STATISTICAL GRAPHICS FOR VISUALIZING DATA

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, 21 http://polisci.msu.edu/jacoby/uic/graphics

Table 1: Hypothetical Data Matrix Containing Four Variables and Twenty Observations. Figure 1: Univariate Scatterplots for Distributions of Hypothetical Variables. Observation: X 1 X 2 X 3 X 4 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 32.3 28. 31.4 29.5 4. 2. 26. 28.6 27.7 27. 17.5 31. 32. 3.5 34. 42.5 35. 29. 25. 33. 33.2 34.2 27. 33. 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. 28.2 4.9 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 3.2 28.7 27.3 31.3 29.5 26.3 29.9 29.8 3.1 37.9 27.6 3.3 22.1 28.1 26.5 3.5 27.4 51. 25.8 Mean: 3. 3. 3. 3. Standard Deviation: 5.8 5.8 5.8 5.8 Variable X4 X3 X2 X1 1 2 3 4 5 Data Values Data Source: Table 1 Figure 2: Example of a Graphical Display for Presentation, Rather Than Analysis. Figure 3: Candidate Vote Percentages in 2 U.S. Presidential Election 1992 Presidential Vote Totals: A. Tabular Display Presidential Candidate Percentage of Popular Vote Popular Vote (in Millions) Bush 47.87 5.46 Gore 48.39 51. Nader 2.74 2.88 Other 1.1 1.6 Total 1. 15.4 Data Source: U.S. Federal Election Commission

Figure 3: Candidate Vote Percentages in 2 U.S. Presidential Election B. Graphical Display Figure 4: Partisanship of State Electorates, 1992. A. Tabular Display Presidential Candidate Other Nader Gore Bush 1 2 3 4 5 Percentage of 2 Popular Vote WY -.488 UT -.322 ID -.26 SD -.161 NE -.14 AZ -.133 VT -.19 DE -.91 NV -.9 VA -.89 ND -.68 NH -.64 OR -.54 MS -.45 NJ -.44 MI -.44 CT -.22 IN -.8 SC -.7 KS.6 FL.7 IL.13 CO.19 WA.21 States and Partisanship Scores* CA.23 NM.29 AL.29 MN.31 OH.31 PA.42 WI.46 MO.52 NY.53 TX.55 ME.92 IA.1 NC.17 MT.18 RI.128 WV.13 TN.142 OK.156 MA.158 GA.18 MD.185 LA.261 AR.267 KY.31 Data Source: U.S. Federal Election Commission Data Source: Gerald C. Wright. Figure 4: Partisanship of State Electorates, 1992. B. Graphical Display Figure 5: Party Affiliation by Age Groups within the American Electorate, 1992. A. Tabular Display Percent of Total 3 2 1 Party Affiliation:* Age Group: Democrats Independents Republicans 18-24 25-34 35-44 45-54 55-64 65-74 75-84 85-94 27.18 32.62 38.65 36.74 45. 45.91 46.29 52.38 49.74 4.29 34.15 36.46 26.25 29.57 21.14 9.52 23.8 27.9 27.2 26.8 28.75 24.51 32.57 38.1 * Table entries are row percentages. -.4 -.2..2 Partisanship of State Electorate Data Source: CPS 1992 National Election Study. Data Source: Gerald C. Wright.

Figure 5: Party Affiliation by Age Groups within the American Electorate, 1992. Figure 6: Graphical Perception Tasks, Ordered from Most Accurate to Least Accurate. B. Graphical Display A. Position Along a Common Scale B. Position Along Common, Nonaligned Scales C. Length D. Angle* 6 5 Party Identification (Percentage) 4 3 2 Democrat Independent Republican E. Slope, Direction* F. Area G. Volume H. Fill Density, Color Saturation 1 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, 21 http://polisci.msu.edu/jacoby/uic/graphics

Figure 8D: Unidimensional Scatterplot of 1992 State Policy Priority Scores..47.49.51.53.55.57 State Policy Priority Scores, 1992 Data Source: Schneider and Jacoby (24). Figure 8E: Unidimensional Scatterplot of 1992 State Policy Priority Scores..47.49.51.53.55.57 State Policy Priority Scores, 1992 Data Source: Schneider and Jacoby (24).

Figure 8F: Unidimensional Scatterplot of 1992 State Policy Priority Scores..47.49.51.53.55.57 State Policy Priority Scores, 1992 Data Source: Schneider and Jacoby (24). Figure 8G: Unidimensional Scatterplot of 1992 State Policy Priority Scores..47.49.51.53.55.57 State Policy Priority Scores, 1992

Figure 9A: Unidimensional Scatterplot of State Policy Priority Scores, 1982-2.46.48.5.52.54.56 State Policy Priorities, 1982-2 Data Source: Schneider and Jacoby (24). Figure 9B: Unidimensional Scatterplot of State Policy Priority Scores, 1982-2.46.48.5.52.54.56 State Policy Priorities, 1982-2 Data Source: Schneider and Jacoby (24).

Figure 1B: Histogram of 1986 State Medicaid Program Quality Scores. 2 Percent of Total 15 1 5 15 2 25 Medicaid Program Quality Score Data Source: Public Citizen Health Research Group Figure 1C: Histogram of 1986 State Medicaid Program Quality Scores. 2 Percent of Total 15 1 5 12 14 16 18 2 22 24 26 28 Medicaid Program Quality Score Note: Bin origin at 12, bin width is 2. Data Source: Public Citizen Health Research Group

Figure 1D: Histogram of 1986 State Medicaid Program Quality Scores. 25 2 Percent of Total 15 1 5 12 14 16 18 2 22 24 26 28 Medicaid Program Quality Score Note: Bin origin at 125, bin width is 2. Data Source: Public Citizen Health Research Group Figure 1E: Histogram of 1986 State Medicaid Program Quality Scores. 1 8 Percent of Total 6 4 2 12 14 16 18 2 22 24 26 28 Medicaid Program Quality Score Note: Bin origin at 12, bin width is 1. Data Source: Public Citizen Health Research Group

Figure 1F: Histogram of 1986 State Medicaid Program Quality Scores. 14 12 1 Percent of Total 8 6 4 2 12 14 16 18 2 22 24 26 28 Medicaid Program Quality Score Note: Bin origin at 12, bin width is 1. Data Source: Public Citizen Health Research Group Figure 11: Smoothed Histogram of 1986 State Medicaid Program Quality Scores..15.1 Density.5. 1 15 2 25 3 Medicaid Program Quality Score Data Source: Public Citizen Health Research Group

Constructing a Smoothed Histogram from Hypothetical Data: A. Univariate Scatterplot of 1 Data Points B. Data Shown as Kernel Densities C. Summing Heights of Kernel Densities D. Smoothed Histogram Figure 13: Changing the Bandwidth on Smoothed Histograms of Medicaid Program Quality Data. A. Bandwidth h = 5 B. Bandwidth, h = 1 C. Bandwidth, h = 15 D. Bandwidth, h = 2 Source: Public Citizen Health Research Group.

Figure 14: The Box Plot State Policy Priorities, 1982-2..56 State Policy Priorities, 1982-2.54.52.5.48.46 Figure 15A: Box Plots and Outliers 3 State Education Spending, 1992 ($ Billions) 25 2 15 1 5

Figure 15B: Box Plots and Outliers 3 State Education Spending, 1992 ($ Billions) 25 2 15 1 5 Figure 16: Parallel Box Plots of 1982-2 State Policy Priorities by Region..56 State Policy Priorities, 1982-2.54.52.5.48.46 MIDWEST NORTHEAST SOUTH WEST Region Data Source: Schneider and Jacoby (24)

Figure 17: Dot Plot of State Medicaid Program Quality Scores. State MN NY WI MA CT CA WA NJ OR DC MI ME MD IA VT RI HI NE PA IL KS UT MT CO KY GA WV OH ND FL IN DE AK SC NM NC TN NH OK TX LA VA NV ID MO AR SD WY AZ AL MS 14 16 18 2 22 24 26 Medicaid Program Quality Score Figure 18: Dot Plot of Median State Medicaid Program Quality Scores within Regions

Figure 19: Bar Charts, Scale Limits, and Visual Perception A. Scale Minimum Value Set Arbitrarily Northeast B. Minimum Scale Value Set to Zero Northeast Midwest Midwest Region Region West West South South 17 18 19 2 21 22 Median Program Quality Score for States within Region 5 1 15 2 Median Program Quality Score for States within Region Figure 2: Dot Plot Showing 1992 Social Welfare Expenditures in the American States. State NY MA NH CA ME PA MN CT NJ WV KY VT LA OH MI TN WI WA MD ND IL MO GA AR OK AZ MS IN IA NM SC OR AL NC NE CO TX WY SD MT UT FL NV KS VA ID..2.4.6.8 1. 1.2 1992 State Welfare Spending (Dollars per Capita)

Figure 21: Value Importance Ratings in the American Public. Value Economic Security Liberty Equality Social Order 2.3 2.4 2.5 2.6 2.7 Mean importance rating 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. Data Source: 1994 Multi-Investigator Study.

STATISTICAL GRAPHICS FOR VISUALIZING DATA Tables and Figures, III William Jacoby Michigan State University and ICPSR University of Illinois at Chicago October 14-15, 21 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 X 1 and Y 1 in the first dataset, X 2 and Y 2 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): 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. 15 15 Y i = 3. +.5 X i + e i R 2 =.67 (1.12) (.12) 1 1 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(1) 5 Y(2) 5 X 1 Y 1 X 2 Y 2 X 3 Y 3 X 4 Y 4 1. 8. 13. 9. 11. 14. 6. 4. 12. 7. 5. 8.4 6.95 7.58 8.81 8.33 9.96 7.24 4.26 1.84 4.82 5.68 1. 8. 13. 9. 11. 14. 6. 4. 12. 7. 5. 9.14 8.14 8.74 8.77 9.26 8.1 6.13 3.1 9.13 7.26 4.74 1. 8. 13. 9. 11. 14. 6. 4. 12. 7. 5. 7.46 6.77 12.74 7.11 7.81 8.84 6.8 5.39 8.15 6.42 5.73 8. 8. 8. 8. 8. 8. 8. 19. 8. 8. 8. 6.58 5.76 7.71 8.84 8.47 7.4 5.25 12.5 5.56 7.91 6.89 15 1 5 1 15 2 X(1) 15 1 5 1 15 2 X(2) Y(3) Y(4) 5 5 Data Source: Anscombe, F. J. (1973) Graphs in Statistical Analysis. American Statistician 27: 17-21. 5 1 15 2 X(3) 5 1 15 2 X(4) Figure 2: A poorly-constructed scatterplot. Figure 3: A Better Version of the scatterplot 1 1 9 8 8 POLICY 7 6 5 4 Policy priorities 6 4 3 2 2 1 4 45 5 55 6 65 7 75 8 GOVSIZE 4 5 6 7 8 Size of government

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. 1 Welfare spending, 1992 ($ billions) 8 6 4 2 Log (base 2) welfare spending, 1992 4 1 2^-2 2^-4 2 4 6 8 1 12 14 Education spending, 1992 ($ billions) 2^-2 2^-1 1 2 4 8 Log (base 2) education spending, 1992 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 4 Ideological self-placement 4 2 2 2 4 6 8 Party identification 2 4 6 8 Party identification Data Source: CPS 2 American National Election Study. Data Source: CPS 2 American National Election Study.

Figure 6: Robbery Rates Versus Burglary Rates in the American States,191. Figure 7A: Point labels in scatterplots. 1 WY Policy priorities 8 6 4 2 PA ID MT NV UT DE ND KS NM WV VTIA CO NCSD WA AR OK VA AZ KY IN MS NE FL ORMN TX MO AL WI SC GA OH LA MD NJ IL ME TN CA RIMI CT NH MA NY 4 5 6 7 8 Size of government Source: 1992 Statistical Abstract of the United States. Data Source: Jacoby and Schneider (21) Figure 7B: Point labels in scatterplots. Policy priorities 1 8 6 4 2 WY NY NH MA 4 5 6 7 8 Size of government Figure 8: Slicing a Scatterplot of the Relationship Between 198 GNP per Capita and Infant Mortality Rates. A. Basic Scatterplot B. Slicing Intervals u C. Box Plots from Sliced Scatterplot Data Source: Jacoby and Schneider (21)

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 75 1992 state voter turnout (percentage) 7 65 6 1992 state voter turnout (percentage) 7 65 6 55 55 65 7 75 8 85 1992 state high school graduation rate (percentage) 65 7 75 8 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 1: Example of a loess "local fitting window" and tricube weights (hypothetical data) 75 8 1992 state voter turnout (percentage) 7 65 6 Values of Y 6 4 55 2 65 7 75 8 85 1992 state high school graduation rate (percentage) 2 4 6 8 1 Values of X Data Source: 1994 Statistical Abstract of the United States

Figure 11: Illustration of Loess Fitting Procedure Using Hypothetical Data. Figure 11: Illustration of Loess Fitting Procedure (Continued). A. Hypothetical Data for Loess Fit. B. Window for v j =5.5 and =.6. E. Complete Set of Fitted Values. F. Loess Curve 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 =.15 B. Loess Curve with =.35 Figure 13A: Residual Plot from Loess Curve Fitted to State Education and Voter Turnout Data A. Residuals from curve fitted with =.65 75 75 1992 state voter turnout (percentage) 7 65 6 1992 state voter turnout (percentage) 7 65 6 1 5 55 65 7 75 8 85 1992 state high school graduation rate (percentage) 55 65 7 75 8 85 1992 state high school graduation rate (percentage) Loess Residuals C. Loess Curve with =.75 D. Loess Curve with = 1. -5 75 75-1 1992 state voter turnout (percentage) 7 65 6 1992 state voter turnout (percentage) 7 65 6 65 7 75 8 85 1992 state high school graduation rate (percentage) 55 55 65 7 75 8 85 1992 state high school graduation rate (percentage) 65 7 75 8 85 1992 state high school graduation rate (percentage)

Figure 13: Residual Plots for Loess Curves Fitted with Different Values. Figure 14: Effect of the Parameter on a Loess Smooth Curve. A. Loess Curve Fitted with = 1 and =.5 B. Loess Curve Fitted with = 2 and =.5 B. Residual Plot for Loess Curve Fitted with =.15 C. Residual Plot for Loess Curve Fitted with = 1. 1 1 4 4 Loess Residuals 5-5 -1 Loess Residuals 5-5 -1 Percent for Mondale Minus Percent for Hart 2-2 Percent for Mondale Minus Percent for Hart 2-2 -4-4 65 7 75 8 85 1992 state high school graduation rate (percentage) 65 7 75 8 85 1992 state high school graduation rate (percentage) 5 1 15 5 1 15 Number of Days into the 1984 Primary Campaign 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 16: Residual-Fit Spread Plot for Robust Loess Fit, Occupational Prestige and Income 1..2.4.6.8 1. Fitted Values minus Mean Residuals 8 4 Prestige Rating for Occupation 6 4 2 Prestige rating for occupation 2-2 1 2 3 4 Mean Income for Occupation 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. -4-6..2.4.6.8 1. p-value

Figure 17: Residual-Fit Spread Plot for OLS Fit, Policy Priorities and Government Size..2.4.6.8 1. Fitted Values minus Mean Residuals 2-2 Policy priorities 4 3 2 1 2 4 6 8 1 12 Month Number Registered A. Aspect Ratio Set to 1. 3 1 2 4 6 8 1 12 Month Number Registered Figure 18: Plot of Hypothetical Data on Voter Registration Figures by Month, to show the Effects of Aspect Ratio on Visual Perception. B. Aspect Ratio Banked to 45 Degrees -4-6..2.4.6.8 1. p-value

STATISTICAL GRAPHICS FOR VISUALIZING DATA Tables and Figures, IV William Jacoby Michigan State University and ICPSR University of Illinois at Chicago October 14-15, 21 http://polisci.msu.edu/jacoby/uic/graphics

8 Figure 1: Bivariate scatterplots showing two possible influences on incumbent margin of victory in the 26 congressional elections. 8 Incumbent margin of victory (percentage) 6 4 2 Incumbent margin of victory (percentage) 6 4 2-2 -2 $1, $1, $1, $1,, Challenger spending, in $1,'s (logarithmic scale) 5 1 15 2 25 Number of 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. 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 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 Logged challenger spending Terms served by incumbent

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. 6 5 Incumbent victory margin 4 3 2 Logged challenger spending Terms served by incumbent 1 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. 6 5 4 Incumbent victory margin 3 2 1 Logged challenger spending Terms served by incumbent -1

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 Logged challenger spending Terms served by incumbent Figure 7: Scatterplot matrix for data on 26 congressional elections. Terms served by incumbent Logged challenger spending Incumbent victory margin

Figure 8: Scatterplot matrix with bivariate OLS lines for data on 26 congressional elections. Terms served by incumbent Logged challenger spending Incumbent victory margin Figure 9: Scatterplot matrix with bivariate loess curves for data on 26 congressional elections. Terms served by incumbent Logged challenger spending Incumbent victory margin

Figure 1: Creating conditioning slices from variable measuring number of incumbent terms. 6 Equally-populated slices from incumbent n of terms 5 4 3 2 1 5 1 15 2 25 Range of data values in each slice Figure 11: Trellis display showing incumbent victory margin versus challenger spending, conditioned on incumbent number of terms in office. $1K $1K $1K $1K Incumbent terms Incumbent terms Incumbent terms 8 Incumbent margin of victory (percentage) 8 6 4 2 Incumbent terms Incumbent terms Incumbent terms 6 4 2-2 -2 $1K $1K $1K $1K $1K $1K $1K $1K Challenger spending, in $1,'s (logarithmic scale)

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 terms $1K $1K $1K $1K Incumbent terms Incumbent terms 8 Incumbent margin of victory (percentage) 8 6 4 2 Incumbent terms Incumbent terms Incumbent terms 6 4 2-2 -2 $1K $1K $1K $1K $1K $1K $1K $1K Challenger spending, in $1,'s (logarithmic scale) 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). 5 1 15 2 Logged spending Logged spending Logged spending 8 Incumbent margin of victory (percentage) 8 6 4 2 Logged spending Logged spending Logged spending 6 4 2-2 -2 5 1 15 2 Number of terms served by incumbent 5 1 15 2

1 8 Figure 14: Bivariate scatterplots showing two possible influences on 1992 state policy priorities. 1 8 Policy priority 6 4 Policy priority 6 4 2 2 1 2 3 4 5 Interest group strength 5 6 7 8 Size of state government (employees per capita) Figure 15: Conditioning slices from variable measuring size of state government, with two-thirds overlap between adjacent slices. 6 Equally-populated slices, 2/3 overlap in adjacent slices 5 4 3 2 1 5 6 7 8 Range of data values (government size) in each slice

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). Govt. size 1 2 3 4 5 Govt. size Govt. size 1 8 6 4 Policy priority 2 Govt. size Govt. size Govt. size 1 8 6 4 2 1 2 3 4 5 Interest group strength 1 2 3 4 5 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). 5 6 7 8 Interest grp. strength Interest grp. strength Interest grp. strength 1 8 6 4 Policy priority 1 8 Interest grp. strength Interest grp. strength Interest grp. strength 2 6 4 2 5 6 7 8 Size of state government (employees per capita) 5 6 7 8

Figure 18: Scatterplot matrix for 1992 state policy priority data. State government size State electorate partisanship Interest group strength State policy priority 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). 1 2 3 4 5 1 Govt size Partisanship Govt size Partisanship Govt size Partisanship 8 6 4 2 State policy priority 1 Govt size Partisanship Govt size Partisanship Govt size Partisanship Govt size Partisanship Govt size Partisanship Govt size Partisanship 1 8 6 4 2 8 6 4 2 1 2 3 4 5 1 2 3 4 5 Interest group strength

Figure 2: 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 1 8 6 4 2 1 8 6 4 2 Int grp strength Partisanship Int grp strength Partisanship Int grp strength Partisanship 5 6 7 8 Int grp strength Partisanship Int grp strength Partisanship Int grp strength Partisanship Int grp strength Partisanship Int grp strength Partisanship Int grp strength Partisanship 1 8 6 4 2 5 6 7 8 5 6 7 8 Size of state government 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). -.4 -.2..2 1 Govt size Int grp strength Govt size Int grp strength Govt size Int grp strength 8 6 4 2 State policy priority 1 Govt size Int grp strength Govt size Int grp strength Govt size Int grp strength Govt size Int grp strength Govt size Int grp strength Govt size Int grp strength 1 8 6 4 2 8 6 4 2 -.4 -.2..2 -.4 -.2..2 Partisanship of state electorate