How to Display Data Badly
\nHoward Wainer
\nThe American Statistician, Vol. 38, No. 2. (May, 1984), pp. 137-147.
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\nSun Jun 24 17:27:05 2007<\/p>\n
—
\ni
\n1.3 -v—,–,– —– ——–T Publ~cand Pr~vate Elementary Schoois
\nSelected Years 1929-!970
\nFigure 2. A low density graph (from Friedman and Rafshy 1981
\n[ddi = .5]).
\nthe worse it is. Tufte (1983) has devised a scheme for
\nmeasuring the amount of information in displays, called
\nthe data density index (ddi), which is “the number of
\nnumbers plotted per square inch.” This easily calculated index is often surprisingly informative. In popular
\nand technical media we have found a range from .1 to
\n362. This provides us with the first rule of bad data
\ndisplay.
\nRule 1-Show as Few Data as Possible (Minimize the
\nData Density)
\nWhat does a data graphic with a ddi of .3 look like?
\nShown in Figure 1 is a graphic from the book Social
\nIndicators I11 (SI3), originally done in four colors (original size 7″ by 9″) that contains 18 numbers (18163 = .3).
\nThe median data graph in S13 has a data density of .6
\nnumberslin2; this one is not an unusual choice. Shown in
\nFigure 2 is a plot from the article by Friedman and
\nRafsky (1981) with a ddi of .5 (it shows 4 numbers in 8
\nLabor Productivitv:US.vs Jam
\n1 I Nopmw doto updated
\n1967 1972 1977 by hreou of lob st0111t1~1
\nhtimtdpdrman-hourin Japanese manufactu&tg ao pmcenbg* d U.S. output
\nFigure 3. A low density graph (01978,The Washington Post) with
\nchart-junk to fill in the space (ddi = .2).
\nI??
\nFigure 4. Hiding the data in the scale (from 33).
\nin2). This is unusual for JASA, where the median data
\ngraph has a ddi of 27. In defense of the producers of this
\nplot, the point of the graph is to show that a method of
\nanalysis suggested by a critic of their paper was not
\nfruitful. I suspect that prose would have worked pretty
\nwell also.
\nAlthough arguments can be made that high data density does not imply that a graphic will be good, nor one
\nwith low density bad, it does reflect on the efficiency of
\nthe transmission of information. Obviously, if we hold
\nclarity and accuracy constant, more information is betTHE NUMBER OF PRIVATE ELEMENTARY SCHOOLS<\/p>\n
FROM 1930-1 970<\/p>\n
1 I I I
\n1930 1940 1950 1960 1
\nYear
\nFigure 5. Expanding the scale and showing the data in Figure 4
\n(from 93).
\n0 The American Statistician, May 1984, Vol. 38, No. 2
\nI
\n138
\n– – —
\nI
\nA New Setof Projections for the U.S. Supply of Gmrgy I
\nComp.r.d.r. hopo*ctla.olUnlt.d SUtr .rrgywmly In therur Xmm.d. bythRntO.nt .Cwncllal
\nEnrlr-UIOualW.nU tM utu.11977 WWlr All Iburr .re In 0u.d. unll.01 Mlw.mnt that repwnf a
\nm~~~bnut~bn–apu~ri~~bn -nrttl~hthvnu~un11.(8 T u .I n~naaran*.our.ot .r*rpr
\n1- 1979 The New York ~~mes 1
\nFigure 6. Ignoring the visual metaphor (01978, The New York
\nTimes).
\nter than less. One of the great assets of graphical techniques is that they can convey large amounts of information in a small space.
\nWe note that when a graph contains little or no information the plot can look quite empty (Figure 2) and
\nthus raise suspicions in the viewer that there is nothing
\nto be communicated. A way to avoid these suspicions is
\nto fill up the plot with nondata figurations-what Tufte
\nhas termed “chartjunk.” Figure 3 shows a plot of the
\nlabor productivity of Japan relative to that of the
\nUnited States. It contains one number for each of three
\nyears. Obviously, a graph of such sparse information
\nwould have a lot of blank space, so filling the space
\nhides the paucity of information from the reader.
\nA convenient measure of the extent to which this
\npractice is in use is Tufte’s “data-ink ratio.” This measure is the ratio of the amount of ink used in graphing
\nthe data to the total amount of ink in the graph. The
\ncloser to zero this ratio gets, the worse the graph. The
\nnotion of the data-ink ratio brings us to the second
\nprinciple of bad data display.
\nRule 2-Hide What Data You Do Show
\n(Minimize the Data-Ink Ratio)
\nOne can hide data in a variety of ways. One method
\nthat occurs with some regularity is hiding the data in the
\ngrid. The grid is useful for plotting the points, but only
\nrarely afterwards. Thus to display data badly, use a fine
\ngrid and plot the points dimly (see Tufte 1983,
\npp. 94-95 for one repeated version of this).
\nA second way to hide the data is in the scale. This
\ncorresponds to blowing up the scale (i.e., looking at the
\ndata from far away) so that any variation in the data is
\nobscured by the magnitude of the scale. One can justify
\nthis practice by appealing to “honesty requires that we
\nstart the scale at zero,” or other sorts of sophistry.
\nIn Figure 4 is a plot that (from S13) effectively hides
\nthe growth of private schools in the scale. A redrawing
\nof the number of private schools on a different scale
\nconveys the growth that took place during the mid1950’s (Figure 5). The relationship between this rise and
\nBrown vs. Topeka School Board becomes an immediate
\nquestion.
\nTo conclude this section, we have seen that we can
\ndisplay data badly either by not including them (Rule 1)
\nmmlhonsof u S dollan) (fn m!ll!ons of U S dollars)
\n3000
\nto Ch~na from Ta~wan
\n2.000 —
\nSource Oamnrnsnl 01 Commerce
\nFigure 7. Reversing the metaphor in mid-graph while changing
\nscales on both axes (O June 14, 1981, The New York Times).
\nor by hiding them (Rule 2). We can measure the extent
\nto which we are successful in excluding the data through
\nthe data density; we can sometimes convince viewers
\nthat we have included the data through the incorporation of chartjunk. Hiding the data can be done either
\nby using an overabundance of chartjunk or by cleverly
\nchoosing the scale so that the data disappear. A measure of the success we have achieved in hiding the data
\nis through the data-ink ratio.
\n3. SHOWING DATA ACCURATELY
\nThe essence of a graphic display is that a set of numbers having both magnitudes and an order are represented by an appropriate visual metaphor-the magnitude and order of the metaphorical representation
\nmatch the numbers. We can display data badly by ignoring or distorting this concept.
\nRule 3-lgnore the Visual Metaphor Altogether
\nIf the data are ordered and if the visual metaphor has
\na natural order, a bad display will surely emerge if you
\nshuffle the relationship. In Figure 6 note that the bar
\nlabeled 14.1 is longer than the bar labeled 18. Another
\nmethod is to change the meaning of the metaphor in the
\nmiddle of the plot. In Figure 7 the dark shading represents imports on one side and exports on the other. This
\nis but one of the problems of this graph; more serious
\nstill is the change of scale. There is also a difference in
\nthe time scale, but that is minor. A common theme in
\nPlayfair’s (1786) work was the difference between imports and exports. In Figure 8, a 200-year-old graph
\ntells the story clearly. Two such plots would have illustrated the story surrounding this graph quite clearly.
\nRule 4–Only Order Matters
\nOne frequent trick is to use length as the visual metaphor when area is what is perceived. This was used quite
\neffectively by The Washington Post in Figure 9. Note
\nthat this graph also has a low data density (.I), and its
\ndata-ink ratio is close to zero. We can also calculate
\nTufte’s (1983) measure of perceptual distortion (PD)
\nfor this graph. The PD in this instance is the perceived
\nAmerican Statistician, May 1984, Vol. 38, No. 2 139
\nFigure 8. A plot on the same topic (sample nursing essay examples by the best nursing assignment writing service) done well two centuries earlier (from Playfair 1786).
\nchange in the value of the dollar from Eisenhower to
\nCarter divided by the actual change. I read and measure
\nthus:
\nActual Measured
\nThis distortion of over 700% is substantial but by no
\nmeans a record.
\nA less distorted view of these data is provided in
\nFigure 10. In addition, the spacing suggested by the
\n0.0 L 1. . I I I
\n1958 1963 1968 1973 1976
\nY EFlR
\nFigure 9. An example of how to goose up the effect by squaring Figure 10. The data in Figure 9 as an unadorned line chart (from
\nthe eyeball (01978, The Washington Post). Wainer, 1980).
\n140 0 The American Statistician, May 1984, Vol. 38, No. 2
\npresidential faces is made explicit on the time scale. scribed previously; that is, the data are displayed, and
\nRule 5-Graph Data Out of Context
\nOften we can modify the perception of the graph
\n(particularly for time series data) by choosing carefully
\nthe interval displayed. A precipitous drop can disappear
\nif we choose a starting date just after the drop. Similarly, we can turn slight meanders into sharp changes by
\nfocusing on a single meander and expanding the scale.
\nOften the choice of scale is arbitrary but can have profound effects on the perception of the display. Figure 11
\nshows a famous example in which President Reagan
\ngives an out-of-context view of the effects of his tax cut.
\nThe Times’ alternative provides the context for a deeper
\nunderstanding. Simultaneously omitting the context as
\nwell as any quantitative scale is the key to the practice
\nof Ordinal Graphics (see also Rule 4). Automatic rules
\ndo not always work, and wisdom is always required.
\nIn Section 3 we discussed three rules for the accurate
\ndisplay of data. One can compromise accuracy by ignoring visual metaphors (Rule 3), by only paying attention
\nto the order of the numbers and not their magnitude
\n(Rule 4), or by showing data out of context (Rule 5).
\nWe advocated the use of Tufte’s measure of perceptual
\ndistortion as a way of measuring the extent to which the
\naccuracy of the data has been compromised by the display. One can think of modifications that would allow it
\nto be applied in other situations, but we leave such
\nexpansion to other accounts.
\n4. SHOWING DATA CLEARLY
\nIn this section we discuss methods for badly displaying data that do not seem as serious as those deTHE NEW YORK TIMES, SUNDAY, AUGUST 2, 1981
\nPayments under the
\nWays and Means
\nYOUR TAXES
\nthey might even be accurate in their portrayal. Yet subtle (and not so subtle) techniques can be used to effectively obscure the most meaningful or interesting aspects of the data. It is more difficult to provide objective
\nmeasures of presentational clarity, but we rely on the
\nreader to judge from the examples presented.
\nRule &Change Scales in Mid-Axis
\nThis is a powerful technique that can make large differences look small and make exponential changes look
\nlinear.
\nIn Figure 12 is a graph that supports the associated
\nstory about the skyrocketing circulation of The New
\nYork Post compared to the plummeting Daily News
\ncirculation. The reason given is that New Yorkers
\n“trust” the Post. It takes a careful look to note the
\n700,000 jump that the scale makes between the two
\nlines.
\nIn Figure 13 is a plot of physicians’ incomes over
\ntime. It appears to be linear, with a slight tapering off
\nin recent years. A careful look at the scale shows that it
\nstarts out plotting every eight years and ends up plotting
\nyearly. A more regular scale (in Figure 14) tells quite a
\ndifferent story.
\nThe soaraway Post<\/p>\n
-the daily paper<\/p>\n
New Yorkers trust<\/p>\n
Figure 11. The White House showing neither scale nor context Figure 12. Changing scale in mid-axis to make large differences
\n(0 1981, The New York Times, reprinted with permission). small (O 1981, New York Post).
\nO The American Statistician, May 1984, Vol. 38, No. 2 141
\n— – —
\nM.d*n Incam of VamrRand. FuYThn
\nInmmes of Doctors W&u 26 to 34 Vun Old. by Sax wd
\nE&atbnd Atakmnt: lmalS77
\nVs Other Profesionals _
\nI
\nI Canltanf 1977dollari MALE
\n(MEDIAN NET INCOMES)
\nXKRCE, bundl on woge d Prin Stobili
\nOFFICEDMSED
\nNONSALARIED PHYSlClANS
\nFigure 13. Changing scale in mid-axis to make exponential growth
\nlinear (OThe Washington Post).
\nRule 7-Emphasize the Trivial (Ignore the Important)
\nSometimes the data that are to be displayed have one
\nimportant aspect and others that are trivial. The graph
\ncan be made worse by emphasizing the trivial part. In
\nFigure 15 we have a page from S13 that compares the
\nincome levels of men and women by educational levels.
\nIt reveals the not surprising result that better educated
\nindividuals are paid better than more poorly educated
\nones and that changes across time expressed in constant
\ndollars are reasonably constant. The comparison of
\ngreatest interest and current concern, comparing salaries between sexes within education level, must be
\nmade clumsily by vertically transposing from one graph
\nto another. It seems clear that Rule 7 must have been
\noperating here, for it would have been easy to place the
\ngraphs side by side and allow the comparison of interest
\nto be made more directly. Looking at the problem from
\na strictly data-analytic point of view, we note that there
\nare two large main effects (education and sex) and a
\nsmall time effect. This would have implied a plot that
\nINCOMES OF DOCTORS VS. OTHER PROFESSIONRLS
\nFEMALE
\n$140W 1 1 1 1 1 1 1 1 1 1 1 1
\nFigure 15. Emphasizing the trivial: Hiding the main effect of sex
\ndifferences ~n income through the vertical placement of plots (from
\nS13).
\nshowed the large effects clearly and placed the smallish
\ntime trend into the background (Figure 16).
\nMEDIAN INCOME OF YEAR-ROUND FULL TIME WORKERS
\n25-34 YEARS OLD BY SEX AND EDUCATIONAL ATTAINMENT:
\n1968-1 977 (IN CONSTANT 1977 DOLLARS)
\nD
\nr —-1
\n= I
\nI ,OOCTORS
\n,,OTHER PROFESSlONRLS
\n–
\nYso , +
\n:20 . a! Z
\n:lo
\n= 0
\n,
\nI
\nL 0
\n[ 1 -minimum
\nI
\n0-8
\nI 1
\n9.1 1 12
\n1 1
\n13.15 16+
\nI
\nMedian Ovar
\nEdualim hl YEAR Years of Educational Altainmenl
\nFigure 14. Data from Figure 13 redone with linear scale (from Figure 16. Figure 15 redone with the large main effects emphaWainer 1980). sized and the small one (time trends) suppressed.
\n142 0The American Statistician, May 1984, Vol. 38, No. 2
\nLih Expectancy at Birth, by Sex, Selected
\nOF RED MEATS* \t Cwn8ios. Moat Recent Available Year:
\nIRTS
\n1670-1676<\/p>\n
BIL. LB. I I I
\nI \t IO ,At lM n lll
\nFigure 17. Jiggling the baseline makes comparisons more difficult
\n(from Handbook of Agricultural Charts).
\nRule 8-Jiggle the Baseline
\nMaking comparisons is always aided when the quantities being compared start from a common base. Thus
\nwe can always make the graph worse by starting from
\ndifferent bases. Such schemes as the hanging or suspended rootogram and the residual plot are meant to
\nfacilitate comparisons. In Figure 17 is a plot of U.S.
\nimports of red meat taken from the Handbook of Agricultural Charts published by the U.S. Department of
\nAgriculture. Shading beneath each line is a convention
\nthat indicates summation, telling us that the amount of
\neach kind of meat is added to the amounts below it.
\nBecause of the dominance of and the fluctuations in
\nimportation of beef and veal, it is hard to see what the
\nchanges are in the other kinds of meat-Is the importation of pork increasing? Decreasing? Staying constant?
\nThe only purpose for stacking is to indicate graphically
\nthe total summation. This is easily done through the
\naddition of another line for TOTAL. Note that a
\nTOTAL will always be clear and will never intersect the
\nother lines on the plot. A version of these data is shown
\nSourcr: \t ltdta~~kk~Agr_~~ltural C!m?-t?, C.S. Department of<\/p>\n
Agriculture, 19i6, p. 93.<\/p>\n
Chart Source : Original
\nFigure 18. An alternative version of Figure 17 with a straight line
\nused as the basis of comparison.
\nYears of lbfe expectanci
\nFigure 19. Austria First! Obscuring the data structure by alphabetizing the plot (from S13).
\nin Figure 18 with the separate amounts of each meat, as
\nwell as a summation line, shown clearly. Note how
\neasily one can see the structure of import of each kind
\nof meat now that the standard of comparison is a
\nstraight line (the time axis) and no longer the import
\namount of those meats with greater volume.
\nRule 9-Austria First!
\nOrdering graphs and tables alphabetically can obscure structure in the data that would have been obvious
\nhad the display been ordered by some aspect of the
\ndata. One can defend oneself against criticisms by
\npointing out that alphabetizing “aids in finding entries
\nof interest.” Of course, with lists of modest length such
\naids are unnecessary; with longer lists the indexing
\nschemes common in 19th century statistical atlases provide easy lookup capability.
\nFigure 19 is another graph from S13 showing life expectancies, divided by sex, in 10 industrialized nations.
\nThe order of presentation is alphabetical (with the
\nUSSR positioned as Russia). The message we get is that
\nthere is little variation and that women live longer than
\nmen. Redone as a stem-and-leaf diagram (Figure 20 is
\nsimply a reordering of the data with spacing proportional to the numerical differences), the magnitude of
\nthe sex difference leaps out at us. We also note that the
\nUSSR is an outlier for men.
\nRule 10-Label (a) Illegibly, (b) Incompletely,
\n(c) Incorrectly, and (d) Ambiguously
\nThere are many instances of labels that either do not
\n0The American Statistician, May 1984, Vol. 38. No. 2 143
\nCommission Payments
\nto Travel Agents
\nFRANCE, 3S, JAPAN, CANADA
\nFINLAND, AUSTRIA, UK
\nUSSR, GERMANY
\nCANADA, YK, US, FRANCE
\nGERMANY, AUSTRIA
\nFINLAND
\nFigure 20. Ordering and spacing the data from Figure 19 as a
\nstem-and-leaf diagram provides insights previously difficult to
\nextract (from S13).
\ntell the whole story, tell the wrong story, tell two or
\nmore stories, or are so small that one cannot figure out
\nwhat story they are telling. One of my favorite examples
\nof small labels is from The New York Times (August
\nComplex web of discount fares and airlines’ telephone
\n–<\/p>\n
delays are rais~ng
\ntravel agents’overhead, offsetting revenue gains from higher volume.
\nFigure 21. Mixing a changed metaphor with a tiny label reverses
\nthe meaning of the data (C 1978, The New York Times).
\nD DELTA
\n0
\nL 30-
\nL
\nA
\nR
\n5 0-
\n1 I
\n1976 1977 1978
\n(e3tImated)
\nYEAR
\nFigure 22. Figure 21 redrawn with 1978 data placed on a
\ncomparable basis (from Wainer 1980).
\n1978), in which the article complains that fare cuts lower
\ncommission payments to travel agents. The graph (Figure 21) supports this view until one notices the tiny label
\nindicating that the small bar showing the decline is for
\njust the first half of 1978. This omits such heavy travel
\nperiods as Labor Day, Thanksgiving, Christmas, and so
\non, so that merely doubling the first-half data is probably not enough. Nevertheless, when this bar is doubled
\n(Figure 22), we see that the agents are doing very well
\nindeed compared to earlier years.
\nRule ll-More Is Murkier: (a) More Decimal<\/p>\n
Places and (b) More Dimensions<\/p>\n
We often see tables in which the number of decimal
\nplaces presented is far beyond the number that can be
\nperceived by a reader. They are also commonly
\npresented to show more accuracy than is justified. A
\ndisplay can be made clearer by presenting less. In Table
\n1 is a section of a table from Dhariyal and Dudewicz’s
\n(1981) JASA paper. The table entries are presented to
\nfive decimal places! In Table 2 is a heavily rounded
\nversion that shows what the authors intended clearly. It
\nalso shows that the various columns might have a substantial redundancy in them (the maximum expected
\ngain with blc = 10 is about 1110th that of blc = 100 and
\n11100th that of blc = 1,000). If they do, the entire table
\ncould have been reduced substantially.
\nJust as increasing the number of decimal places can
\nmake a table harder to understand, so can increasing
\nthe number of dimensions make a graph more conC The American Statistician, Mav 1984. Vol. 38. No. 2
\nL
\nI
\n144
\nTable 1. Optimal Selection From a Finite
\nSequence With Sampling Cost
\nblc = 10.0 –
\nN r* (G) -a) r*
\n3 2 .20000 2
\n4 2 ,26333 2
\n5 2 ,32333 3
\n6 3 ,38267 3
\n7 3 ,44600 3
\n8 3 ,50743 4
\n9 3 ,56743 4
\n10 4 ,62948 4
\nNOTE:g(Xs+rl)=bR(Xs+rl)+a,ifS=s,andg(Xs+r-l)=O,othewise
\nSource: Dharlyal and Dudewlcz (1981).
\nfusing. We have already seen how extra dimensions can
\ncause ambiguity (Is it length or area or volume?). In
\naddition, human perception of areas is inconsistent.
\nJust what is confusing and what is not is sometimes only
\na conjecture, yet a hint that a particular configuration
\nwill be confusing is obtained if the display confused the
\ngrapher. Shown in Figure 23 is a plot of per share earnings and dividends over a six-year period. We note (with
\nsome amusement) that 1975 is the side of a bar-the
\nthird dimension of this bar (rectangular parallelopiped?) chart has confused the artist! I suspect that 1975
\nis really what is labeled 1976, and the unlabeled bar at
\nthe end is probably 1977. A simple line chart with this
\ninterpretation is shown in Figure 24.
\nIn Section 4 we illustrate six more rules for displaying
\ndata badly. These rules fall broadly under the heading
\nof how to obscure the data. The techniques mentioned
\nwere to change the scale in mid-axis, emphasize the
\ntrivial, jiggle the baseline, order the chart by a characteristic unrelated to the data, label poorly, and include
\nmore dimensions or decimal places than are justified or
\nneeded. These methods will work separately or in combination with others to produce graphs and tables of
\nlittle use. Their common effect will usually be to leave
\nthe reader uninformed about the points of interest in
\nthe data, although sometimes they will misinform us;
\nthe physicians’ income plot in Figure 13 is a prime example of misinformation.
\nFinally, the availability of color usually means that
\nthere are additional parameters that can be misused.
\nThe U.S. Census’ two-variable color map is a wonderful
\nexample of how using color in a graph can seduce us
\nTable 2. Optimal Selection From a Finite Sequence
\nWith Sampling Cost (revised)
\nblc = 10 blc = 100 blc = 1,000
\nN r7 G r* G r’ G
\ninto thinking that we are communicating more than we
\nare (see Fienberg 1979; Wainer and Francolini 1980;
\nWainer 1981). This leads us to the last rule.
\nRule 12-If It Has Been Done Well in the Past, Think of
\nAnother Way to Do It
\nThe two-variable color map was done rather well by
\nMayr (1874), 100 years before the U.S. Census version.
\nHe used bars of varying width and frequency to accomplish gracefully what the U.S. Census used varying
\nsaturations to do clumsily.
\nA particularly enlightening experience is to look
\ncarefully through the six books of graphs that William
\nPlayfair published during the period 1786-1822. One
\ndiscovers clear, accurate. and data-laden graphs containing many ideas that are useful and too rarely applied
\ntoday. In the course of preparing this article, I spent
\nmany hours looking at a variety of attempts to display
\nb J
\nEankle;sPer Share And
\nDividaids
\n(Dollars)
\nr”J
\nEarnings .,.,…:I:! Dividends
\nA A
\nFigure 23. An extra dimension confuses even the grapher
\n(@ 1979, The Washington Post).
\n0The American Statistician, May 1984. Vol. 38, No. 2 145
\nI I I I I I
\n1972 1971 1976
\nYERR
\nFigure 24. Data from Figure 23 redrawn s~mply (from Wainer
\n1980).
\ndata. Some of the horrors that I have presented were
\nthe fruits of that search. In addition, jewels sometimes
\nemerged. I saved the best for last, and will conclude
\nwith one of those jewels-my nominee for the title of
\n“World’s Champion Graph.” It was produced by
\nMinard in 1861 and portrays the devastating losses suffered by the French army during the course of Napoleon’s ill-fated Russian campaign of 1812. This graph
\n(originally in color) appears in Figure 25 and is reproduced from Tufte’s book (1983, p. 40). His narrative
\nfollows.
\nBeginning at the left on the Polish-Russian border near the
\nNiemap River, the thick band shows the size of the army (422.000
\nmen) as it invaded Russia in June 1812. The width of the band
\nindicates the size of the army at each place on the map. In September, the army reached Moscow, which was by then sacked and
\ndeserted, with 100,000men. The path of Napoleon’s retreat from
\nMoscow is depicted by the darker, lower band, which is linked to
\na temperature scale and dates at the bottom of the chart. It was a
\nbitterly cold winter, and many froze on the march out of Russia.
\nAs the graphic shows, the crossing of the Berezina River was a
\ndisaster, and the army finally struggled back to Poland with only
\n10,000men remaining. Also shown are the movements of auxiliary
\ntroops, as they sought to protect the rear and flank of the advancing army. Minard’s graphic tells a rich, coherent story with its
\nmultivariate data, far more enlightening than just a single number
\nbouncing along over time. Six variables are plotted: the size of the
\narmy, its location on a two-dimensional surface. direction of the
\narmy’s movement, and temperature on various dates during the
\nretreat from Moscow.
\nIt may well be the best statistical graphic ever drawn.
\n5. SUMMING UP
\nAlthough the tone of this presentation tended to be
\nlight and pointed in the wrong direction, the aim is
\nserious. There are many paths that one can follow that
\nwill cause deteriorating quality of our data displays; the
\n12 rules that we described were only the beginning.
\nNevertheless, they point clearly toward an outlook that
\nprovides many hints for good display. The measures of
\ndisplay described are interlocking. The data density
\ncannot be high if the graph is cluttered with chartjunk;
\nthe data-ink ratio grows with the amount of data displayed; perceptual distortion manifests itself most freDres~CepuIl.Minud.Inspcc~ur Ceniral des Pontr et ChaussCe~en rnra’ce.
\nXpnr”= Iktc~~~hcr O1’r8′ = Nt7~ctt~lxr 8″” = O~robcr
\nFigure 25. Minard’s (1861) graph of the French Army’s ill-fated foray into Russia-A candidate for the title of “World’s Champion Graph” (see
\nTufte 1983 for a superb reproduction of this in its original color-p. 176).
\n146 0The American Statistician, May 1984, Vol. 38, No. 2
\nquently when additional dimensions or worthless metaphors are included. Thus, the rules for good display are
\nquite simple. Examine the data carefully enough to
\nknow what they have to say, and then let them say it
\nwith a minimum of adornment. Do this while following
\nreasonable regularity practices in the depiction of scale,
\nand label clearly and fully. Last, and perhaps most important, spend some time looking at the work of the
\nmasters of the craft. An hour spent with Playfair or
\nMinard will not only benefit your graphical expertise
\nbut will also be enjoyable. Tukey (1977) offers 236
\ngraphs and little chartjunk. The work of Francis Walker
\n(1894) concerning statistical maps is clear and concise,
\nand it is truly a mystery that their current counterparts
\ndo not make better use of the schema developed a century and more ago.
\n[Received September 1982. Revised September 1983. ]
\nREFERENCES
\nBERTIN, J. (1973), Semiologie Graphique (2nd ed.). The Hague:
\nMouton-Gautier.
\n(1977), La Graphique et le Traitement Graphique de
\nl’lnformation, France: Flammarion.
\n(1981), Graphics and the Graphical Analysis of Data, translation, W. Berg, tech. ed., H. Wainer, Berlin: DeGruyter.
\nCOX, D.R. (1978), “Some Remarks on the Role in Statistics of
\nGraphical Methods,” Applied Statistics, 27, 4-9.
\nDHARIYAL, I.D., and DUDEWICZ, E.J. (1981). “Optimal Selection From a Finite Sequence With Sampling Cost,” Journal of the
\nAmerican Statistical Association, 76, 952-959.
\nEHRENBERG, A.S.C. (1977), “Rudiments of Numeracy.” Journal
\nof the Royal Sraristical Society, Ser. A, 140, 277-297.
\nFIENBERG, S.E. (1979), Graphical Methods in Statistics, The
\nAmerican Statistician, 33, 165-178.
\nFRIEDMAN, J.H., and RAFSKY. L.C. (1981). “Graphics for the
\nMultivariate Two-Sample Problem,” Journal of the American Statistical Associarion, 76, 277-287.
\nJOINT COMMIITEE ON STANDARDS FOR GRAPHIC
\nPRESENTATION, PRELIMINARY REPORT (1915), Journal
\nof the American Sraristical Association, 14, 790-797.
\nMACDONALD-ROSS, M. (1977), “How Numbers Are Shown: A
\nReview of Research on the Presentation of Quantitative Data in
\nTexts,” Audiovisual Communications Review, 25, 359-409.
\nMAYR, G. VON (1874), “Gutachen Uber die Anwendung der Graphischen und Geographischen,” Method in der Statistik, Munich.
\nMINARD, C.J. (1845-1869), Tableaus Graphiques et Cartes Figurarives de M. Minard, Bibliotheque de I’Ecole Nationale des Ponts et
\nChaussees, Paris.
\nPLAYFAIR, W. (1786). The Commercial and Political Atlas, London: Corry.
\nSCHMID, C.F. (1954). Handbook of Graphic Presentation, New
\nYork: Ronald Press.
\nSCHMID, C.F., and SCHMID, S.E. (1979), Handbook of Graphic
\nPresentation (2nd ed.), New York: John Wiley.
\nTUFTE, E.R. (1977), “Improving Data Display,” University of Chicago, Dept. of Statistics.
\n(1983), The Visual Display of Quantitative Information,
\nCheshire, Conn.: Graphics Press.
\nTUKEY, J.W. (1977). Exploratory Data Analysis, Reading, Mass:
\nAddison-Wesley.
\nWAINER, H. (1980), “Making Newspaper Graphs Fit to Pridt,” in
\nProcessing of Visible Language, Vol. 2, eds. H. Bouma, P.A.
\nKolers, and M.E. Wrolsted, New York: Plenum, 125-142.
\n, “Reply” to Meyer and Abt (1981), The American Statistician.
\n57.
\n(1983), “How Are We Doing? A Review of Social Indicators
\n111.” Journal of the American Statistical Association, 78, 492-496.
\nWAINER, H., and FRANCOLINI, C. (1980), “An ~m~iricgl Inquiry Concerning Human Understanding of Two-Variable Color
\nMaps,” The American Statistician, 34, 8 1-93.
\nWAINER, H., and THISSEN, D. (1981), “Graphical Data Analysis,” Annual Review of Psychology, 32, 191-241.
\nWALKER, F.A. (1894), Statistical Atlas of the United States Based on
\nthe Resuln of the Ninth Census, Washington, D.C.: U.S. Bureau of
\nthe Census.
\nO The American Statistician, May 1984, Vol. 38, No. 2<\/p>\n","protected":false},"excerpt":{"rendered":"
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