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Graphical Methods in Statistics Author(S): Stephen E Graphical Methods in Statistics Author(s): Stephen E. Fienberg Source: The American Statistician, Vol. 33, No. 4 (Nov., 1979), pp. 165-178 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2683729 Accessed: 16/09/2010 12:29 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=astata. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to The American Statistician. http://www.jstor.org Graphical Methodsin Statistics STEPHEN E. FIENBERG* do we have a systematicbody of experimentalresults to use as a guide. We have seen considerable in- Graphical methodshave played a centralrole in the developmentof novation in graphics during the past 20 years, but statisticaltheory and practice.This presentationbriefly reviews some the advances in statistical methodologyhave made of the highlightsin the historical developmentof statisticalgraphics room for even greaterinnovation in the future.These and gives a simple taxonomythat can be used to characterize the currentuse of graphicalmethods. This taxonomyis used to describe are the themes of this article. the evolution of the use of graphics in some major statisticaland The qualities and values of charts and graphs as related scientificjournals. compared withtextual and tabular formsof presenta- Some recent advances in the use of graphicalmethods for statis- tion have been summarizedby Calvin Schmid (1954) tical analysis are reviewed, and several graphical methods for the in his Handbook of Graphic Prese4t-ation: statisticalpresentation of data are illustrated,including the use of multicolormaps. 1. In comparison with other types of presentation, KEY WORDS: Diagnostic plots; Graphical methods; History of well-designed charts are more effectivein creating statistics; Maps, statistical; Standards for graphics; Statistical interestand in appealingto the attentionof the reader. graphics. 2. Visual relationships,as portrayedby charts and graphs, are more clearly grasped and more easily 1. INTRODUCTION remembered. 3. The use of charts and graphs saves time, since For no study is less alluring or more dry and tedious than the essential meaning of large masses of statistical statistics,unless the mind and imaginationare set to work or data can be visualized at a glance. thatthe person studyingis particularlyinterested in the subject; 4. Charts and graphs can provide a comprehensive which is seldom the case with young men in any rank in life. pictureof a problemthat makes possible a more com- These words were written178 years ago by William plete and better-balancedunderstandihg than could be Playfair,one of the fathersof statisticalgraphics, in derived fromtabular or textualforms of presentation. his The Statistical Breviary(1801). Playfair'spurpose 5. Charts and graphscan bringout hiddenfacts and in developinghis graphicalrepresentations of statistical relationshipsand can stimulate,as well as aid, analyti- data was to make the statisticsa littlemore palatable. cal thinkingand investigation. We have come a long way since Charts and 1801. This is, of course, what Playfair'swork was all about. graphsnow play an importantrole in data presentation. He said, 'I have succeeded in proposing and putting They are used in our textbooks and classrooms; they in practice a new and useful mode of stating ac- summarize data in our technical journals; they are counts, . as much informationmay be obtained in playingan increasingrole in governmentreports; they five minutesas would require whole days to imprint appear daily in our newspapers and popular maga- on the memory,in a lasting manner, by a table of zines. In the fieldof statistics,graphs and charts are figures." used not only to summarizedata but also as diagnostic aids in analysis, to organize Monte Carlo results,and, of course, to display theoreticalrelations. We have come far since the timeof Playfair,but we 2. LANDMARKS IN THE HISTORY OF have farto go. Actual practice in statisticalgraphics is STATISTICAL GRAPHICS highly varied, good graphics being overwhelmed by distorteddata presentation,cumbersome charts, and A paper on graphic methods in statisticswould be perplexingpictures. Although advice on how and when incomplete without some attentionto historical de- to draw graphs is available, we have no theory of velopment.This briefaccotint owes much to the work statisticalgraphics, nor, as Kruskal (1977) has noted, of Beniger and Robyn (1978) and the social graphics project at the Bureau of Social Science Research * Stephen E. Fienbergis Professor,Department of Applied Statis- (also see Feinberg and Franklin 1975) led by Albert tics, School of Statistics, Universityof Minnesota, St. Paul, MN Biderman. 55108. This article is based on a portionof a General Methodology AlthoughBeniger and Robyn (1978) trace attempts Lecture deliveredat the 137thannual meetingof the AmericanStatis- at graphic depictionof empiricaldata back to at least tical Association, Chicago, Illinois,August 18, 1977,and its prepara- the 10th or 11th centuryA.D;, it was only afterthe tion was supported in part by grant NIE-G-76-0096 from the National Instituteof Education, U.S. Departmentof Health, Educa- work of Crome and Playfair,in the late 18thand early tion and Welfare. The opinions do not necessarily reflect the 19th centuries,that the use of graphs and charts for positions or policies of the National Instituteof Education. The data displaybecame accepted practice.Playfair gave us U.S. Bureau of the Census has provided funds for the reproduc- the bar chartin his Commercial and Political Atlas tion of the color maps in Section 7. The authorwishes to acknowl- (1786) and the pie chart and circle graph in his The edge the assistance of Phillip Chapman and Stanley Wasserman in the preparationof this articleand the helpfulcomments and sugges- StatisticalBreviary (1801). His workprovides excellent tions of Albert Biderman, David Hoaglin, Kinley Larntz, William examples of good graphics;it conveys informationand Kruskal, Howard Wainer, the editor,and two anonymousreferees. is pleasing to the eye. (Also see the discussion of \? The American Statistician,November 1979, Vol. 33, No. 4 165 Playfair's work in Funkhouser 1937 and Funkhouser curve, published in JASA (Lorenz 1905), which com- and Walker 1935.) pares percentilesof cumulativedistributions. Such a An examination of Playfair's An Inquiry Into the comparisonof two cumulativedistributions is the first Permanent Causes of the Decline and Fall of Power- example of what Wilk and Gnanadesikan (1968) have ful and Wealthy Nations (1805) illustrateshow far labeled as P-P plots. ahead of his time Playfair really was. Particularly noteworthyin that volume is Playfair's Figure 4, which is a circle chart givingthe extent, population, 3. PUBLISHED STANDARDS FOR GRAPHICS and revenue of the principal nations in Europe in 1804. (This figure was not in a form suitable for Withthe rapid growthof graphicpresentation came reproductionhere.) The circles are proportionalto a professionalconcern forthe need of standards.This the areas of the countries or territories(the figures concern was reflected in the proceedings of the are on the chart as well). The red line on the leftis InternationalStatistical Congresses, held in Europe the number of inhabitants; the yellow line on the from 1853 to 1876, and in abortive attemptsto de- rightis the revenue in pounds. The scales for these velop rules and standardsfor graphics at the sessions lines are the same. of the InternationalStatistical Institute at the beginning The dotted lines, to connect the extremitiesof the lines of of the 20th century. populationand revenue, serve by theirdescent fromright to Then, in 1914, as a result of invitationsextended left,or fromleft to right,to show how revenue and popu- by the American Society of Mechanical Engineers, a lation are proportionalto each other. The impressionmade by this chart is such that it is impossible not to see by what numberof nationalassociations formeda joint commit- means Sweden and Denmark are of littleimportance, as to tee on standards for graphic presentation.The com- wealth or power; for,though population and territoryare the mittee'spreliminary report, published inJASA in 1915, original foundation of power, finances are the means of consisted of 17 basic rules of elementarygraphic pre- exertingit. (Playfair 1805, p. 190) sentation,each illustratedby one or more figures.The This figureand the related one in Playfair's The rules are simple
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