using graphs instead of tables in political sciencetabular or graphical form), along with the...

Using Graphs Instead of Tables inPolitical ScienceJonathan P Kastellec and Eduardo L Leoni

When political scientists present empirical results they are much more likely to use tables than graphs despite the fact that graphsgreatly increases the clarity of presentation and makes it easier for a reader to understand the data being used and to draw clear andcorrect inferences Using a sample of leading journals we document this tendency and suggest reasons why researchers prefer tablesWe argue that the extra work required in producing graphs is rewarded by greatly enhanced presentation and communication ofempirical results We illustrate their benefits by turning several published tables into graphs including tables that present descriptivedata and regression results We show that regression graphs emphasize point estimates and confidence intervals and that they cansuccessfully present the results of regression models A move away from tables towards graphs would improve the disciplinersquos com-municative output and make empirical findings more accessible to every type of audience

While political science is a diverse field whose prac-titioners employ a variety of methodologies andtools a significant portion of the disciplinersquos out-

put includes the study of data and drawing inferencesfrom statistical analyses As such the conclusions one drawsfrom political science papers books and presentationsoften hinge on the successful communication of the dataa researcher is using and the inferences she is drawingfrom them Yet much more often than not political sci-entists choose to present empirical results in the form oftables rather than using graphical displays a tendency thatweakens the clarity of presentation and makes it moredifficult for a reader to draw clear and correct inferences

In this paper we seek to highlight the disciplinersquos reli-ance on tables and to offer suggestions for how to usegraphs instead of tables to improve the presentation ofempirical results Six years ago King et alrsquos influentialpaper urged social scientists to present quantities of inter-est rather than parameter estimates from statistical analy-

ses1 Our paper follows up on this effort We seek to movebeyond what researchers should communicate to their audi-ence by offering suggestions on how they should do so2

Other scholars have made similar recommendations3

But as we show political scientists are not heeding theadvice to use graphs4 Following the example of Gelmanet al we went through every article from five issues ofthree leading political science journalsmdashthe February andMay 2006 American Political Science Review the July 2006American Journal of Political Science and the Winter andSpring 2006 issues of Political Analysis5mdashand counted thenumber of tables and graphs presented in each6 We alsoanalyzed the basic characteristics and purpose of eachtable and graph to get a sense of how researchers use themto communicate empirical results

This undertaking led to two main conclusions Firstpolitical scientists rely on tables far more than graphsmdashtwice as often in fact Second tables are used mainly topresent data summaries and the results of regression mod-els Indeed tables presenting parameter estimates and stan-dard errors comprised about 50 percent of the tables inour sample In addition we found that political scientistsnever use graphs to present regression results

Our goal in this paper is to demonstrate directly howresearchers can use graphs to improve the quality of empir-ical presentations Unlike previous attempts to promotethe use of graphs we devote a significant portion of ouranalysis to showing how graphs can greatly improve thecommunication of regression results which are almostalways presented in tables whose features can strain eventhe most seasoned journal reader Rather than presentingan abstract review of the benefits of graphs we take asample of tables from the various journal issues and turn

Jonathan P Kastellec (jpk2004columbiaedu) and Edu-ardo L Leoni (eleonihmdcharvardedu) are DoctoralCandidates in Political Science at Columbia UniversityThe authorsrsquo names appear in alphabetical order Theywould like to thank Andrew Gelman Rebecca Weitz-Shapiro Gary King David Epstein Jeff Gill Piero Stanigand three anonymous reviewers for helpful comments andsuggestions We also thank Noah Kaplan David Park andTravis Ridout for generously making their data publiclyavailable Eduardo Leoni is grateful for support from theHarvard MIT Data Center where he was a fellow whileworking on this project

| |

ARTICLES

DOI 101017S1537592707072209 December 2007 | Vol 5No 4 755

httpsdoiorg101017S1537592707072209Downloaded from httpswwwcambridgeorgcore Princeton Univ on 17 Apr 2017 at 124254 subject to the Cambridge Core terms of use available at httpswwwcambridgeorgcoreterms

them into graphs showing that it is possible and desirableto do so for any table that presents numeric informationincluding data summaries and parameter estimates Weshow that graphs better communicate relevant informa-tion from both data summaries and regression modelsincluding comparing values across variables or models andthe sign and significance of predictors We argue that whilegraphs are almost never used to present regression resultsthe benefits from doing so are significant In particulargraphs are superior at displaying confidence intervals forparameter estimates (and thus their uncertainty) and formaking comparisons across models We believe that schol-ars who follow our advice will both understand their databetter and present their empirical results more clearly totheir audience thereby increasing the value and impact oftheir research

The Use of Tables versus Graphs inPolitical ScienceBefore presenting examples of using graphs instead of tablesit is useful to examine when and how political scientistscurrently use each The five issues we looked at contained52 articles 40 of which presented at least one table orgraph These 40 articles contained 150 tables and 89 graphsa roughly 2-to-1 ratio7 To understand the motivation ofpolitical scientists in presenting empirical results we coded

the type of information conveyed by each such as sum-mary statistics parameter estimates and uncertainty andpredicted values Figure 1 presents both the frequencywith which each type of information appears (in eithertabular or graphical form) along with the percentage ofgraphs that are used within each category (More detailedinformation on our coding can be found in the caption)

The most striking findings center around the presenta-tion of regression results which comprise more than 30percent of all tables and graphs combined We find thatmore than half the tables in our sample were used to presentsuch resultsmdashthat is point estimates and uncertainty usu-ally accompanied by some combination of asterisks boldtypeface or letters to indicate statistical significance8 Inaddition not a single graph presented in the five issues westudied communicated regression results Clearly politicalscientists are of the belief that tables are the most effectivewaymdashit seems in fact the only waymdashto present pointestimates and uncertainty

We turn next to summary statistics which include quan-tities suchasmeans standarddeviations and frequency sum-maries These types of statistics comprised 32 percent of allthe graphs and tables in our sample or roughly the samepercentage as regression results Given that the traditionaluse of statistical graphics focuses on data summaries9

we might expect researchers to use graphs frequently to

Figure 1Tables and graphs in political science journals

The left graph depicts the percentage of all graphs and tables presented in five political sciencejournals that fall into the categories on the y-axis (ie the number of graphs and tables that fall intoeach category divided by the total number of tables and graphs) the right graph depicts thepercentage of graphs within each category (ie the number of graphs in each category divided bythe total number of tables and graphs in the respective category) ldquoEstimates and uncertaintiesrdquoinclude such quantities as regression coefficients and standard errors ldquoSummary statisticsrdquo includedescriptive statistics like means and standard deviations ldquoPredicted valuesrdquo include post-regressionestimations such as changes in predicted probabilities ldquoNon-numericrdquo includes any information thatis not quantitative ldquoMathematicalrdquo generally includes figures from formal models finally ldquootherrdquo is aresidual category The plots show that summary stats and estimates and uncertainties comprise themajority of graphical and tabular presentationmdashwhile the former are sometimes displayed graphically(about 40 of the time in our sample) the latter are always displayed as tables

| |

ARTICLES | Using Graphs Instead of Tables in Political Science

756 Perspectives on Politics


present summary statistics Nevertheless the authors in oursample did so only about 40 percent of the time choosingto use tables more often than not

On the other hand our results show that political scien-tists overwhelmingly use graphs to present post-estimationresults such as predicted probabilities While the reasonsfor this contrast are unclear it appears that researchers arecomfortable presenting these quantities in graphical form

Nevertheless the results are unambiguous political sci-entists are far more likely to use tables than graphs exceptwhen presenting post-estimation results And they never(at least in our sample) use graphs when presenting regres-sion results

Why TablesIt is not difficult to discern why researchers choose topresent empirical results using tables Compared to graphstables are much easier to produce In fact it is often pos-sible to convert statistical output automatically into atypeset-quality table using a single command10 In addi-tion tables are standard in teaching presentation andpublishing thereby providing incentives for scholars tocontinue producing them Finally since tables communi-cate precise numbers they are valuable for aiding replica-tion studies (a point we return to in our conclusion)

At the same time it is easy to understand why research-ers are reluctant to use graphs For one it simply takesmore work to produce graphs With current softwaregreater knowledge of the nuances of the statisticalgraphicalpackages is needed to produce effective graphs11 Moreimportantly creating informative statistical graphs involvesrepeated iterations trial-and-error and much thought aboutboth the deeper issue of what message the researcher istrying to convey and the practical issue of producing agraph that effectively communicates that message Thisprocess can be quite time-consuming simply put it takesmuch greater effort to produce a quality graph than atable12

Another reason why researchers hesitate to use graphs maybe their belief that it is simply not feasible to present certaininformation graphically Relatedly some may believe thatgraphs take up much more space than tables Both of theseconcerns are likely to be paramount particularly with respectto regression tables which can include multiple models thatmay involve various combinations of variables observa-tions and estimation techniques Researchers may believeit impossible to present results from regressions graphically

Why GraphsWe argue however that the costs of producing graphs areoutweighed by the benefits and many of the concernsregarding their production are either overstated or mis-guided altogether While producing graphs does requiregreater effort the very process of graph creation is one of

the main benefits of using graphs instead of tables in thatit provides incentives for the researcher to present the resultsmore directly and cleanly Like Gelman et al we strug-gled with several versions of each graph presented in thispaper before settling on the versions that appear13 Whileat times frustrating the iterative process forced us to care-fully consider our communications goals and the meansof accomplishing them with each graph Such iteration ofcourse is not needed with tables Thus the very strengthof tables (their ease of production) can also be seen as aweakness

In addition concerns about the infeasibility of graphswhen presenting certain numeric summaries and aboutthe size of graphs relative to tables are unwarranted As weillustrate it is not only possible to present regressionresultsmdashincluding multiple specificationsmdashin graphicalform but it is desirable as well In addition most of ourgraphs take up no more room than the tables they replaceincluding regression tables And for those that do webelieve the benefit of graphical presentation outweighs thecost of greater size

Once performed the extra work put into producinggraphs can reap large benefits in communicating empiri-cal results Extensive experimental research has shown thatwhen the presentation goal is comparison (as opposed tocommunicating exact values for which tables are supe-rior) good statistical graphs consistently outperformtables14 Our goal in this paper is not to add to the volu-minous literature systematically investigating the virtuesof graphs versus tables Rather our approach is practicalwe take a sample of representative tables from politicalscience journals present them graphically and then qual-itatively compare the two We believe that these examplesillustrate that graphs are simply better devices than tablesfor making comparisons which is almost always the goalwhen presenting data and empirical results And for thosewho are convinced we have created a web site (wwwtables2graphscom) that contains complete replication codefor producing our graphs which can help researchers turntheir tables into graphs

Using Graphs Instead of TablesDescriptive StatisticsWe begin our conversion of tables into graphs by analyz-ing tables with descriptive statistics Although most of theliterature on statistical graphics deals with exploratory dataanalysis and descriptive statistics political scientists stillchoose more often than not to present such informationin the form of tables (64 percent of the time in our sam-ple as seen in figure 1)

When assessing the use of graphs or tables it is usefulto consider why researchers might present descriptive sta-tistics If the goal is to facilitate replication and henceallow follow-up researchers to be confident that they are

| |

December 2007 | Vol 5No 4 757


using the same data as the original analysis then tables areindeed superior But if the goal is to give an audience asense of the data in order to lay a foundation for sub-sequent statistical analyses then we believe that graphingdescriptive statistics is a superior choice For one graphsallow for easy comparison of variables which can be impor-tant for assessing regression analyses Graphs as we dem-onstrate also make it much easier to compare variablesacross two or more settings such as different time periodsinstitutions and countries Finally graphs of descriptivestatistics also provide a better summary of the distributionof variables

Using a Mosaic Plot to Present Cross TabulationsWe begin with a table presented in Iversen and Soskicewhose study of redistribution in advanced democraciesincludes nine tables seven of which present numericalinformation15 Of these five present descriptive statisticsand two present regression results It is commendable thatthe authors chose to present in detail much of the dataused notably however they chose not to use a singlegraph in their article

Their first table (reproduced in our table 1) presents across tabulation of electoral systems and government par-tisanship for a sample of advanced democracies The keycomparison here is whether majoritarian electoral systemsare more likely to feature right governments and propor-tional representation systems are more likely to feature leftgovernments a comparison presented in numeric form inthe last column The raw numbers that go into this com-parison are presented in the main columns Although theinformation in this 2-by-2 table is relatively easy to digestwe think that the same information can be more clearly andsuccinctly presented by using a mosaic plot a type of graphthat is specifically designed to represent contingencytables graphically16 The top plot depicts the relationshipbetween electoral system and partisanship of governmentwhile the bottom plot depicts how often countries featuredcenter-left governments at least 50 percent of the time

Table 1Iversen and Soskice 2006 table 1Electoral system and the number of yearswith left and right governments (1945ndash98)

Government Partisanship

Left Right

Proportionof Right

Governments

Electoral Proportional 342 120 26system (8) (1)

Majoritarian 86 256 75(0) (8)

Figure 2Using a Mosaic Plot to Present CrossTabulations

Table 1 from Iversen and Soskice (2006) displays a cross-tabulation of electoral systems and government partisan-ship We turn the table into a two-dimensional mosaicplot The top plot depicts the relationship between elec-toral system and partisanship of government while the bot-tom plot depicts how often countries featured center-leftgovernments at least 50 of the time broken down by theirelectoral systems (defined as an ldquooverweightrdquo in the textof the paper) also across proportional and majoritarian sys-tems A key feature of the mosaic plot is that the area ofeach rectangle is proportional to the number of observa-tions that fall within their respective contingencies Themosaic plot clearly displays the key comparisons while retain-ing the actual counts Titles above each graph make itclear to the reader what is being compared unlike in thetable

| |




broken down by their electoral systems A key feature of themosaic plot (in contrast to a standard bar plot for example)is that the area of each rectangle is proportional to the num-ber of observations that fall within their respective contin-gencies Thus the larger width of the rectangles underproportional systems indicates that the majority of coun-tries in the sample have such systems

The first thing to note about the graph is that the maincomparison the authors are attempting to make immedi-ately stands out as the graph shows that proportionalsystems are significantly more likely to produce left gov-ernments and that nearly every country with a propor-tional system featured center-left governments more than50 percent of the time from 1945ndash1998 (defined as anldquooverweightrdquo in their paper) while no countries with amajoritarian system featured center-left governments morethan 50 percent of the time We add the raw counts fromeach category inside the rectangles the use of a mosaicplot allows us to combine the best feature of a tablemdashitsability to convey exact numbersmdashwith the comparativevirtues of a graph While actual values are frequently notof interest (and hence do not need to be displayed in agraph) the inclusion of counts here alerts the reader thatsmall samples are involved in the calculation of countrieswith an overweight of left countries without either addingunnecessary clutter to the graph or increasing its sizeFinally the titles above each plot make it clear what isbeing plotted while one has to read the actual text in theoriginal article to understand the table

This example illustrates that even simple and easy-to-read tables can be improved through graphical presenta-tion As the complexity of a table grows the gains fromgraphical communication will only increase Indeed mosaicplots can easily be extended to display multidimensionalcontingency relationships17

Using a Dot Plot to Present Meansand Standard DeviationsAnother common type of table is one presenting descrip-tive statistics about central tendencies (eg means) andvariation (eg standard deviations) As we discuss belowpresenting only means and standard deviations (along withminimums and maximums) may not be the best choicedepending on the nature of the variables involved How-ever even when they are sufficient it can be difficult tomake comparisons across variables and to inspect the dis-tribution of individual variables when data is presentedtabularly Graphs on the other hand accomplish bothgoals

As an example we turn to Table 1 panel A fromMcClurg (reproduced in our table 2) which presents sum-mary statistics from his study of the relationship betweensocial networks and political participation18 We trans-form the table into a modified dot plot which is very wellsuited for presenting descriptive information19 We use asingle plot taking advantage of the fact that the scales ofall variables are similar The dots depict the means of eachvariable the solid line extends from the mean minus oneto the mean plus one standard deviation and the dashedline extends from the minimum to the maximum of eachvariable Rather than ordering the variables randomly oralphabetically we order them by their mean values indescending order which eases comparison of variables20

Because the number of respondents covered under eachvariable is not a feature of the variables themselves we

Table 2McClurg 2006 table 1 (panel A) Thepolitical character of social networks

MeanStandardDeviation Min Max N

Panel A Descriptive StatisticsSizea 313 149 1 5 1260Political Talk 182 061 0 3 1253Political

Agreement043 041 0 1 1154

PoliticalKnowledge

122 042 0 2 1220

Notes This table provides descriptive statistics for the politicalcharacter of the social networks as perceived by respondentsaWhen respondents who report having no network are includedthe mean of this variable drops to 257 with a standarddeviation 181 (n = 1537)

Figure 3Using a Single Dot Plot to Present SummaryStatistics

Table 1 (panel A) from McClurg (2006) presents descriptive sta-tistics from his study of social networks We turn it into a graphby using a single dot plot taking advantage of the fact that thescales of all variables are similar The dots depict the meansof each variable the solid line extends from the mean minus one stan-dard deviation to the mean plus one deviation and the dashedline extends from the minimum to the maximum of each variableThe number of respondents covered under each variable isgiven under the y-axis labels The variables are ordered accord-ing to their mean values in descending order The graph allowsfor easy lookup and comparison of the means while the lines visu-ally depict the distribution of each variable

| |



note them under the labels on the y-axis (if we were inter-ested in comparing sample sizes across variables we couldeither include a separate graph or make the area of thedots proportional to sample size) The benefits of the graphare apparent the dots allow for easy lookup and compar-ison of the means while the lines visually depict the dis-tribution of each variable For example the graph revealsthat political talk is right-skewed which is not easily con-cluded from the table

Using Dot Plots and Violin Plots to PresentDistributions of Variables with Differing ScalesIn many instances it will be worthwhile to go beyondsimple descriptions of variables and present more com-plete summaries of distributions As Cleveland and McGillnote ldquoGraphing means and sample standard deviationsthe most commonly used graphical method for conveyingthe distributions of groups of measurements is frequentlya poor method We cannot expect to reduce distributionsto two numbers and succeed in capturing the widely var-ied behavior that data sets in science can haverdquo21

For an example of when it is useful to depict fullerrepresentations of variables we turn to table 2 of Kaplanet al (reproduced in our table 3) which displays sum-mary statistics from their analysis of issue convergenceand campaign competitiveness22 This table presents a chal-lenge for graphical representation that did not arise in theprevious example the scales of the variables differ dramat-ically A quick check of the table reveals that the meanvariance and maxima differ significantly across variablesthe mean issue convergence and percent negative ads forexample are much higher than the other variables Includ-ing all the variables in a single graph would result in severecompression in a majority of the variables rendering thegraph uninformative

Scale difference is likely to occur in many datasets andsuch situations will require the analyst to be creative aboutthe best way to present her data We suggest two optionsthe first of which we pursue here Instead of using a singlegraph we decided to group similar variables and presentseparate graphs for each group allowing for comparisonswithin each graph

There are three main categories of variables in Kaplanet alrsquos table 2 binary variables those measured in mil-lions and those measured in percents (including issue con-vergence which is defined as the percentage of combinedattention that Democratic and Republican candidates giveto a particular issue) Since competitiveness and issue saliencedo not fall into any of these categories we group themwith similarly distributed variables

We begin the construction of our graph presented infigure 4 by considering what type of display is best suitedfor each group of variables Because binary variables cantake on only two values their distribution is fully charac-

terized by their means and sample size Accordingly in thetop panel we plot the means of the binary variables order-ing the variables in descending order and placing samplesize in the y-axis labels (We use diamonds to distinguishthem from the median values plotted in the two panelsbelow) This allows for clear comparison of how ofteneach variable is coded as ldquo1rdquo

We next consider the variables measured in percentsand those measured in millions While on different scalesboth sets of variables are continuous A range of optionsexist for graphing the distribution of continuous vari-ables including histograms kernel density plots and box-plots23 A recent graphical innovation called the ldquoviolinplotrdquo combines the virtues of the latter two by overlayinga density trace onto the structure of a box plot24 Theresulting plot presents both central tendencies and detailedinformation on the distribution of variables includingwhether they are skewed and the presence of outliers Foreach set of variables we present a panel including violinplots for each variable The center of each violin plot givesinformation similar to that presented in a traditional box-plot the points depict median values the white boxesconnect the 25th and 75th percentiles and the thin blacklines connect the lower adjacent value to the upper adja-cent value which help identify skewness or the presenceof outliers or both25 The shaded area depicts a densitytrace of each variable which is plotted symmetrically aboveand below the horizontal box plot in order to aid visual-ization As with a kernel density plot a hill distribution(such as ldquoState Voting Age Poprdquo in figure 4) indicatesnormality while a rectangle distribution (such as ldquoCom-petitivenessrdquo) indicates a more uniform distribution

The violin plots reveal several characteristics of thedata that are not apparent from the table First many ofthe variables exhibit substantial skewness For instancewhile the median of both ldquoIssue Convergencerdquo and ldquoIssueSaliencerdquo are 0 their tails extend well to the right Inaddition the presence of observations well beyond theupper adjacent values of ldquoTotal SpendingCapitardquo andldquoDifference SpendingCapitardquo indicates the existence ofoutliers (indeed there is only one observation of thelatter that is greater than four)

These are details that one would be hard-pressed toglean from a table even one that went beyond reportingonly means and standard deviations Greater understand-ing of distributions can aid researchers as they move fromexploratory data analysis to model fitting And as theseviolin plots illustrate they can increase the readerrsquos under-standing of the data that is presented and analyzed

Using an Advanced Dot Plot to Present MultipleComparisonsThe second option for graphing descriptive plots of vari-ables with different scales is to alter the scales themselves

| |




We illustrate this option by converting table 2 fromSchwindt-Bayerrsquos study of the attitudes and bill initiationbehavior of female legislators in Latin America (repro-duced in our table 4) into a graph26 Most of the rows ofthe table are devoted to displaying the number of billsintroduced by lawmakers in four Latin American legisla-tive chambers across two time periods (which vary by cham-ber) While the text of the paper does not explicitly statewhat comparisons the reader should draw from the tablethere are three main comparisons one could make acrossissue areas across countries and across time periods Thestructure of the table however only allows for easy com-parison of issue areasmdashfor a single country and a singletime period The use of absolute counts for the number ofbills introduced in each issue area instead of percentageshinders cross-column comparisons (ie across countriesand time periods) Using percentages would improve thepresentation but would still place the burden on the readerto find patterns in the data

Instead we turn the table into an advanced dot plotpresented in figure 5 We begin by converting the countsof each bill introduced in each issue area into a propor-tion with the total number of bills initiated serving as thedenominator For each chamber and for each issue areawe present the proportions for both the first and secondtime periods using different symbols open circles for thefirst period ldquordquos for the second (Because the ldquonumber oflegislators who sponsored at least one billrdquo and the ldquototalnumber of bills initiatedrdquo seem tangential to the table weinclude them only as counts under the name of each coun-try or chamber in the panel strips) One option of coursewould be simply to scale the x-axes on a linear proportionscale ranging from 0 to 1 this however would mask

differences among several issue areas for which relativelyfew bills were introduced27 Instead we follow the adviceof Cleveland and scale the x-axes on the log 2 scale andprovide for easy lookup by placing tick mark labels atboth the top and bottom of the graph28 Given this scal-ing each tick mark (indicated vertically by the solid graylines) represents a proportion double that of the tick mark

Table 3Kaplan et al 2006 table 2 Descriptivestatistics of campaign and issue-levelvariables

Variable N Mean SD Min Max

Issue Convergence 982 2485 3473 000 9998Competitiveness

(CQ Ranking)65 154 12 000 3

Total SpendingCapita (millions)

65 347 271 028 1339

Difference SpendingCapita (millions)

65 112 132 003 926

State Voting Age Pop(millions-ln)

65 12 085 minus065 313

Percent Negative Ads 65 2138 1684 000 54962000 Year (binary) 65 038 049 000 12002 Year (binary) 65 032 047 000 1Consensual Issue

(binary)43 028 045 000 1

Issue Owned (binary) 43 049 051 000 1Issue Salience 43 286 638 000 3563

Figure 4Using a Dot Plot and Violin Plots to PresentSummary Statistics

Table 2 from Kaplan Park and Ridout (2006) presents summarystatistics from their study of issue convergence and campaigncompetitiveness We group similar variables and present sepa-rate graphs for each group allowing for comparisons withineach graph and greater understanding of variable distributionsThe top graph plot the means of the binary variables ordering thevariable in descending order and placing sample size in they-axis labels For percentage variables and variables measuredin millions we present individual violin plots of each variableThe points depict median values the white boxes connect the 25thand 75th percentiles and the thin black lines connect the lower adja-cent value to the upper adjacent value The shaded area depictsa density trace plotted symmetrically above and below the hori-zontal box plot The violin plots clearly depict the distributionof each variable and allow for the detection of skewness andoutliers

| |



Table 4Schwindt-Bayer 2006 table 2 Number of bills sponsored in each thematic area

Argentina Colombia-Chamber Colombia-Senate Costa Rica

1995 1999 1994ndash1998 1998ndash2002 1994ndash1998 1998ndash2002 1994ndash1998 1998ndash2002 Total

Number of legislators whosponsored at least one bill

246 257 139 165 87 94 57 57 1102

Womenrsquos Issues 33 30 23 9 16 18 23 35 187ChildrenFamily 28 40 13 7 22 9 25 27 171Education 44 66 67 72 42 29 56 75 451Health 27 51 13 14 13 5 16 33 172Economics 208 305 74 80 113 65 120 160 1125Agriculture 28 49 23 18 22 19 34 38 231Fiscal Affairs 45 61 11 17 21 13 27 51 246Other Bills 567 901 405 406 371 356 628 764 4398Total number of bills initiated 980 1503 629 623 620 514 929 1183 6981

Note ldquoOther Billsrdquo include all bills that do not fall into the seven thematic areas This would include bills related to publicadministration the environment foreign affairs culture and public welfare among others

Figure 5Using an Advanced Dot Plots to Present Proportions

Table 2 from Schwindt-Bayer (2006) presents counts of the type ofbills initiated in four Latin American legislative chambers in twotime periods each We turn the table into a graph that allows for com-parisons across time periods chambers and issue areas Foreach country or chamber the ldquoorsquosrdquo indicate the percentage of all ini-tiated bills pertaining to the issue area listed on the y-axis in thefirst period while the ldquo+rsquosrdquo indicate the percentages from the sec-ond period The grey strips indicate the country or chamber ana-lyzed in the panel immediately below along with the relevant timeperiods For each period the first count in parentheses gives the num-ber of legislators who sponsored at least one bill while the sec-ond count gives the total number of bills initiated We scale the x-axison the log 2 scale each tick mark is double the percentage ofthe tick mark to its left

to the left Looking at the Colombia Senate for examplewe can see that the proportion of bills related to healthissues declined by half from the 1994ndash1998 period to the1998ndash2002 period We can also compare easily across issueareas in Argentina in 1999 for example it is easy to seethat twice as many fiscal affairs bills were introduced aswomenrsquos issues bills

The graph thus allows for all three types of compari-sons The use of dual symbols allows for easy comparisonboth across time periods within a given issue area andacross issue areas within a single time period The graphalso facilitates cross-legislature comparison by placing allplots in a single column by reading vertically down thegraph for example we can see that proportionally morebills pertaining to womenrsquos issues were introduced in theColombia Senate than the Colombia Chamber from 1998ndash2002 This plot from the choice of scaling to the tool weutilized follows the principles outlined in Cleveland

| |




showcasing the ability of Trellis plots to allow compari-sons within and across panels29 The technique of usingseveral smaller graphs instead of one big graphmdashcoinedldquosmall multiplesrdquo by Tuftemdashcan greatly enhance the pre-sentation of data and empirical results in a wide range ofsituations30

In summary we believe that these examples demon-strate the benefits of graphing descriptive statistics Ofcourse there are many other types of descriptive data sum-maries such as correlation matrices and time series thatwill require different graphing strategies31 Our purpose isnot to exhaust all of these but to illustrate how descrip-tive tables can be turned into graphs with great benefit

Using Graphs Instead of TablesRegression AnalysesOn Regression Tables and Confidence IntervalsRegression tables are meant to communicate two essentialquantities point estimates (coefficients) and uncertaintyestimates (usually in the form of standard errors confi-dence intervals or null hypothesis tests) In our sample74 of the regression tables presented standard errorsusually supplemented by asterisks labeling coefficients thathave attained conventional levels of statistical signifi-cance Thus tables typically seek to draw attention tocoefficients that are significant at the p 01 p 05 orp 10 levels

This tendency likely stems from the disciplinersquos relianceon null hypothesis significance testing in conducting regres-

sion analyses Articles in fields as diverse as wildlife man-agement psychology medicine statistics forecasting andpolitical science argue that null hypothesis significancetesting and reliance on p-values can lead to serious mis-takes in statistical inference32 These articles suggest sub-stituting confidence intervals for p-values and significancetesting when presenting regression results

These criticisms notwithstanding it is likely that polit-ical scientists will continue to rely on null hypothesis sig-nificance testing Given this reality can graphs improveon standard regression tables We believe the answer isyes due to the simple fact that graphs of point estimatesand confidence intervals can communicate the same infor-mation as standard regression tables while adding the vir-tues of emphasizing effect size and easy comparison ofcoefficients A confidence interval effectively presents thesame information as a null hypothesis significance test forexample a 95 percent confidence interval that does notinclude the null hypothesis (typically zero) is equivalentto a coefficient being statistically significant at p 0533

In addition ldquoconfidence intervals have a great virtue asthe sample size increases the size of the interval decreasescorrectly expressing our increased certainty about theparameter of interestrdquo34

Of course it is possible to present confidence intervalsin regression tables35 Notably however none of thetables in our sample featured confidence intervals Whilethe disciplinersquos reliance on null hypothesis testing is per-haps the main cause of this tendency the practicality of

Table 5Ansolabehere and Konisky (2006) table 4 Registration effects on turnout in New York andOhio counties fixed effects model 1954ndash2000

Dependent Variable = County-Level Turnout

FullSample

(1)

Excludingcountiesw partial

registration(2)

Full samplew state-year

dummies(3)

FullSample

(4)

ExcludingCountiesw partial

registration(5)

Fullsample

w state-yearDummies

(6)

of county registration minus0039 minus0036 minus0051 minus0037 minus0034 minus0050(0003) (0003) (0003) (0003) (0003) (0003)

Law change minus0020 minus0018 minus0023(0005) (0005) (0006)

Log population 0048 0036 0017 0047 minus0035 0016(0011) (0012) (0010) (0011) (0021) (0010)

Log median family income minus0133 minus0142 0050 minus0131 minus0139 minus0049(0013) (0014) (0013) (0013) (0014) (0013)

population with hs education 0071 0070 0011 0072 0071 0013(0028) (0029) (0024) (0028) (0029) (0024)

population African American minus0795 minus0834 minus0532 minus0783 minus0822 minus0521(0056) (0059) (0044) (0055) (0059) (0044)

Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572

Note p lt 05 p lt 01 Huber-White standard errors in parentheses Year dummies and state-year dummies are not reported

| |



incorporating confidence intervals may also play a role itis simply difficult to present such tables in particular whenmultiple specifications or subsamples are compared (asoccurred in about 88 percent of the regression tables in oursample) Consider table 4 of Ansolabehere and Koniskywhich we replicate in table 5 (we present the graphical ver-sion of the table later in this section)36 The authors esti-mate the effect of voter registration laws on county-levelturnout in New York and Ohio and do robustness checksby presenting six different models as seen in columns onethrough six in the tableNote that there are about threedozencoefficients and standard errors pairs to compare

Would the use of confidence intervals improve interpre-tation In table 6 we present the same table but instead ofstandard errors and asterisks we use confidence intervalsAlthough inferences are more direct when estimates are pre-sented in this form it gets confusing quickly when com-paring across models Even a simple question such aswhich confidence intervals overlap demands careful atten-tion to signs and comparisons must be done one by one

These difficulties point to a main advantage of the stan-dard regression table it is less confusing than the alterna-tive There are others it is clear from the table whichindependent variables are present or missing in each modelIn addition information such as model fit statistics andthe number of observations can easily be added to thetable In summary regression tables are able to display alarge wealth of information about the models in a very

compact and mostly readable format They also clearlycommunicate the results of null hypothesis significancetesting It is no surprise that they are so popular

Could graphs do a better job As we illustrate belowgraphs can easily display point estimates and confidenceintervals including those from multiple models In doingso they can clearly convey the results of null significancehypothesis testing And once we move beyond the soleconsideration of whether a coefficient is significantly dif-ferent from zero we believe the benefits of graphs becomeeven more apparent allowing for the proper highlightingof effect size and comparison of coefficients both withinand across models

In summary as we move to graphing regression resultsand given the aforementioned strengths and weaknessesof tables we look for a good regression graph to satisfy thefollowing criteria

1 It should make it easy to evaluate the statistical sig-nificance of coefficients

2 It should also be able to display several regressionmodels in a parallel fashion (as tables currently do)

3 Relatedly when models differ by which variables areincluded it should be clear to the reader which vari-ables are included in which models

4 It should be able to incorporate model information5 Finally the plot should focus on confidence inter-

vals and not (only) on p-values

Table 6Presenting regression results with confidence intervals


FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)

of county registration minus0039[minus0045minus0033]

minus0036[minus0042minus003]





Law change minus0020[minus003minus001]



Log population 0048[0026007]

0036[0012006]

0017[minus00030037]

0047[00250069]

minus0035[minus00770007]

0016[minus00040036]

Log median family income minus0133[minus0159minus0107]


0050[00240076]


0139[minus0167minus0111]


population with hs education 0071[00150127]

0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]

population African American minus0795[minus09070683]






Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572

Note We reproduce table 4 from Ansolabehere and Konisky (2006) but with 95 confidence intervals instead of standard errorsdisplayed under each parameter estimate

| |




Plotting a Single RegressionWe start by plotting a simple regression table Table 2 fromStevens et al (reproduced in our table 7) displays resultsfrom a single least squares regression37 Using a survey ofelites from six Latin American countries the authors studythe effects of economic perceptions ideology and demo-graphic variables and a set of country dummies on the sur-vey respondentrsquos ldquoindividual authoritarianismrdquo measuredon a seven-point scale The table condenses a large wealthof information regression fit summaries the number of

cases point estimates standard errors significance tests formultiple comparisons among the country dummies andasterisks denoting 01 05 and 10 two-tailed p-values

In figure 6 we condense the same information into asimple dot plot much like those used in the previoussection We take advantage of the similar scaling acrossthe estimates and display the results in a single plot Thedots represent the point estimates while the horizontallines depict 95 percent confidence intervals38 We placea vertical line at zero for convenience and make the lengthof the x-axis symmetric around this reference line for easycomparison of the magnitude of positive and negative coef-ficients Each independent variable is displayed on they-axis Finally we omit the estimate and standard error ofthe constant since it is not substantively meaningful inthis instance (the constant is the predicted value for some-one who among other unlikely if not impossible charac-teristics is age zero) Finally we use the empty space inthe plot region to display R2 adjusted R2 and the numberof observations this information however could just as

Table 7Stevens et al 2006 table 2 Determinantsof authoritarian aggression

VariableCoefficient

(Standard Error)

Constant 41 (93)Countries

Argentina 131 (33)BM

Chile 93 (32)BM

Colombia 146 (32)BM

Mexico 07 (32)ACHCOV

Venezuela 96 (37)BM

ThreatRetrospective egocentric

economic perceptions20 (13)

Prospective egocentriceconomic perceptions

22 (12)

Retrospective sociotropiceconomic perceptions

minus21 (12)

Prospective sociotropiceconomic perceptions

minus32 (12)

Ideological distance frompresident

minus27 (07)

IdeologyIdeology 23 (07)

Individual DifferencesAge 00 (01)Female minus03 (21)Education 13 (14)Academic Sector 15 (29)Business Sector 31 (25)Government Sector minus10 (27)

R 2 15Adjusted R 2 12N 500

p lt 01 p lt 05 p lt 10 (twotailed)ACoefficient is significantly different from Argentinarsquos atp lt 05

BCoefficient is significantly different from Brazilrsquos at p lt 05CHCoefficient is significantly different from Chilersquos at p lt 05COCoefficient is significantly different from Colombiarsquos at

p lt 05MCoefficient is significantly different from Mexicorsquos at p lt 05VCoefficient is significantly different from Venezuelarsquos atp lt 05

Figure 6Presenting a single regression model usinga dot plot with error bars

Table 2 from Stevens et al 2006 displays a single least squaresregression model that examines the relationship between indi-vidual authoritarianism and economic perceptions ideology anddemographic variables in six Latin American countries We turnthe table into a single regression graph taking advantage of the sim-ilar scaling across the estimates The dots represent the point esti-mates while the horizontal lines depict 95 confidence intervalsThe range of parameter estimates is displayed on the x-axis whilethe variable labels are displayed on the y-axis We place a ver-tical line at zero for convenience and make the length of the x-axissymmetric around this reference line for easy comparison ofthe magnitude of positive and negative coefficients

| |



well be displayed in the caption if more desirable or ifthere is not enough room in the plot region

This figure shows several advantages of using graphsFirst information regarding statistical significance is dis-played without any asterisks bars or superscripted lettersInstead the length of the error bars visually signal whichvariables are significant those that do not cross the refer-ence line which is zero in this case Thus a vertical scanof the graph allows the reader to assess quickly whichvariables are significantly different from the null hypothesis

In addition the visual display of the regression resultsalso focuses the attention of the reader away from statis-tical significance towards the more relevant and perhapsmore interesting information revealed by a regression analy-sis the estimated effect size and the degree of uncertaintysurrounding it The vertical placement of coefficients makesit easy to compare their relative magnitudes while the sizeof the error bars provide information on how preciselyeach parameter is estimated

The use of confidence intervals also provides much moreinformation displayed intuitively than a regression tableFor instance when confidence intervals do not overlap wecan conclude that two estimates are statistically signifi-cantly different from each otherThus if one goal of a regres-sion analysis is to compare two or more parameter estimatesthen this simple type of graph is sufficient However even ifthe confidence intervals of two coefficients overlap it is pos-sible that they are still significantly different39 One possi-bility would be to move beyond this basic graph and plot allcontrasts of interest (the estimates of the differences in thecountrycoefficients andtheir corresponding standarderrorsfor example bArgentinabChilebArgentinabColombia etc)40

Plotting Multiple Models in a Single PlotAs noted earlier in our survey of political science tables wefound that more often than not researchers present mul-tiple models Graphing multiple models presents new chal-lenges as we must be sure that a reader can distinguish theparameter estimates and confidence intervals from eachmodel and that the differences between models in termsof which variables are included are visually apparent

We begin with the case of two regression models Table 1of Pekkanen et al (replicated in our table 8) displays twologistic regression models that examine the allocation ofposts in the LDP party in Japan41 In the first model PROnly and Costa Rican in PR are included and Vote sharemargin is excluded while in the second model the reverseis true We present the two models by plotting parallellines for each of them grouped by coefficients as can beseen in figure 7 We differentiate the models by plottingdifferent symbols for the point estimates filled (black)circles for the first model and empty (white) circles for thesecond The similar scaling of the coefficients again allowsus to graph all the estimates in a single plot Because most

of the coefficients fall below zero to save space we do notmake the x-axis symmetric around zero And because theplot region features little empty space in this case wewould present model information in the caption Unlikein the previous example we include the constant in thegraph since it is substantively meaningful in these models(the inverse logit of the constant in each model gives thepredicted probability that a third-term Member of Parlia-ment who is coded as 0 on all the other predictors in themodelmdashtheoretically possible given that they are all cat-egorical variablesmdashholds a senior political position

By plotting the two models we can now easily compareboth the coefficients within each model and across thetwo models The fact that only single estimates are plottedfor PR Only Costa Rican in PR and Vote share marginsignals that these predictors appear in only one modelRather than having to compare individual parameter esti-mates (and the presence or absence of asterisks) acrossmodels in a regression table a vertical scan of the graphshows that the estimates are mostly robust across modelsas the parameter estimates and their respective confidenceintervals vary little Finally plotting the coefficients forthe term indicators shows that LDP members in their firstterm are much less likely to receive leadership posts allthings equal than members in their third terms an intu-itive result that does not necessarily stand out in thecrowded regression table

Using Multiple Plots to Present Multiple ModelsAs the number of models increase we suggest a differentstrategy Instead of presenting all the models and predic-tors in a single plot we use ldquosmall multiplerdquo plots to presentresults separately for each predictor The main objectivewhen presenting results from multiple models is to explorehow inferences change as we change the model specifica-tion or use different subsamples or both Using multipledot plots with error bars allows the researcher to commu-nicate the information in a multiple regression table withmuch greater clarity and also make it much easier to com-pare parameter estimates across models This strategy alsoovercomes any problems that might arise from having pre-dictors with greatly varying scales since the coefficientsfrom each independent variable are presented in a sepa-rate plot

As an example we return to table 4 of Ansolabehereand Konisky (see table 5 above) turning it into the graphpresented in figure 842 Rather than placing all the predic-tors in a single plot which would make it difficult tocompare individual estimates we created a separate panelfor each of the six predictors with the panels presented ina single column We also shift strategy and display theparameter estimates on the y-axes along with 95 percentconfidence intervals This maximizes efficiency since wecan stack more plots into a single column than into a

| |




single row given the portrait orientation of journals Thex-axis depicts which model is being displayed To facilitatecomparison across predictors we center the y-axis at zerowhich is the null hypothesis for each of the predictors

The regression table presents six models which varywith respect to sample (full sample vs excluding partisansregistration counties) and predictors (withwithout stateyear dummies and withwithout law change) On the x-axiswe group each type of model ldquofull samplerdquo ldquoexcludingcounties with partial registrationrdquo and ldquofull sample withstate year dummiesrdquo Within each of these types two dif-ferent regressions are presented including the dummy vari-able law change and not including it Thus for each typewe plot two point estimates and intervalsmdashwe differenti-ate the two models by using solid circles for the models inwhich law change is included and empty circles for themodels in which it is not We again choose not to graph

the estimates for the constants because they are not sub-stantively meaningful

This graphing strategy allows us to easily compare pointestimates and confidence intervals across models Althoughin all the specified models the percent of county with regis-tration predictor is statistically significant at the 95 per-cent level it is clear from the graph that estimates fromthe full sample with stateyear dummies models are sig-nificantly different from the other four models In addi-tion by putting zero at the center of the graph it becomesobvious which estimates have opposite signs depend-ing on the specification (log population and log medianfamily income) By contrast it is much more difficult tospot these changes in signs in the original table Thus byusing a graph it is easy to visually assess the robustness ofeach predictormdashboth in terms of its magnitude and con-fidence intervalmdashsimply by scanning across each panelIn summary the graph appropriately highlights the insta-bility in the estimates depending on the choice of model

Table 8Pekkanen Nyblade and Krauss (2006)table 1 Logit analysis of electoralincentives and LDP post allocation(1996ndash2003)

Variable Model 1 Model 2

Block 1 MP TypeZombie 018 (22) 027 (022)SMD Only minus019 (022) minus019 (024)PR Only minus039 (018) mdashCosta Rican in PR minus009 (029) mdash

Block 2 Electoral StrengthVote share margin mdash 0005 (0004)Margin Squared mdash mdash

Block 3 Misc ControlsUrban-Rural Index 004 (008) 004 (009)No Factional

Membershipminus086 (026) minus098 (031)

Legal Professional 039 (029) minus36 (030)Seniority

1st Term minus376 (036) minus366 (037)2nd Term minus161 (019) minus159 (021)4th Term minus034 (019) minus045 (021)5th Term minus117 (022) minus124 (024)6th Term minus115 (022) minus104 (024)7th Term minus152 (025) minus183 (029)8th Term minus166 (028) minus182 (032)9th Term minus134 (032) minus121 (033)10th Term minus289 (048) minus277 (049)11th Term minus188 (043) minus134 (046)12th Term minus108 (041) minus094 (049)

Constant 020 (20) 013 (026)Log-likelihood minus91724 minus76477N 1895 1574

Notes Dependent Variables 1 if MP holds a post of ministervice minister PARC or HoR Committee Chair

Base categories SMD dual-listed 3rd term Excluded obser-vations senior MPs that held no post (gt 12 terms PR-OnlyMPs in Model 2)

p lt 10 p lt 05 p lt 001

Figure 7Using parallel dot plots with error bars topresent two regression models

Table 1 from Pekkanen et al 2006 displays two logistic regres-sion models that examine the allocation of posts in the LDP partyin Japan We turn the table into a graph and present the two mod-els by plotting parallel lines for each of them grouped by coef-ficients We differentiate the models by plotting different symbolsfor the point estimates filled (black) circles for Model 1 andempty (white) circles for Model 2

| |



ConclusionAs a largely empirical discipline the quality of politicalscience depends on how well its practitioners can commu-nicate their findings to audiences professional and publicWe believe that a turn towards greater use of graphicalmethods particularly for regression results can onlyincrease our ability to communicate successfully

A potential objection to our approach is that the ben-efits of graphs in terms of aiding comparisons are out-weighed by the corresponding loss of precision inpresenting data or results This objection certainly holdswith respect to aiding replication studies as it is difficultto measure replication against a graph43 Greater use ofgraphs will increase the burden on researchers to aid rep-lication studies in other ways by publishing correspond-ing tables or replication materials on public archives orweb sites or both Yet with respect to the broader goal ofpresentation the choice of precision versus communica-tion is in fact false given the nature of the phenomenastudied by political scientists measurement error and othersources of uncertainty renders an illusion the precisionimplied by tables Indeed the inherent ability of graphsto present uncertainty efficiently is one of their majorstrengths

The range of graphs we have presented in this paper isnot exhaustive With respect to descriptive statistics forinstance we have not discussed scatterplots which canprove useful in a variety of situations44 And with respectto regression results graphs provide a powerful way todepict regression coefficients over time45 In many instancesit should be possible to take our graphical examples hereand apply them as needed to other types of graphs But asour graphs demonstrate different empirical quantitiesrequire different strategies for presentation which in turnwill require researchers to be creative Examples of suchscenarios might include graphing one-tailed confidenceintervals or plotting single regression models where theindependent variables have varying scales

As our graphical examples and these possibilities indi-cate the methods we propose are ldquomore onerous than themethods currently used in political sciencerdquo to echo thewords of King et al in their call for researchers to presentquantities of interest46 Nevertheless we believe the extraeffort undertaken will lead to clearer and more accessi-ble papers lectures and presentations in political scienceand that the discipline has much to gain by moving fromtables to graphs

NotesWe have created a web site httptables2graphscomthat contains complete replication code for all thegraphs that appear in this article as well as additionalgraphs that we did not present due to space limitations

1 King et al 2000

Figure 8Using ldquosmall multiplerdquo plots to presentregression results from several models

Table 4 from Ansolabehere and Konisky 2006 presents regres-sion results from six separate models We turn the table into agraph that displays a single plot for each predictor varyingacross models The models vary with respect to sample (full sam-ple vs excluding partisans registration counties) and predictors(withwithout state year dummies and withwithout law change) Onthe x-axis we group each type of model ldquofull samplerdquo ldquoexclud-ing counties with partial registrationrdquo and ldquofull sample with stateyear dummiesrdquo Within each of these types two different regres-sions are presented including the dummy variable law change andnot including it For each type we plot two point estimates and inter-vals using solid circles for the models in which law change isincluded and empty circles for the models in which it is not

| |




2 We should note that King et al (2000) did implic-itly urge researchers to use graphs by presentingtheir results mainly in graphical displays their mainfocus however was on call on researchers to usequantities of interest rather than on how to commu-nicate these quantities

3 See eg Bowers and Drake 2005 Epstein et al2006 Epstein et al 2007 and Gelman et al 2002

4 This neglect may be due in part to the fact that thiswork is likely to reach only a small subset of thediscipline or is narrow in focus Epstein et al 2006and Epstein et al 2007 which are aimed at legalresearchers appear in the Vanderbilt Law Review andare likely to be seen only by political scientists whostudy law and courts Bowers and Drake 2005 doesappear in a political science journal (Political Analy-sis) but its focus is on using exploratory graphicaldisplays to improve inferences drawn from multi-level models and not the general use of graphs in-stead of tables Finally the main inspiration for ourpapermdashGelman et al 2002mdashwas written by and forstatisticians and hence is unlikely to have been seenby many political scientists

5 We examined only one issue of the AJPS because ofthe large number of papers in that issue relative tothe other two journals

6 Gelman et al 20027 One point of comparison for this measure can be

found in Gelman et al 2002 the issue of the Jour-nal of the American Statistical Association (March 2000)that they analyzed contained 72 graphs and 60 tables

8 For clarity we distinguish these results from ldquoquanti-ties of interestrdquo such as changes in predicted proba-bilities while still recognizing that the latter resultfrom regression analyses

9 See eg du Toit et al 1986 Cleveland 1993 andJacoby 1997

10 STATA for example has user-written commandsavailable (eg ESTOUT by Jann 2005) that convertregression output to a table in LATEX or textformat

11 We prepared the graphs in this paper using the R (RDevelopment Core Team 2006) statistical environ-ment While we used the base graphics package forthe majority of graphs in figure 5 we used Sarkar2006rsquos implementation of Trellis (Cleveland 1993Cleveland et al 1996) graphics in R and in Figure 8we used the grid package For an excellent introduc-tion to R graphics that includes discussion of basegrid and lattice graphics see Murrell 2006

12 Which is not to say that the quality of tables inpolitical science and elsewhere could not be im-proved For advice in constructing good tables seechapter 10 in Wainer 2000

13 Gelman et al 2002

14 See eg Cleveland 1993 Jacoby 1997 ch 1 andthe studies cited in Gelman et al 2002 121ndash2

15 Iversen and Soskice 200616 Hartigan and Kleiner 1981 1984 Friendly 1994

199917 Friendly 199418 McClurg 200619 Cleveland 1993 Jacoby 200620 Numerical ordering is especially important when

presenting the values of an individual variable sinceit in effect presents its empirical distribution SeeWainer (2001) Wainer (2005 ch 11ndash12) andFriendly and Kwan (2003) for discussions on graph-ical ordering

21 Cleveland and McGill 1985 83222 Kaplan Park and Ridout 200623 On kernel density plots see Chambers et al 1983

on boxplots see Tukey 197724 Hintze and Nelson 199825 Letting t 15 (75th percentilendash25th percentile) the

lower adjacent value equals the smallest observationgreater than or equal to the 25th percentilemdasht the upperadjacent value equals the largest observation lessthan or equal to the 75th percentile t The presenceof many values below and above the lower and uppervalues can be caused by either outliers or skewness(Cleveland and McGill 1985 832)

26 Schwindt-Bayer 200627 For each chamber and time period ldquoother billsrdquo

constitute a majority of all bills Another optionwould be to exclude these bills and use the sum ofthe other seven issue areas as the denominator

28 Cleveland 1985 4ndash529 Cleveland 1993 For excellent examples of dot plots

sorting and general guidance on how to use R andlattice graphics to create dot plots see Jacoby 2006

30 Tufte 198331 See the paperrsquos web site for examples of these types

of graphs32 Johnson 1999 for wildlife management Schmidt

1996 for psychology Sterne et al 2001 for medi-cine Gelman and Stern 2006 for statistics Arm-strong 2007 for forecasting Gill 1999 for politicalscience

33 Greene 1997 15834 Gill 1999 66335 Indeed Political Analysis advises authors that when

constructing tables ldquo[i]n most cases the uncertaintyof numerical estimates is better conveyed by confi-dence intervals or standard errors (or completelikelihood functions or posterior distributions)rather than by hypothesis tests and p-valuesrdquo (Politi-cal Analysis Information for Authors 2007)

36 Ansolabehere and Konisky 200637 Stevens et al 2006

| |



38 We could of course indicate any number of confi-dence intervals (using vertical tick marks or thin andthick lines for example) if desired including inter-vals analogous to commonly reported 90 percentsignificance levels (ie when p 1) See Clevelandand McGill 1985 figure 5 for an example usingtick marks to report 50 percent intervals and thepaperrsquos website for a version of figure 6 that plots 90percent and 95 percent confidence intervals

39 Austin and Hux 2002 Schenker and Gentleman2001

40 Multiple comparisons raise various methodologicalissues See Hsu and Peruggia 1994 for a discussionof Tukeyrsquos multiple comparisons method and a novelgraphical display

41 Pekkanen et al 200642 Ansolabehere and Konisky 2006 This plot was

inspired by the plotbugs function available in Sturtzet al 2005 where it serves a different purpose (con-vergence diagnostics)

43 King 199544 Cleveland and McGill 198445 See eg Gelman et al 200746 King et al 2000 360

ReferencesAnsolabehere Stephen and David M Konisky 2006

The introduction of voter registration and its effecton turnout Political Analysis 14 (1) 83ndash100

Armstrong J Scott 2007 Significance tests harmprogress in forecasting International Journal of Fore-casting 23 (2) 321ndash27

Austin Peter C and Janet E Hux 2002 A brief noteon overlapping confidence intervals Journal of Vascu-lar Surgery 36 (1) 194ndash95

Bowers Jake and Katherine W Drake 2005 EDA forHLM Visualization when probabilistic inference failsPolitical Analysis 13 (4) 301ndash26

Chambers John M Cleveland William S Kleiner andPaul A Tukey 1983 Graphical Methods for DataAnalysis Murray Hill NJ Bell Telephone Laborato-ries Incorporated

Cleveland William S 1985 The Elements of GraphingData Murray Hill NJ Bell Telephone LaboratoriesInc_ 1993 Visualizing Data Murray Hill NJ ATampT

Bell LaboratoriesCleveland William S Richard A Becker and MingJen

Shyu 1996 The visual design and control of trellisdisplay Journal of Computational and Graphical Statis-tics 5 (2) 123ndash55

Cleveland William S and Robert McGill 1984 Themany faces of a scatterplot Journal of the AmericanStatistical Association 79 (388) 807ndash22

_ 1985 Graphical perception and graphical meth-ods for analyzing scientific data Science 229 (4716)828ndash33

du Toit SHC AGW Steyn and RH Stumpf1986 Graphical Exploratory Data Analysis New YorkSpringerVerlag

Epstein Lee Andrew D Martin and Christina LBoyd 2007 On the effective communication of theresults of empirical studies part II Vanderbilt LawReview 60 101ndash46

Epstein Lee Andrew D Martin and Matthew MSchneider 2006 On the effective communication ofthe results of empirical studies part I Vanderbilt LawReview 59 1811ndash871

Friendly Michael 1994 Mosaic displays for multi-waycontingency tables Journal of the American StatisticalAssociation 89 (425) 190ndash200_ 1999 Extending mosaic displays Marginal con-

ditional and partial views of categorical data Journalof Computational and Graphical Statistics 8 (3)373ndash95

Friendly Michael and Ernest Kwan 2003 Effect order-ing for data displays Computational Statistics andData Analysis 43 (4) 509ndash39

Gelman Andrew Boris Shor Joseph Bafumi and DavidPark 2007 ldquoRich State Poor State Red state Bluestate Whatrsquos the matter with Connecticutrdquo Colum-bia University technical report

Gelman Andrew Cristian Pasarica and Rahul Dodhia2002 Letrsquos practice what we preach turning tables intographs American Statistician 56 (2) 121ndash30

Gelman Andrew and Hal Stern 2006 The differencebetween ldquosignificancerdquo and ldquonot significantrdquo is notitself statistically significant American Statistician 60(4) 328ndash31

Gill Jeff 1999 The insignificance of null hypothesissignificance testing Political Research Quarterly 52 (3)647ndash74

Greene William H 1997 Econometric Analysis UpperSaddle River NJ Prentice Hall Inc

Hartigan John A and Beat Kleiner 1981 Mosaics forcontingency tables In Computer Science and StatisticsProceedings of the 13th Symposium on the Interface edW F Eddy New York SpringerVerlag_ 1984 A mosaic of television ratings American

Statistician 38 (1) 32ndash5Hintze Jerry L and Ray D Nelson 1998 Violin plots

A box plot-density trace synergism American Statisti-cian 52 (2) 181ndash84

Hsu Jason C and Mario Peruggia 1994 Graphicalrepresentations of Tukeyrsquos multiple comparisonmethod Journal of Computational and GraphicalStatistics 3 (2) 143ndash61

Iversen Torben and David Soskice 2006 Electoralinstitutions and the politics of coalitions Why some

| |




democracies redistribute more than others AmericanPolitical Science Review 100 (2) 165ndash81

Jacoby William G 1997 Statistical Graphics for Univar-iate and Bivariate Data Thousand Oaks CA SagePublications_ 2006 The dot plot A araphical display for la-

beled quantitative values Political Methodologist 14(1) 6ndash14

Jann Ben 2005 Making regression tables from storedestimates Stata Journal 5 (3) 288ndash308

Johnson Douglas H 1999 The insignificance of statis-tical significance testing Journal of Wildlife Manage-ment 63 (3) 763ndash72

Kaplan Noah David K Park and Travis N Ridout2006 Dialogue in American political campaigns Anexamination of issue convergence in candidate televi-sion advertising American Journal of Political Science50 (3) 724ndash36

King Gary 1995 Replication replication PS PoliticalScience 28 (3) 443ndash52

King Gary Michael Tomz and Jason Wittenberg2000 Making the most of statistical analyses Im-proving interpretation and presentation AmericanJournal of Political Science 44 (2) 347ndash61

McClurg Scott D 2006 The electoral relevance ofpolitical talk Examining disagreement and expertiseeffects in social networks on political participationAmerican Journal of Political Science 50 (3) 737ndash54

Murrell Paul 2006 R Graphics Boca Raton FL Chap-man amp HallCRC

Pekkanen Robert Benjamin Nyblade and Ellis SKrauss 2006 Electoral incentives in mixed-membersystems Party posts and zombie oliticians in JapanAmerican Political Science Review 100 (2) 183ndash93

Political Analysis Information for Authors 2007 availableat httpwwwoxfordjournalsorgpolanafor_authorsgeneralhtml [accessed 24 June 2007]

R Development Core Team 2006 R A Language andEnvironment for Statistical Computing Vienna Aus-tria R Foundation for Statistical Computing

Sarkar Deepayan 2006 lattice Lattice Graphics Rpackage version 0149

Schenker Nathaniel and Jane F Gentleman 2001 Onjudging the significance of differences by examiningthe overlap between confidence intervals AmericanStatistician 55 (3) 182ndash86

Schmidt Frank L 1996 Statistical significance testingand cumulative knowledge in psychology Implica-tions for training of researchers Psychological Methods1 (2) 115ndash29

Schwindt-Bayer Leslie A 2006 Still supermadresGender and the policy priorities of Latin Americanlegislators American Journal of Political Science 50 (3)570ndash85

Sterne Jonathan AC George Davey Smith and DRCox 2001 Sifting the evidencemdashWhatrsquos wrong withsignificance tests Another comment on the role ofstatistical methods British Medical Journal 322(7280) 226ndash31

Stevens Daniel Benjamin G Bishin and Robert RBarr 2006 Authoritarian attitudes democracyand policy preferences among Latin Americanelites American Journal of Political Science 50 (3)606ndash20

Sturtz Sibylle Uwe Ligges and Andrew Gelman 2005R2WinBUGS A package for running WinBUGSfrom R Journal of Statistical Software 12 (3) 1ndash16

Tufte Edward R 1983 The Visual Display of Quantita-tive Information CheshireCT Graphics Press

Tukey John W 1977 Exploratory Data Analysis Read-ing MA AddisonWesley

Wainer Howard 2000 Visual Revelations GraphicalTales of Fate and Deception From Napoleon BonaparteTo Ross Perot Mahwah NJ LEA Inc_ 2001 Order in the Court Chance 14 (2) 43ndash6_ 2005 Graphic Discovery A Trout in the Milk and

Other Visual Adventures Princeton NJ PrincetonUniversity Press

| |



them into graphs showing that it is possible and desirableto do so for any table that presents numeric informationincluding data summaries and parameter estimates Weshow that graphs better communicate relevant informa-tion from both data summaries and regression modelsincluding comparing values across variables or models andthe sign and significance of predictors We argue that whilegraphs are almost never used to present regression resultsthe benefits from doing so are significant In particulargraphs are superior at displaying confidence intervals forparameter estimates (and thus their uncertainty) and formaking comparisons across models We believe that schol-ars who follow our advice will both understand their databetter and present their empirical results more clearly totheir audience thereby increasing the value and impact oftheir research

The Use of Tables versus Graphs inPolitical ScienceBefore presenting examples of using graphs instead of tablesit is useful to examine when and how political scientistscurrently use each The five issues we looked at contained52 articles 40 of which presented at least one table orgraph These 40 articles contained 150 tables and 89 graphsa roughly 2-to-1 ratio7 To understand the motivation ofpolitical scientists in presenting empirical results we coded

the type of information conveyed by each such as sum-mary statistics parameter estimates and uncertainty andpredicted values Figure 1 presents both the frequencywith which each type of information appears (in eithertabular or graphical form) along with the percentage ofgraphs that are used within each category (More detailedinformation on our coding can be found in the caption)

The most striking findings center around the presenta-tion of regression results which comprise more than 30percent of all tables and graphs combined We find thatmore than half the tables in our sample were used to presentsuch resultsmdashthat is point estimates and uncertainty usu-ally accompanied by some combination of asterisks boldtypeface or letters to indicate statistical significance8 Inaddition not a single graph presented in the five issues westudied communicated regression results Clearly politicalscientists are of the belief that tables are the most effectivewaymdashit seems in fact the only waymdashto present pointestimates and uncertainty

We turn next to summary statistics which include quan-tities suchasmeans standarddeviations and frequency sum-maries These types of statistics comprised 32 percent of allthe graphs and tables in our sample or roughly the samepercentage as regression results Given that the traditionaluse of statistical graphics focuses on data summaries9

we might expect researchers to use graphs frequently to

Figure 1Tables and graphs in political science journals

The left graph depicts the percentage of all graphs and tables presented in five political sciencejournals that fall into the categories on the y-axis (ie the number of graphs and tables that fall intoeach category divided by the total number of tables and graphs) the right graph depicts thepercentage of graphs within each category (ie the number of graphs in each category divided bythe total number of tables and graphs in the respective category) ldquoEstimates and uncertaintiesrdquoinclude such quantities as regression coefficients and standard errors ldquoSummary statisticsrdquo includedescriptive statistics like means and standard deviations ldquoPredicted valuesrdquo include post-regressionestimations such as changes in predicted probabilities ldquoNon-numericrdquo includes any information thatis not quantitative ldquoMathematicalrdquo generally includes figures from formal models finally ldquootherrdquo is aresidual category The plots show that summary stats and estimates and uncertainties comprise themajority of graphical and tabular presentationmdashwhile the former are sometimes displayed graphically(about 40 of the time in our sample) the latter are always displayed as tables

| |
















| |








Left Right

Proportionof Right

Governments





| |













Agreement043 041 0 1 1154

PoliticalKnowledge

122 042 0 2 1220




| |














| |










(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |















| |








Left Right

Proportionof Right

Governments





| |













Agreement043 041 0 1 1154

PoliticalKnowledge

122 042 0 2 1220




| |














| |










(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |








Left Right

Proportionof Right

Governments





| |













Agreement043 041 0 1 1154

PoliticalKnowledge

122 042 0 2 1220




| |














| |










(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |












Agreement043 041 0 1 1154

PoliticalKnowledge

122 042 0 2 1220




| |














| |










(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |














| |










(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |









(CQ Ranking)65 154 12 000 3


65 347 271 028 1339


65 112 132 003 926


65 12 085 minus065 313


(binary)43 028 045 000 1




| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |







246 257 139 165 87 94 57 57 1102







| |














FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |













FullSample

(1)


registration(2)


dummies(3)

FullSample

(4)


registration(5)

Fullsample

w state-yearDummies

(6)







Constant 147 170 0775 145 168 0819(0152) (0171) (0124) (0152) (0170) (0127)

R 2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |
















FullSample

(1)


registration(2)

Fullsample

w state-yeardummies

(3)Full

Sample (4)


registration(5)

Fullsample

w state-yearDummies

(6)











0036[0012006]

0017[minus00030037]

0047[00250069]


0016[minus00040036]



0050[00240076]





0070[00120128]

0011[minus00370059]

0072[00160128]

0071[00130129]

0013[minus00350061]







Constant 1470[1166 1774]

1700[13582042]

0775[05271023]

1450[11461754]

1680[134202]

0819[05651073]

R2 091 091 094 091 091 094N 3572 3153 3572 3572 3153 3572


| |








VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |







VariableCoefficient

(Standard Error)



Chile 93 (32)BM

Colombia 146 (32)BM


Venezuela 96 (37)BM




22 (12)


minus21 (12)


minus32 (12)


minus27 (07)









| |













| |



















p lt 10 p lt 05 p lt 001



| |








1 King et al 2000



| |

































| |




































| |




























| |
































| |




































| |




























| |




































| |




























| |



























| |



using graphs instead of tables in political sciencetabular or graphical form), along with the...

Documents