

(1 – Pi

Group-level categorical variables.

Index of heterogeneity (Blau, 1977; Bantel & Jackson, 1989);

Diversity or entropy index (Teachman, 1980; Ancona & Caldwell, 1992).

P ii

s

1(ln )P i

x


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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)

– 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.

2 2

1 1

2 2

1 1 1

1,2,... ,gk

pg

jk jkj k

g np

jijkj k i

n x x

Fau g S

x x


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Measuring Faultlines

0.463 (strongest split is AC, BD but AB, CD is also a strong split)

Weak

(1 align; 4 ways)

0.996 (strongest split is AB, CD)

Very Strong

(4 align; 1 way)

0.688 (strongest split is AC, BD)

Strong

(3 align; 2 ways)

0.557 (strongest split is AB, CD, but BC, AD is also close)

Weak

(1 align; 3 ways)

0None

FAU ALGORITHM based on Euclidean distance formula

FAULTLINE STRENGTH/ L & M

A B C D

A B C D

A B C D

A B C D

gender d iff.

race diff.

age diff.

occupation diff.

CODES

A B C D


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How?Revisiting Step 1: Faultline Distance

Faultline distance reflects how far apart the subgroups are from each other

Age

Education

Tenure

Age

Education

Tenure

3055

M.S.Ph.D.

1122

55

Ph.D.

22

21

B.A.

3

Group B: Closer TogetherGroup A: Farther Apart


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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 = ( ), centroid for subgroup 2 = ( ).

Group faultline score

Fau = Strength (Faug) x Distance (Dg)

X , X , X , … , X11 12 13 1P. . . .

X , X , X , … , X21 22 23 2P. . . .


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Faultlines Strength and Distance, and Group Faultlines Scores

Member Age Race Gender Tenure Function Education

Team 1 0.8057 2.9334 2.3634

1 65 1 1 26 3 5

2 37 1 1 2 3 7

3 50 1 0 26 3 4

4 36 1 1 4 3 7

5 46 1 0 1 3 7

Team 2 0.8304 2.0265 1.6828

1 61 2 1 6 1 7

2 34 1 0 10 1 5

3 45 1 0 4 1 5

4 47 2 1 9 1 7

5 37 1 0 1 1 5

Faultline Strength

Faultline Distance

Group Faultlines Score


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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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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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Sex1= 1x

Rescaled Data

Age= 3x

Member Sex1 Sex2 Age Race1 Race21 0.000 0.707 5.750 0.707 0.0002 0.707 0.000 6.000 0.707 0.0003 0.000 0.707 5.375 0.000 0.7074 0.000 0.707 5.500 0.707 0.000

Rescaled Means 0.177 0.530 5.656 0.530 0.177

Race2= 5x Sex1= 1x


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Subgroup Characteristic Averages

Sex1= 1kx

Age= 3kx

Race1= 4kx

Split (g) Members ng Sex1 Sex2 Age Race1 Race2Split #1 (g=1)Subgroup 1 (k=1) 1 1.000 0.000 0.707 5.750 0.707 0.000Subgroup 2 (k=2) 2,3,4 3.000 0.236 0.471 5.625 0.471 0.236Split #2 (g=2)Subgroup 1 (k=1) 2 1.000 0.707 0.000 6.000 0.707 0.000Subgroup 2 (k=2) 1,3,4 3.000 0.000 0.707 5.542 0.471 0.236Split #3 (g=3)Subgroup 1 (k=1) 3 1.000 0.000 0.707 5.375 0.000 0.707Subgroup 2 (k=2) 1,2,4 3.000 0.236 0.471 5.750 0.707 0.000Split #4 (g=4)Subgroup 1 (k=1) 4 1.000 0.000 0.707 5.500 0.707 0.000Subgroup 2 (k=2) 1,2,3 3.000 0.236 0.471 5.708 0.471 0.236Split #5 (g=5)Subgroup 1 (k=1) 1,2 2.000 0.354 0.354 5.875 0.707 0.000Subgroup 2 (k=2) 3,4 2.000 0.000 0.707 5.438 0.354 0.354Split #6 (g=6)Subgroup 1 (k=1) 1,3 2.000 0.000 0.707 5.563 0.354 0.354Subgroup 2 (k=2) 2,4 2.000 0.354 0.354 5.750 0.707 0.000Split #7 (g=7)Subgroup 1 (k=1) 1,4 2.000 0.000 0.707 5.625 0.707 0.000Subgroup 2 (k=2) 2,3 2.000 0.354 0.354 5.688 0.354 0.354

Subgroup Characteristic Averages


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Between Group Characteristic Averages

Sex1= 2

1 1gk kn x x

Age=

2

3 3gk kn x x

Race1= 2

4 4gk kn x x

Split (g) Members ngSplit #1 (g=1)Subgroup 1 (k=1) 1 1.000Subgroup 2 (k=2) 2,3,4 3.000Split #2 (g=2)Subgroup 1 (k=1) 2 1.000Subgroup 2 (k=2) 1,3,4 3.000Split #3 (g=3)Subgroup 1 (k=1) 3 1.000Subgroup 2 (k=2) 1,2,4 3.000Split #4 (g=4)Subgroup 1 (k=1) 4 1.000Subgroup 2 (k=2) 1,2,3 3.000Split #5 (g=5)Subgroup 1 (k=1) 1,2 2.000Subgroup 2 (k=2) 3,4 2.000Split #6 (g=6)Subgroup 1 (k=1) 1,3 2.000Subgroup 2 (k=2) 2,4 2.000Split #7 (g=7)Subgroup 1 (k=1) 1,4 2.000Subgroup 2 (k=2) 2,3 2.000

Sex1 Sex2 Age Race1 Race2

0.031 0.031 0.009 0.031 0.0310.010 0.010 0.003 0.010 0.010

0.281 0.281 0.118 0.031 0.0310.094 0.094 0.039 0.010 0.010

0.031 0.031 0.079 0.281 0.2810.010 0.010 0.026 0.094 0.094

0.031 0.031 0.024 0.031 0.0310.010 0.010 0.008 0.010 0.010

0.062 0.062 0.096 0.062 0.0620.062 0.062 0.096 0.062 0.062

0.062 0.062 0.018 0.062 0.0620.062 0.062 0.018 0.062 0.062

0.062 0.062 0.002 0.062 0.0620.062 0.062 0.002 0.062 0.062

Between Group Sum of Squares for Characteristics


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Subgroup and Between SS

6

2

1

Subgroup Between SS =p

gk jk j

j

n x x

62 2

1 1

Total Between SS=p

gk jk j

k j

n x x


Subgroup TotalBetween SS Between SS

0.1340.045 0.178

0.7430.248 0.991

0.7040.235 0.939

0.1490.050 0.199

0.3460.346 0.691

0.2680.268 0.535

0.2520.252 0.504

p=5

p=5


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Total Sum of Squares and Fau


Fau-g

0.103

0.573

0.543

0.115

0.400

0.309

0.291

62 2

1 1

62 2

1 1 1

gk

pgk jk j

k jg np

ijk jk j i

n x x

Fau

x x

62 2

1 1 1

Total Sum of Squares =

gknp

ijk jk j i

x x

1,2,...7max ( )gg

Fau Fau

p=5

p=5

p=5

Total Sum of Squares

(denominator of Fau-g)

1.730

Overall Fau= 0.400

excl. 1 pers. split g=5,6,7


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DistanceDistance-g

0.238

1.321

1.251401

0.2655579

0.6912553

0.535005

0.503755


D = max (Dg) excl. 1 pers. split g=5,6,7

Overall Distance= 0.691


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SAS Faultline Calculation (Version 1.0, July 26, 2004)

1. WHAT THIS CODE DOES• faultline strength and distance for groups of size 3 to 16 (two

sets: incl and excl 1-person subgroups).

2. WHAT WE ASSUME ABOUT THE DATA• 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)

3. 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?

academy of management, new orleans, 2004 1 taking a crack at measuring faultlines sherry m.b....

Documents

academy of management

new orleans

pp pp pp pp pp pp

x slide

race sex pp hh pp hh

split g

strongest split

jehn leiden university