STATISTICAL GRAPHICS
FOR VISUALIZING DATA
Tables and Figures, I
William G. Jacoby
Michigan State University and ICPSR
University of Illinois at Chicago
October 14-15, 2010
http://polisci.msu.edu/jacoby/uic/graphics
Figure 1: Univariate Scatterplots for Distributions of Hypothetical Variables.
Table 1: Hypothetical Data Matrix Containing Four Variables and Twenty Observations.
X1
X2
X3
X4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
32.3
28.0
31.4
29.5
40.0
20.0
26.0
28.6
27.7
27.0
17.5
31.0
32.0
30.5
34.0
42.5
35.0
29.0
25.0
33.0
33.2
34.2
27.0
33.0
35.8
34.6
24.2
34.9
25.1
37.3
22.7
25.4
25.8
38.2
26.5
38.4
26.8
21.6
33.5
21.8
24.7
29.4
28.5
25.6
27.6
32.0
28.2
40.9
37.5
26.3
33.9
36.7
25.2
23.8
26.1
28.2
31.8
39.7
19.1
34.8
29.7
30.2
28.7
27.3
31.3
29.5
26.3
29.9
29.8
30.1
37.9
27.6
30.3
22.1
28.1
26.5
30.5
27.4
51.0
25.8
30.0
30.0
30.0
30.0
Mean:
Standard
Deviation:
X4
X3
Variable
Observation:
X2
X1
10
20
30
40
50
Data Values
5.8
5.8
5.8
5.8
Data Source: Table 1
Figure 2: Example of a Graphical Display for Presentation, Rather Than Analysis.
Figure 3: Candidate Vote Percentages in 2000 U.S. Presidential Election
1992 Presidential Vote Totals:
A. Tabular Display
Presidential
Candidate
Percentage of
Popular Vote
Popular Vote
(in Millions)
Bush
47.87
50.46
Gore
48.39
51.00
Nader
2.74
2.88
Other
1.01
1.06
Total
100.00
105.40
Data Source: U.S. Federal Election Commission
Figure 4: Partisanship of State Electorates, 1992.
Figure 3: Candidate Vote Percentages in 2000 U.S. Presidential Election
A. Tabular Display
B. Graphical Display
States and
Partisanship Scores*
WY
UT
ID
SD
NE
AZ
VT
DE
NV
VA
ND
NH
OR
MS
NJ
MI
CT
IN
SC
KS
FL
IL
CO
WA
Presidential Candidate
Other
Nader
Gore
Bush
0
10
20
30
40
50
Percentage of 2000 Popular Vote
-0.488
-0.322
-0.260
-0.161
-0.140
-0.133
-0.109
-0.091
-0.090
-0.089
-0.068
-0.064
-0.054
-0.045
-0.044
-0.044
-0.022
-0.008
-0.007
0.006
0.007
0.013
0.019
0.021
CA
NM
AL
MN
OH
PA
WI
MO
NY
TX
ME
IA
NC
MT
RI
WV
TN
OK
MA
GA
MD
LA
AR
KY
0.023
0.029
0.029
0.031
0.031
0.042
0.046
0.052
0.053
0.055
0.092
0.100
0.107
0.108
0.128
0.130
0.142
0.156
0.158
0.180
0.185
0.261
0.267
0.301
Data Source: U.S. Federal Election Commission
Data Source: Gerald C. Wright.
Figure 4: Partisanship of State Electorates, 1992.
Figure 5: Party Affiliation by Age Groups within the American Electorate, 1992.
B. Graphical Display
A. Tabular Display
Party Affiliation:*
Percent of Total
30
Age Group:
Democrats
Independents
Republicans
18-24
27.18
32.62
38.65
36.74
45.00
45.91
46.29
52.38
49.74
40.29
34.15
36.46
26.25
29.57
21.14
9.52
23.08
27.09
27.20
26.80
28.75
24.51
32.57
38.10
25-34
35-44
45-54
55-64
65-74
75-84
85-94
20
10
* Table entries are row percentages.
0
-0.4
-0.2
0.0
Partisanship of State Electorate
Data Source: Gerald C. Wright.
0.2
Data Source: CPS 1992 National Election Study.
Figure 6: Graphical Perception Tasks, Ordered from Most Accurate to Least Accurate.
Figure 5: Party Affiliation by Age Groups within the American Electorate, 1992.
B. Graphical Display
A. Position Along a
Common Scale
B. Position Along Common,
Nonaligned Scales
C. Length
D. Angle*
E. Slope, Direction*
F. Area
G. Volume
H. Fill Density, Color
Saturation
60
Party Identification (Percentage)
50
40
Democrat
Independent
Republican
30
20
10
0
18-24
25=34
35-44
45-54
55-64
65-74
75-84
85-95
Age Group
* Perceptual judgments about angles and slopes/directions are carried out with equal accuracy, so their
relative ordering in this figure is arbitrary.
Data Source: CPS 1992 National Election Study.
Source: Created from information provided in Cleveland (1994).
STATISTICAL GRAPHICS
FOR VISUALIZING DATA
Tables and Figures, II
William G. Jacoby
Michigan State University and ICPSR
University of Illinois at Chicago
October 14-15, 2010
http://polisci.msu.edu/jacoby/uic/graphics
Figure 8D: Unidimensional Scatterplot of 1992 State Policy Priority Scores.
0.47
0.49 0.51 0.53 0.55 0.57
State Policy Priority Scores, 1992
Data Source: Schneider and Jacoby (2004).
Figure 8E:
Unidimensional Scatterplot of 1992 State Policy Priority Scores.
0.47
0.49 0.51 0.53 0.55 0.57
State Policy Priority Scores, 1992
Data Source: Schneider and Jacoby (2004).
0.47
0.49 0.51 0.53 0.55 0.57
State Policy Priority Scores, 1992
Figure 8G: Unidimensional Scatterplot of 1992 State Policy Priority Scores.
Data Source: Schneider and Jacoby (2004).
0.49 0.51 0.53 0.55 0.57
State Policy Priority Scores, 1992
Unidimensional Scatterplot of 1992 State Policy Priority Scores.
0.47
Figure 8F:
0.48 0.50 0.52 0.54 0.56
State Policy Priorities, 1982-2000
0.48 0.50 0.52 0.54 0.56
State Policy Priorities, 1982-2000
Data Source: Schneider and Jacoby (2004).
0.46
Figure 9B: Unidimensional Scatterplot of State Policy Priority Scores, 1982-2000
Data Source: Schneider and Jacoby (2004).
0.46
Figure 9A: Unidimensional Scatterplot of State Policy Priority Scores, 1982-2000
150
200
Medicaid Program Quality Score
250
120
140
160
180
200
220
Medicaid Program Quality Score
Data Source: Public Citizen Health Research Group
Note: Bin origin at 120, bin width is 20.
0
5
10
15
20
240
260
280
Figure 10C: Histogram of 1986 State Medicaid Program Quality Scores.
Data Source: Public Citizen Health Research Group
0
5
10
15
20
Figure 10B: Histogram of 1986 State Medicaid Program Quality Scores.
Percent of Total
Percent of Total
120
140
160
180
200
220
240
Medicaid Program Quality Score
260
280
120
140
160
180
200
220
240
Medicaid Program Quality Score
Data Source: Public Citizen Health Research Group
Note: Bin origin at 120, bin width is 10.
0
2
4
6
8
10
260
280
Figure 10E: Histogram of 1986 State Medicaid Program Quality Scores.
Data Source: Public Citizen Health Research Group
Note: Bin origin at 125, bin width is 20.
0
5
10
15
20
25
Figure 10D: Histogram of 1986 State Medicaid Program Quality Scores.
Percent of Total
Percent of Total
120
140
160
180
200
220
Medicaid Program Quality Score
240
260
280
0.010
0.015
150
200
Medicaid Program Quality Score
Data Source: Public Citizen Health Research Group
0.0
0.005
100
250
300
Figure 11: Smoothed Histogram of 1986 State Medicaid Program Quality Scores.
Data Source: Public Citizen Health Research Group
Note: Bin origin at 120, bin width is 10.
0
2
4
6
8
10
12
14
Figure 10F: Histogram of 1986 State Medicaid Program Quality Scores.
Percent of Total
Density
D. Bandwidth, h = 20
C. Bandwidth, h = 15
Source: Public Citizen Health Research Group.
B. Bandwidth, h = 10
A. Bandwidth h = 5
Changing the Bandwidth on Smoothed Histograms of Medicaid Program Quality Data.
D. Smoothed Histogram
C. Summing Heights of Kernel Densities
Figure 13:
B. Data Shown as Kernel Densities
A. Univariate Scatterplot of 10 Data Points
Constructing a Smoothed Histogram from Hypothetical Data:
0.54
0.56
Figure 14: The Box Plot– State Policy Priorities, 1982-2000 .
State Education Spending, 1992 ($ Billions)
0
5
10
15
20
25
30
Figure 15A: Box Plots and Outliers
0.46
0.48
0.50
0.52
State Policy Priorities, 1982-2000
0.46
0.48
0.50
0.52
0.54
0.56
MIDWEST
Region
NORTHEAST
Data Source: Schneider and Jacoby (2004)
State Policy Priorities, 1982-2000
SOUTH
WEST
Figure 16: Parallel Box Plots of 1982-2000 State Policy Priorities by Region.
0
5
10
15
20
25
30
Figure 15B: Box Plots and Outliers
State Education Spending, 1992 ($ Billions)
Figure 18:
140
180
200
220
240
Medicaid Program Quality Score
160
260
Dot Plot of Median State Medicaid Program Quality Scores within Regions
MN
WI
NY
MA
CT
CA
NJ
WA
OR
MI
DC
ME
IA
MD
VT
RI
HI
IL
PA
NE
KS
UT
MT
KY
CO
GA
WV
OH
IN
FL
ND
AK
DE
SC
TN
NC
NM
NH
LA
TX
OK
VA
ID
NV
SD
AR
MO
AL
AZ
WY
MS
Figure 17: Dot Plot of State Medicaid Program Quality Scores.
State
170
180
190
200
210
220
Median Program Quality Score for States within Region
South
West
Midwest
Northeast
50
100
150
200
Median Program Quality Score for States within Region
0
B. Minimum Scale Value Set to Zero
NY
MA
NH
CA
ME
PA
NJ
CT
MN
VT
KY
WV
LA
MI
OH
WI
TN
WA
MD
IL
ND
AR
GA
MO
OK
AZ
IA
IN
MS
SC
NM
AL
OR
NE
NC
TX
CO
WY
SD
MT
FL
UT
KS
NV
ID
VA
0.2
0.4
0.6
0.8
1.0
1.2
1992 State Welfare Spending (Dollars per Capita)
0.0
Figure 20: Dot Plot Showing 1992 Social Welfare Expenditures in the American States.
South
West
Midwest
Northeast
A. Scale Minimum Value Set Arbitrarily
State
Region
Figure 19: Bar Charts, Scale Limits, and Visual Perception
Region
2.3
2.5
2.6
Mean importance rating
2.4
2.7
Data Source: 1994 Multi-Investigator Study.
Note: The plotted points correspond to the mean importance rating assigned to each of the values, on a scale ranging from a minimum
of zero to a maximum of three. The horizontal error bars show 95% confidence intervals for each of the means. Nonoverlapping
confidence intervals imply that the means are reliably different from each other; that is, their difference is probably not merely due
to sampling error.
Social Order
Equality
Liberty
Economic Security
Figure 21: Value Importance Ratings in the American Public.
Value
STATISTICAL GRAPHICS
FOR VISUALIZING DATA
Tables and Figures, III
William Jacoby
Michigan State University and ICPSR
University of Illinois at Chicago
October 14-15, 2010
http://polisci.msu.edu/jacoby/uic/graphics
Table 1: The following table shows four bivariate datasets. Each one contains eleven hypothetical
observations on two variables. The variables are designated X1 and Y1 in the first dataset, X2 and
Y2 in the second dataset, and so on. These datasets have a remarkable feature: They produce
identical regression results. When the Y variable is regressed on the X variable in each of these
datasets, the following equation is produced (the figures in parentheses are standard errors):
15
15
10
10
Because the OLS estimates are identical for each of the four datasets, one could easily conclude
that they all have the same bivariate structure.
Y(2)
R2 = 0.67
Y(1)
Yi = 3.00 + 0.50 Xi + ei
(1.12) (0.12)
Figure 1: The following bivariate scatterplots show the relationships within each of the four datasets listed
in Table 1. Clearly, these datasets differ markedly from each other, contrary to the conclusions
that one might reach based upon the OLS regression estimates, alone.
5
5
0
X2
Y2
X3
Y3
X4
Y4
10.0
8.0
13.0
9.0
11.0
14.0
6.0
4.0
12.0
7.0
5.0
8.04
6.95
7.58
8.81
8.33
9.96
7.24
4.26
10.84
4.82
5.68
10.0
8.0
13.0
9.0
11.0
14.0
6.0
4.0
12.0
7.0
5.0
9.14
8.14
8.74
8.77
9.26
8.10
6.13
3.10
9.13
7.26
4.74
10.0
8.0
13.0
9.0
11.0
14.0
6.0
4.0
12.0
7.0
5.0
7.46
6.77
12.74
7.11
7.81
8.84
6.08
5.39
8.15
6.42
5.73
8.0
8.0
8.0
8.0
8.0
8.0
8.0
19.0
8.0
8.0
8.0
6.58
5.76
7.71
8.84
8.47
7.04
5.25
12.50
5.56
7.91
6.89
0
0
5
10
15
20
0
5
10
X(1)
15
20
15
20
X(2)
15
15
10
10
Y(4)
Y1
Y(3)
X1
5
5
Data Source: Anscombe, F. J. (1973) “Graphs in Statistical Analysis.” American Statistician 27: 17-21.
0
0
0
5
10
15
20
0
5
10
X(3)
Figure 2: A poorly-constructed scatterplot.
X(4)
Figure 3: A Better Version of the scatterplot
100
100
90
80
POLICY
70
60
50
Policy priorities
80
60
40
40
30
20
20
10
0
400 450 500 550 600 650 700 750 800
GOVSIZE
0
400
500
600
Size of government
700
800
Figure 4A: Transforming variable values in order to improve visual resolution in a scatterplot.
Figure 4B: Transforming variable values in order to improve visual resolution in a scatterplot.
Log (base 2) welfare spending, 1992
Welfare spending, 1992 ($ billions)
10
8
6
4
2
4
1
2^-2
2^-4
0
0
2
4
6
8
10
12
14
2^-2
Education spending, 1992 ($ billions)
2^-1
1
2
Data Source: 1994 Statistical Abstract of the United States.
Data Source: 1994 Statistical Abstract of the United States.
Figure 5A: Jittering to reduce overplotting of data points
Figure 5B: Jittering to reduce overplotting of data points
8
8
6
6
Ideological self-placement
Ideological self-placement
4
8
Log (base 2) education spending, 1992
4
2
4
2
0
0
0
2
4
Party identification
Data Source: CPS 2000 American National Election Study.
6
8
0
2
4
Party identification
Data Source: CPS 2000 American National Election Study.
6
8
Figure 6: Robbery Rates Versu
sB
u
rglary Rates in the American States,19
9
1.
Figure 7A: Point labels in scatterplots.
100
WY
ID
MT
Policy priorities
80
NV
UT DE
60
40
PA
ND
KS
NM
WV VT IA
SD
NC
CO
OK
AR
WA
VA
AZ
KY
MS NE
IN
FL
OR
MN TX
MO
AL
WI SC GA
OH
LA
NJ
MD
IL ME
TN
CA
RIMI
CT
20
NY
NH
MA
0
400
500
600
Size of government
Sou
rce:
Data Source: Jacoby and Schneider (2001)
1992 Statistical Abstract of the United States.
40
20
NY
NH
0
MA
400
500
600
Size of government
Data Source: Jacoby and Schneider (2001)
700
800
B. Slicing Intervals
C. Box Plots from Sliced Scatterplot
60
u
Policy priorities
80
A. Basic Scatterplot
WY
Figure 8:
100
Slicing a Scatterplot of the Relationship Between 1980 GNP per Capita and
Infant Mortality Rates.
Figure 7B: Point labels in scatterplots.
700
800
Figure 9A: The relationship between education and voter turnout in the American states, 1992.
Figure 9B: The relationship between education and voter turnout in the American states, 1992.
75
1992 state voter turnout (percentage)
1992 state voter turnout (percentage)
75
70
65
60
55
70
65
60
55
65
70
75
80
85
65
1992 state high school graduation rate (percentage)
70
75
80
85
1992 state high school graduation rate (percentage)
Data Source: 1994 Statistical Abstract of the United States
Data Source: 1994 Statistical Abstract of the United States
Figure 9C: The relationship between education and voter turnout in the American states, 1992.
Figure 10: Example of a loess "local fitting window" and tricube weights (hypothetical data)
75
70
Values of Y
1992 state voter turnout (percentage)
8
65
60
6
4
55
2
65
70
75
80
85
1992 state high school graduation rate (percentage)
Data Source: 1994 Statistical Abstract of the United States
2
4
6
Values of X
8
10
Figure 11: Illustration of Loess Fitting Procedure Using Hypothetical Data.
A. Hypothetical Data for Loess Fit.
Figure 11: Illustration of Loess Fitting Procedure (Continued).
B. Window for vj=5.5 and =0.6.
E. Complete Set of Fitted Values.
C. Tricube Neighborhood Weights.
D. Initial Regression Line and Fitted Value.
Figure 12: Effect of the Parameter on the Loess Smooth Curve.
A. Loess Curve with = 0.15
A. Residuals from curve fitted with = .65
75
70
65
60
55
70
10
65
5
60
55
65
70
75
80
85
65
1992 state high school graduation rate (percentage)
70
75
80
85
1992 state high school graduation rate (percentage)
C. Loess Curve with = 0.75
D. Loess Curve with = 1.00
75
1992 state voter turnout (percentage)
75
70
65
60
55
70
75
80
85
1992 state high school graduation rate (percentage)
0
-5
-10
70
65
65
70
75
80
85
1992 state high school graduation rate (percentage)
60
55
65
Loess Residuals
1992 state voter turnout (percentage)
1992 state voter turnout (percentage)
Figure 13A: Residual Plot from Loess Curve Fitted to State Education and Voter Turnout Data
B. Loess Curve with = 0.35
75
1992 state voter turnout (percentage)
F. Loess Curve
65
70
75
80
85
1992 state high school graduation rate (percentage)
Figure 14: Effect of the Parameter on a Loess Smooth Curve.
Figure 13: Residual Plots for Loess Curves Fitted with Different Values.
A. Loess Curve Fitted with = 1 and = 0.50
B. Loess Curve Fitted with = 2 and = 0.50
10
5
5
0
0
-5
-5
-10
-10
40
Percent for Mondale Minus Percent for Hart
10
Percent for Mondale Minus Percent for Hart
C. Residual Plot for Loess Curve Fitted with = 1.00
Loess Residuals
Loess Residuals
B. Residual Plot for Loess Curve Fitted with = 0.15
20
0
-20
-40
65
70
75
80
85
65
1992 state high school graduation rate (percentage)
70
75
80
40
20
0
-20
-40
85
0
1992 state high school graduation rate (percentage)
50
100
150
0
Number of Days into the 1984 Primary Campaign
50
100
150
Number of Days into the 1984 Primary Campaign
Note: The data show public preferences between Walter Mondale and Gary Hart (among Democrats only) during the 1984
Presidential primary campaign. Data source is the 1984 CPS Continuous Monitoring Survey.
Figure 15: The Effect of Including Robustness Weights in the Loess Fitting Process.
Figure 1
6
:
Residual-Fit Spread Plot for Robust Loess Fit, Occupational Prestige and Income
100
0.0
80
40
60
20
Prestige rating for occupation
Prestige Rating for Occupation
Fitted Values minus Mean
40
20
20
30
0
-20
40
Mean Income for Occupation
-60
0.0
Note: The data are fifteen observations sampled from the Duncan Occupational Prestige Dataset. The solid line in the
figure represents the robust loess fit. The dotted line shows the loess fit obtained without robustness iterations.
0.2
0.4
0.6
0.8
0.4
0.6
Residuals
-40
10
0.2
1.0
p-value
0.8
1.0
0.0
0
-20
-40
0.0
0.2
0.4
0.6
0.8
p-value
1.0
0.4
Residuals
0.6
0.8
1.0
10
30
0
10
20
30
40
20
40
60
Month
80
100
120
20
40
Month
60
80
100
B. Aspect Ratio Banked to 45 Degrees
0
A. Aspect Ratio Set to 1.0
120
Plot of Hypothetical Data on Voter Registration Figures by
Month, to show the Effects of Aspect Ratio on Visual
Perception.
20
0.2
Figure 1
8
:
-60
Number Registered
Policy priorities
Fitted Values minus Mean
Number Registered
Figure 1
7
:
Residual-Fit Spread Plot for OLS Fit, Policy Priorities and Government Size
STATISTICAL GRAPHICS
FOR VISUALIZING DATA
Tables and Figures, IV
William Jacoby
Michigan State University and ICPSR
University of Illinois at Chicago
October 14-15, 2010
http://polisci.msu.edu/jacoby/uic/graphics
Incumbent margin of victory (percentage)
-20
0
20
40
60
80
$10,000
$100,000
$1,000,000
Challenger spending, in $1,000's (logarithmic scale)
0
5
10
15
20
Number of terms served by incumbent
Incumbent
victory
margin
Logged
challenger
spending
Terms served
by incumbent
Figure 2: Three-dimensional scatterplot showing the trivariate relationship between incumbent margin
of victory, challenger spending, and incumbent longevity in office.
$1,000
-20
0
20
40
60
80
Figure 1: Bivariate scatterplots showing two possible influences on incumbent margin of victory in the
2006 congressional elections.
Incumbent margin of victory (percentage)
25
Logged
challenger
spending
Terms served
by incumbent
Incumbent
victory
margin
Logged
challenger
spending
Terms served
by incumbent
Figure 3: Adding motion to a three-dimensional scatterplot to enhance visual perception of threedimensional structure.
Incumbent
victory
margin
Figure 3: Adding motion to a three-dimensional scatterplot to enhance visual perception of threedimensional structure.
Logged
challenger
spending
Terms served
by incumbent
0
10
20
30
40
Incumbent
victory
margin
Logged
challenger
spending
Terms served
by incumbent
-10
0
10
20
30
40
50
60
Figure 5: Three-dimensional plot showing fitted surface for the nonparametric regression (loess) of
incumbent margin of victory on challenger spending, and incumbent longevity in office.
Incumbent
victory
margin
50
60
Figure 4: Three-dimensional plot showing the OLS surface for the regression of incumbent margin of
victory on challenger spending, and incumbent longevity in office.
Logged
challenger
spending
Terms served
by incumbent
Incumbent
victory
margin
spending
Logged
challenger
Terms served
by incumbent
Figure 7: Scatterplot matrix for data on 2006 congressional elections.
Incumbent
victory
margin
Figure 6: Three-dimensional scatterplot showing the trivariate relationship between incumbent margin
of victory, challenger spending, and incumbent longevity in office (Figure 2, repeated).
Incumbent
victory
margin
spending
Logged
challenger
Terms served
by incumbent
Figure 9: Scatterplot matrix with bivariate loess curves for data on 2006 congressional elections.
Incumbent
victory
margin
spending
Logged
challenger
Terms served
by incumbent
Figure 8: Scatterplot matrix with bivariate OLS lines for data on 2006 congressional elections.
0
5
15
Range of data values in each slice
10
20
25
-20
0
20
40
60
80
$1K
$1K
$10K $100K $1000K
Incumbent terms
Incumbent terms
$1K
$10K $100K $1000K
Incumbent terms
Incumbent terms
Challenger spending, in $1,000's (logarithmic scale)
$10K $100K $1000K
Incumbent terms
Incumbent terms
-20
0
20
40
60
80
Figure 11: Trellis display showing incumbent victory margin versus challenger spending, conditioned
on incumbent number of terms in office.
1
2
3
4
5
6
Figure 10: Creating conditioning slices from variable measuring number of incumbent terms.
Equally-populated slices from incumbent n of terms
Incumbent margin of victory (percentage)
$1K
$1K
$10K $100K $1000K
Challenger spending, in $1,000's (logarithmic scale)
$10K $100K $1000K
Incumbent terms
Incumbent terms
-20
0
20
40
60
80
-20
0
20
40
60
80
0
5
10
15
20
0
5
10
15
Logged spending
Logged spending
20
0
5
10
15
Logged spending
Logged spending
Number of terms served by incumbent
Logged spending
Logged spending
20
-20
0
20
40
60
80
Figure 13: Trellis display showing incumbent victory margin versus incumbent number of terms,
conditioned on logged challenger spending (bivariate loess curves added to each panel).
-20
0
20
40
60
80
Incumbent terms
Incumbent terms
$10K $100K $1000K
Incumbent terms
Incumbent terms
$1K
Figure 12: Trellis display showing incumbent victory margin versus challenger spending, conditioned
on incumbent number of terms in office (bivariate loess curves added to each panel).
Incumbent margin of victory (percentage)
Incumbent margin of victory (percentage)
0
20
40
60
80
100
300
Interest group strength
200
400
500
0
20
40
60
80
100
500
600
700
Size of state government (employees per capita)
1
2
3
4
5
6
600
700
Range of data values (government size) in each slice
500
800
Figure 15: Conditioning slices from variable measuring size of state government, with two-thirds
overlap between adjacent slices.
100
Equally-populated slices, 2/3 overlap in adjacent slices
Policy priority
Figure 14: Bivariate scatterplots showing two possible influences on 1992 state policy priorities.
Policy priority
800
100 200 300 400 500
Interest group strength
Govt. size
Govt. size
100 200 300 400 500
Govt. size
Govt. size
0
20
40
60
80
100
0
20
40
60
80
100
500
700
800
500
600
700
800
Interest grp. strength
Interest grp. strength
500
600
700
800
Interest grp. strength
Interest grp. strength
Size of state government (employees per capita)
600
Interest grp. strength
Interest grp. strength
0
20
40
60
80
100
Figure 17: The relationship between 1992 state policy priorities and state government size, conditioned
on interest group strength (Bivariate OLS line shown within each panel).
0
20
40
60
80
100
Govt. size
Govt. size
100 200 300 400 500
Figure 16: The relationship between 1992 state policy priorities and interest group strength within
state, conditioned on size of state government (Bivariate OLS line shown within each
panel).
Policy priority
Policy priority
State
electorate
partisanship
0
20
40
60
80
100
0
20
40
60
80
100
Govt size
Partisanship
Govt size
Partisanship
Interest group strength
100 200 300 400 500
Govt size
Partisanship
Govt size
Partisanship
100 200 300 400 500
Govt size
Partisanship
Govt size
Partisanship
100 200 300 400 500
Govt size
Partisanship
Govt size
Partisanship
Govt size
Partisanship
0
20
40
60
80
100
Figure 19: Relationship between 1992 state policy priorities and interest group strength, conditioned on
size of state government and electorate partisanship (bivariate OLS line shown in panels).
State
policy
priority
Interest
group
strength
State
government
size
Figure 18: Scatterplot matrix for 1992 state policy priority data.
State policy priority
500 600 700 800
Int grp strength
Partisanship
Int grp strength
Partisanship
500 600 700 800
Int grp strength
Partisanship
Int grp strength
Partisanship
Int grp strength
Partisanship
Size of state government
500 600 700 800
Int grp strength
Partisanship
Int grp strength
Partisanship
Int grp strength
Partisanship
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
Govt size
Int grp strength
Govt size
Int grp strength
-0.4 -0.2 0.0 0.2
Govt size
Int grp strength
Govt size
Int grp strength
Govt size
Int grp strength
Partisanship of state electorate
-0.4 -0.2 0.0 0.2
Govt size
Int grp strength
Govt size
Int grp strength
-0.4 -0.2 0.0 0.2
Govt size
Int grp strength
Govt size
Int grp strength
0
20
40
60
80
100
Figure 21: Relationship between 1992 state policy priorities and electorate partisanship, conditioned
on interest group strength and state government size (bivariate OLS line shown in panels).
0
20
40
60
80
100
0
20
40
60
80
100
Int grp strength
Partisanship
Figure 20: Relationship between 1992 state policy priorities and state government size, conditioned on
interest group strength and electorate partisanship (bivariate OLS line shown in panels).
State policy priority
State policy priority