Encyclopedia of Sociology Vol

had always rested on coercion and demands for the dispensation of order and been supported by religious belief and tradition, but from the age of constitutions, the legitimacy of state authority rested on whether the ruler abided by the limits in the constitution and recognized the rights of the elites and popular groups that had established that constitution.

Constitutions meant that a new relationship was forged between the state and the population of the territory it ruled. Under empires, the state established order and most people were simply economic producers, not political actors. By contrast, under constitutions, the people, or at least those involved in creating and establishing constitutional rule, were the ultimate controllers and beneficiaries of state power. This new relationship led to new demands by various groups.

One demand was for greater and more regular political participation by groups that had been excluded: religious and ethnic minority groups, women, and the poor. Though frequently resisted by elites and state rulers, in many areas those groups gained elite allies and acquired rights to regular political participation, most notably through voting (Reuschemeyer et al. 1992). States where voting rights are widespread and the state’s power over its subjects has significant limits are commonly described as democratic or ‘‘liberal’’ states. By the late nineteenth century, most of the states in Europe west of Russia and in North and South America were liberal states.

Another demand came from professionals, merchants, and sometimes military officers who lived under empires and wanted to take control of their positions and territories under something like the relationship that prevailed in constitutional regimes, where the state was identified as an instrument of the people rather than the reverse. Those elites argued that every ethnic group should be entitled to its ‘‘own’’ state and its own rulers. The resulting ideology was known as ‘‘nationalism’’ (Calhoun 1998), and it spread widely throughout the world. Nationalism fueled the revolutions of 1830 in Poland and Greece; those of 1848 in Hungary, Germany, Italy, and Romania; the effort

to expel the Austro-Hungarians and unify Italy under Italian rule in the 1860s; and the Serb liberation movement that helped start World War I. Nationalist sentiments also fueled revolts in Ireland throughout the nineteenth and twentieth centuries; the Chinese Republican Revolution of 1911; the anticolonial revolutions in India, Algeria, Indonesia, and Vietnam after World War II; and a host of other anticolonial revolts in Africa and Asia.

Nationalism fostered the ideal that states should be ‘‘national’’ states, reflecting the identity and promoting the aspirations of their inhabitants as a united community rooted in shared traditions and culture (Anderson 1991). In fact, to comply with this ideal, many traditions had to be invented and national languages had to be created. Even today, it often is ambiguous whether a given nation-state reflects a nation (Is there is British nation or only English, Welsh, and Scottish nations plus portions of Scot-settled Ireland sharing the state of Great Britain?). However, the ideal of the nation-state spread widely, even to older states, so that it became expected that modern nation-states would have a national language, a national flag and anthem, national systems of schooling and communications (newspapers, radio, and television), national systems of transportation (highways, railways, and airlines), and a national army.

Nonetheless, since almost all existing states included members of more than one ethnic, linguistic, or cultural group within their boundaries, most nation-states inevitably failed to satisfy to a greater or lesser degree the aspirations of subnational groups, which in turn often developed their own nationalist ambitions. A large number of the violent conflicts in the world in recent years are the result of nationalist movements within nation-states, such as the Chechens in Russia, the Basques in Spain, the Kurds in Turkey, the Uighurs in China, and the Albanian Kosovars in Yugoslavia.

While nationalism seemed poised to bring more liberal, constitutional states into being, things did not develop that way. The defeat of many early nationalist movements led nationalist leaders to conclude that above all else, a people needed a

strong state to protect them from control by others, whether multinational empires or other nations. As a result, many nationalist movements gave rise to authoritarian, populist dictatorships. Those dictatorships often promulgated constitutions and claimed to draw their legitimacy—in the modern fashion—from their service to and identification with the people of the territories they ruled, but in fact they operated in as absolute a manner as any older imperial state, only now they were backed by the latest industrial and military technology. Thus, while nationalism was destroying the old traditional empires and replacing them with modern states, those modern states were following divergent paths into democracy and dictatorship.

DEMOCRACIES AND DICTATORSHIPS

The history of the state in the twentieth century has largely been one of a struggle between democracies and dictatorships. In the liberal states over the course of the twentieth century, the range of citizen rights has been expanding, the participation in politics of ordinary citizens (through rallies, financial contributions, petitions, and voting) has grown, and the obligations of the state to support its citizens (the modern ‘‘welfare state’’) have been extended. A major result of these patterns is that women, the working class, and the poor are far more closely integrated into political life in liberal states as voters and direct recipients of state actions than ever before (O’Conner et. al, 1999). To accommodate and channel this political participation, most liberal states have a number of political parties that organize and control the competition for political power. At the end of the twentieth century, as a result of growing state obligations, the personnel and budget of modern liberal states has swollen to the point where state expenditures make up one-quarter to one-half of the entire national product of their societies.

However, the model of the liberal state did not triumph in every place where empires collapsed. In many regions, spurred by nationalist sentiment and the failure of liberal states to provide economic and military security under the chaotic

conditions that followed military defeat or economic crises, modern dictatorships emerged. Some of those dictatorships, such as those of Adolph Hitler and his Nazi Party in Germany and Benito Mussolini and his Fascist Party in Italy, did not outlast their founders. However, in Russia and China, Communist parties took on a dominant life of their own, and those countries became oneparty states in which everything of economic, military, and political importance was controlled by the party-state. In other countries, notably in Africa (e.g., Nigeria), Latin America, and eastern Asia (e.g., Korea and Indonesia), military personnel seized power and held on for periods ranging from years to generations. For most of the twentieth century, such modern one-party and military dictatorships, all professing nationalist ideals and even staging (controlled) popular elections, controlled the vast majority of the states and peoples of the world.

In the last two decades of the twentieth century, however, the majority of those one-party states and military dictatorships collapsed (Walder 1995; Goldstone et al. 1991). Their extensive control of the economy stifled innovation and encouraged corruption, leading their revenues to fall well below those of the leading liberal states. Within dictatorial states, even the elites looked on the far greater material wealth and personal freedom of their counterparts in liberal states with envy. Efforts at reform in one-party and military states thus quickly turned into movements to establish liberal regimes. As a result, for the first time in history, it appears that humankind will enter a new millennium with a majority of its nations and populations living under liberal constitutional states (Huntington 1991).

BEYOND THE NATION-STATE

While the twentieth century has closed with the national, liberal state seemingly triumphant, there is no assurance that this form of state will endure. Constitutional states often have been overthrown by dictatorships, both military and populist, when they encounter severe military or economic setbacks. The Great Depression led a host of democ-

racies to collapse into dictatorships, and struggles with economic development led many Latin American and African states into communist takeovers and military coups in the 1960s and 1970s. In most of the world outside Europe and North America, liberal states are not firmly established and may be vulnerable if another major economic trauma sweeps the globe. Thus, the past threats to the continuance of liberal states may reemerge.

In addition, new threats to the primacy of the nation-state have arisen in the form of supranational organizations with genuine sovereignty and military power. The most notable of these organizations are NATO (a military alliance with a unified command embracing the forces of most European nations and the United States) and the European Union (a supranational body ruled by representatives from most European nations with taxing and legislative authority over certain aspects of its member states). A variety of cooperative multinational organizations established by treaty, such as the United Nations, the International Monetary Fund, the International Court of Justice, and various environmental commissions and human rights organizations, also have impinged on state sovereignty. The future may see still greater transfers of state power to such supranational bodies as the problems of establishing human rights, safeguarding the global environment, and maintaining stable and sound financial institutions may grow beyond the capacity of any single state or ad hoc arrangement of states to resolve.

REFERENCES

Anderson, Benedict 1991 Imagined Communities. Lon-

don: Verso.

Calhoun, Craig 1998 Nationalism. Minneapolis: Univer-

sity of Minnesota Press.

Eisenstadt, S. N. 1963 The Political Systems of Empires. London: Macmillan.

Goldstone, Jack A. 1991 Revolution and Rebellion in the Early Modern World. Berkeley: University of California Press.

———, Ted Robert Gurr, and Farrokh Moshiri 1991

Revolutions of the Late Twentieth Century. Boulder, Colo.: Westview.

Huntington, Samuel P. 1991 The Third Wave: Democratization in the Late Twentieth Century. Norman: Oklahoma University Press.

Mann, Michael 1986 The Sources of Social Power. Cambridge, U.K: Cambridge University Press.

O’Conner, Julia S, Ann Shola Orloff, and Sheila Shaver 1999 States, Markets, Families: Gender, Liberalism, and Social Policy in Australia, Canada, Great Britain, and the United States. Cambridge: Cambridge University Press.

Poggi, Gianfranco 1990 The State: Its Nature, Development, and Prospects. Stanford, Calif.: Stanford University Press.

Rueschemeyer, Dietrich, Evelyn Huber Stephens, and John D. Stephens 1992 Capitalist Development and Democracy. Chicago: University of Chicago Press.

Tilly, Charles 1990 Coercion, Capital, and European States, AD 990–1990. Oxford, UK: Basil Blackwell.

Walder, Andrew 1995 The Waning of the Communist State. Berkeley and Los Angeles: University of California Press.

Weber, Max 1968 Economy and Society, edited by Guenther Roth and Claus Wittich. New York: Bedminster.

JACK A. GOLDSTONE

STATISTICAL GRAPHICS

Statistical graphs present data and the results of statistical analysis, assist in the analysis of data, and occasionally are used to facilitate statistical computation. Presentation graphs include the familiar bar graph, pie chart, line graph, scatterplot, and statistical map. Data analysis employs these graphical forms as well as others. Computational graphs (‘‘nomographs’’) sometimes display data but usually show theoretical quantities such as power curves for determining sample size. Computational graphs are convenient when statistical tables would be unwieldy, but computer programs are even more convenient, and so nomographs are used with decreasing frequency. This article emphasizes the role of graphs in data analysis, although many of the considerations raised here also apply to graphical presentation.

Although it generally is recognized that the pictorial representation of information is a par-

J GEOPHYS RES: PHYS

J APPL POLYM SCI: CHEM J EXP BIOL: BIO

J CHEM (FARADAY TRANS): CHEM J APPL PHYSICS: PHYS

JEEE COMM RADAR SIG: ENG BELL SYST TECH J: ENG

LIFE SCIENCES: BIO

J PHYS CHEM: CHEM JEEE TRANS COMMUN: ENG J CLIN INVESTIGATION: MED

J PHYSICS (C): PHYS PROC R SOC (SER B): BIO

SCIENTIFIC AM: GEN

PHYS REV (LETT): PHYS J EXP MED: MED

J AM CHEM SOC: CHEM PHYS REV (A): PHYS

NATURE (LONDON): GEN PROFESS GEOGR: GEOG

LANCET: MED SCIENCE (REPORTS): GEN IBM J RES DEVELOP: ENG NEW ENG J MED: MED

ANN AS AM GEOGR: GEOG GEOGR J: GEOG GEOGR REV: GEOG

SCIENCE (ARTICLES): GEN CELL: BIO

J R STAT SOC (SER C): PSYC J AM STST AS (APPLIC): STAT COMPUT GRA IM PROC: COMP J AM STAT AS (THEORY): STAT

COMPUTER J: COMP

AM MATH MO: MATH

COMMUN ACM: COMP BIOMETIKA: STAT COMPUTER: COMP

ANN STATIST: MATH T AM MATH SOC: MATH

PERCEPT PSYCHOPHYS: STAT J EXP PSYCHOL: PSYC BR J PSYCHOL: PSYC AM EDUC RES: EDUC AM ECON REV: ECON BELL J ECON: ECON J POLIT ECON: ECON EDUC RES: EDUC

ECONOMETRICA: ECON

REV ECON STAT: ECON

AM J SOCIOL: SOC AM SOCIOL REV: SOC SOCIAL FORCES: SOC

REV EDUC RES: EDUC

BR J SOCIOL: SOC OXFORD REV EDUC: EDUC

J SOC PSYCHOL: PSYC

Graph Area (Fraction of Total)

0.00.05 0.10 0.15 0.20 0.25 0.30 0.35

NATURAL

MATHEMATICAL

SOCIAL

ticularly effective mode of communication, statistical graphs seldom appear in sociological publications. Figure 1, from Cleveland (1984), shows the relative space devoted to graphs in leading scientific publications, including four sociology journals. Sociology, of course, is not a wholly quantitative discipline. Nevertheless, even a cursory examination of publications in the field reveals that sociologists much more frequently report numerical information in tabular than in graphical form. Informal observation also suggests that sociologists usually analyze numerical data without the assistance of statistical graphs, a situation that may be changing.

HISTORY

Broadly construed, graphic communication dates to the cave paintings of human prehistory and to the earliest forms of writing, which were pictorial or semipictorial. The first diagrams to communicate quantitative information—about location and distance—were maps: Egyptian cartographers employed coordinate systems in maps prepared 5,000 years ago, and cartography remains a relatively well developed area of graphical representation. Musical notation, which charts pitch as a function of time, also has an ancient origin and illustrates the spatial display of essentially nonspatial information. Rectilinear coordinate graphs are so familiar that it is easy to lose sight of the radical abstraction required to represent diverse quantities, such as pitch, as distances along an axis.

In the seventeenth century, the French mathematician and philosopher René Descartes established the relationship between algebraic equations and curves in a rectilinear coordinate space. The graphical representation of functions is not logically necessary for the display of empirical data as points in space, and there are isolated examples before Descartes of statistical graphs that employ abstract coordinate systems. Nevertheless, Descartes’s analytic geometry no doubt provided the impetus for the development of statistical graphics, and the most common forms of statistical graphs evolved slowly over the subsequent three and a half centuries.

Among many individuals’ contributions to this evolution, the work of William Playfair at the turn of the nineteenth century is of particular importance. First, Playfair either invented or popularized several common graphical forms, including the line graph, the bar graph, the pie chart, and the circle chart (in which areas of circles represent quantities). Second, Playfair employed statistical graphs to display social and economic data. Figure 2a, from Playfair’s 1786 Commercial and Political Atlas, is a time series line graph of imports to and exports from England in the period 1771–1782. In the original graph, the space between the two curves is colored green when the balance of trade favors England (i.e., when the curve for exports is above that for imports) and red when the balance favors England’s trading partners. Of the forty-two graphs in Playfair’s atlas, all but one depict time series. The sole exception is a bar graph of imports to and exports from Scotland (Figure 2b), the data for which were available only for the year 1780– 1781, precluding the construction of time series plots. Playfair’s 1801 Statistical Breviary included a wider variety of graphical forms.

The first half of the nineteenth century was a period of innovation in and dissemination of statistical graphics, particularly in England and France. The ogive (cumulative frequency curve), the histogram, the contour map, and graphs employing logarithmic and polar coordinates all appeared before 1850. Later in the century, the British scientist Sir Francis Galton exploited an analogy to contour maps in his determination of the bivari- ate–normal correlation surface, illustrating the role of graphs in discovery.

The nineteenth-century enthusiasm for graphic representation of data produced many memorable and high-quality statistical graphs, such as those of Playfair, Florence Nightingale, E. J. Marey, and Charles Joseph Minard (several of which are reproduced in Tufte 1983). The same enthusiasm produced early abuses, however, including the graph from M. G. Mulhall’s 1892 Dictionary of Statistics shown in Figure 3: The heights of the triangles indicate the accumulated wealth of each country, but their areas are wildly disproportionate to the quantities represented, conveying a misleading

Figure 2a

impression of the data. Furthermore, the horizontal arrangement of the countries bears no relationship to the purpose of the graph and apparently was done for artistic effect: It would be more natural to order the countries by wealth. Many modern graphs have similar problems, a situation that has motivated a substantial literature of graphic criticism (such as the works by Schmidt, Tufte, and Wainer discussed below).

The evolution of statistical graphics paralleled the general growth of statistical science well into the twentieth century. This relationship changed radically in the 1930s as statisticians such as R. A. Fisher emphasized the development of procedures for statistical inference. Fisher’s influential Statistical Methods for Research Workers, first published in 1925, includes a brief chapter on ‘‘diagrams’’; this chapter incorporates line graphs, scatterplots, and a histogram with a superimposed normal-density

curve. The remainder of the book, however, contains many numerical tables but just five additional figures, none of which presents empirical information. Fisher’s 1935 The Design of Experiments includes just three graphs, all of which are theoretical.

The rebirth of interest in statistical graphics may be traced to John W. Tukey’s work on exploratory data analysis, beginning in the 1960s and culminating in the publication of his text on this subject in 1977. Tukey’s coworkers and students, most importantly the group at Bell Laboratories and its successors associated with William S. Cleveland, continue to contribute to the modern development of statistical graphics (see, in particular, Chambers et al. 1983; Cleveland 1993, 1994). Further information on the history of statistical graphics can be found in Funkhouser (1937), Tufte (1983), and Beninger and Robyn (1978), the last of which contains a useful chronology and bibliography.

GRAPHIC STANDARDS

After several abortive efforts, the International Statistical Congresses held in Europe in the nineteenth century abandoned the attempt to formulate graphical standards. Since that time, many authors have proposed standards and principles for the construction of statistical graphs, but consensus on these matters remains elusive. Schmidt (1983, p. 17), for example, suggests that grid lines should always appear on rectilinear line graphs, while Tufte (1983, p. 112) maintains that grids ‘‘should usually be muted or completely suppressed,’’ an instance of his more general principle that good graphs maximize the ‘‘dataink ratio’’ (the amount of ink devoted to the display of data as a proportion of all the ink used to draw the

graph) and eliminate ‘‘chartjunk’’ (extraneous graphical elements).

Disagreements such as this are due partly to the lack of systematic data on graphical perception (a situation that is improving), partly to differences in style and taste, and partly to the absence of adequate general theories of graph construction and perception (although there have been attempts, such as Bertin 1973). Also, good graphical display depends on the purposes for which a graph is drawn and on particular characteristics of the data, factors that are difficult to specify in advance and in a general manner.

Huff (1954, chap. 5), for example, argues that scales displaying ratio quantities should always start at zero to avoid exaggerating the magnitude

of differences between data values. This principle, however, often disguises patterns in data that are revealed clearly by graphical magnification. Consider Figure 4, a and b, which shows the relative value of the Canadian and U.S. dollars in the eight weeks surrounding the June 23, 1990, deadline for the ratification of the ill-fated ‘‘Meech Lake’’ amendment to the Canadian constitution. This period was widely interpreted, both domestically and abroad, as one of constitutional crisis and uncertainty for Canada. Because in the short term the Canadian dollar traditionally trades in a narrow range against the U.S. dollar, Figure 4a is essentially uninformative, while Figure 4b reveals that the Canadian dollar fell slightly as the Meech deadline approached and rose afterward.

Despite some areas of disagreement, commentators on the design of statistical graphs, such

as Tufte (1983, 1990, 1997), Schmidt, and Wainer, offer a great deal of uncontroversially sound advice. In a tongue-in-cheek essay (reprinted in Wainer 1997: chap. 1), Wainer enumerates twelve rules to help the reader ‘‘display data badly.’’ Several of these rules are illustrated in Figure 5a, which appeared in the Miami Herald in 1984: ‘‘Rule 7, Emphasize the trivial (ignore the important)’’; ‘‘Rule 11, More is murkier: (a) more decimal places and

(b) more dimensions’’; and ‘‘Rule 12, If it has been done well in the past, think of a new way to do it.’’ The graph in Figure 5a is meant to show the presumably negative relationship between the success of the twenty-six major league baseball teams in the 1984 season and the average salaries paid to the players on those teams. The lengths of the bars represent average players’ salaries, while the teams’ records of wins and losses are hidden in parenthe-

ses within the bars, making it essentially impossible to tell whether the two variables are related—os- tensibly the point of the graph. The bars are drawn in three-dimensional perspective, apparently for artistic effect, but the result is that the quantities represented are slightly distorted: For example, the average salary of the New York Yankees, $458,544, appears to be about $410,000. A standard representation of these data appears in the scatterplot in Figure 5b, revealing a slight positive relationship between salary and success.

RESEARCH ON GRAPHIC PERCEPTION

The earliest psychophysical research on perception of graphs, conducted in the 1920s, focused on the relative merits of pie charts and bar charts for displaying percentage data and was inconclusive. More recently, statisticians and psychologists have undertaken systematic experimentation on graphical perception. Spence and Lewandowsky (1990) review the literature in this area up to 1990.

Cleveland and McGill (1984), for example, conducted a series of experiments to ascertain the

relative accuracy of ten elementary perceptual tasks that extract quantitative information from graphs, as represented schematically in Figure 6. Ranked in order of decreasing average accuracy, these tasks involve judgment of position along a common scale; position along nonaligned scales; length, direction, or angle; area; volume or curvature; and shading or color saturation. Similarly, Spence (reported in Spence and Lewandowsky 1990) has shown in an experiment that categorical information differentiating points on a scatterplot is encoded most effectively by colors and least effectively by confusable letters (e.g., E, F, H); other coding devices, such as different shapes (circles, squares, triangles), degrees of fill, and discriminable letters (H, Q, X), were intermediate in effectiveness.

Cleveland (1993) demonstrates that slope judgments are most accurate for angles close to fortyfive degrees and least accurate for angles near zero or ninety degrees. Cleveland therefore suggests that the aspect ratio of graphs (the relative lengths of the axes) be set so that average slopes are close to forty-five degrees, a procedure he terms ‘‘banking to forty-five degrees.’’ This process is illus-

Figure 5a

trated in Figure 7. Both graphs in this figure plot the same data, but the periodic pattern of the data is nearly impossible to discern in Figure 7a because the average slope of the curve is too steep.

Cleveland and his colleagues have designed new graphical forms that apply these and similar findings by encoding important information through the employment of accurately judged graphic elements. One such form is the dot graph, an exam-

Figure 5b. Major League Baseball salaries and team success in the 1984 season. (a) As depicted in the Miami Herald. The lengths of the bars (slightly distorted) represent the average salaries paid to players from each team; the teams’ won–lost records appear in parentheses within the bars. The apparent point of the graph is that there is a negative relationship between salaries and success. (b) The same data in standard scatterplot. The line on the plot, derived from a logistic regression of wins on average salaries, indicates a weak positive relationship between salaries and success.

ple of which appears in Figure 1. Similarly, Cleveland and McGill (1984) suggest the replacement of quantitative statistical maps that use shading or hue (e.g., Figure 8a) with maps that employ framed rectangles (Figure 8b), which exploit the more accurate judgment of position along nonaligned scales. Despite the inferiority of Figure 8a for judging differences in murder rates among the states, however, this map more clearly reveals regional variations in rates, illustrating the principle that the purpose for which a graph is drawn should influence its design.

The effectiveness of statistical graphs is rooted in the remarkable ability of people to apprehend, process, and remember pictorial information. The human visual system, however, is subject to distortion and illusion, processes that can affect the perception of graphs. Good graphical design can minimize and counteract the limitations of human vision. In Figure 9, for example, it appears that the difference between the hypothetical import and export series is changing when this difference