EXHIBIT 2
`
`TUFTE VISUAL AND
`STATISTICAL THINKING
`
`
`TRADING TECH EXHIBIT 2193
`IBG ET AL. v. TRADING TECH
`CBM2016-00032
`
`Page 1 of 32
`
`

`
`EDWARD R. TUFTE
`
`VISUAL AND STATISTICAL THINKING:
`
`DISPLAYS OF EVIDENCE FOR MAKING DECISIONS
`
`0-ring damage
`index, each launch
`12.
`
`4_I__
`ge of fore
`26°—29°
`,
`(as ofJan
`of space s uttle Chall
`
`ted tcmpe tures
`
`r on Jan ary 28
`
`35°
`
`40‘
`
`45°
`
`50°
`
`55‘
`
`60°
`
`Temperature (T) offield joints at time of launch
`
`JOHN SNOW AND THE CHOLERA EPIDEMIC
`
`THE DECISION TO LAUNCH THE SPACE SHUTTLE CHALLENGER
`
`Page 2 of 32
`
`

`
`Edward Tufte has written seven books, including Visual Explanations, Envisioning Information, The Visual
`Display of Quantitative Information, Data Analysisfor Politics and Policy, Political Control of the Economy, and
`Size and Democracy (with Robert A. Dahl). He writes, designs, and self-publishes his books on information
`design, which have received more than 40 awards for content and design. I-Ie is Professor Emeritus at
`Yale University, where he taught courses in statistical evidence, information design, and interface design.
`His current work includes a new book called Beautiful Evidence, landscape sculpture, and printmaking.
`
`Copyright © 1997 by Edward Rolf Tufte
`PUBLISHED BY GRAPHICS Puss LLC
`
`Posr OFFICE Box 430, CHESHIRE, CONNECTICUT 06410
`WWW.EDWARDTUETE.COM
`
`All rights to illustrations and text reserved by Edward RolfTufte. This work may not be copied, reproduced, or translated in whole or in
`part without written permission of the publisher, except for brief exceryts in connection with reviews or scholarly analysis. Use in any form
`of information storage and retrieval, electronic adaptation or whatever, computer software, or by similar or dissimilar methods now known
`or developed in the future is also strictly forbidden without written permission of the publisher.
`
`Printed in the United States ofAmerica
`
`Third printing, November 2005
`
`Page 3 of 32
`
`

`
`Introduction
`
`THIS booklet, meant for students of quantitative thinking, reproduces
`chapter 2 of my recent book Visual Explanations: Images and Quantities,
`Evidence and Narrative.
`‘
`
`The general argument is straightforward:
`
`An essential analytic task in making decisions based on evidence
`is to understand how things Work—mechanism, trade—ofls, process
`and dynamics, cause and effect. That is, intervention—thi_nking and
`policy-thinking demand causality-thinking.
`
`Making decisions based on evidence requires the appropriate display
`of that evidence. Good displays of data help to reveal knowledge
`relevant to understanding mechanism, process and dynamics, cause
`and eflect. That is, displays of statistical data should directly serve the
`analytic task at hand.
`
`What is reasonable and obvious in theory may not be implemented
`in the actual practice of assessing data and making decisions. Here we
`will see two complex cases of the analysis and display of evidence-the
`celebrated investigation of a cholera epidemic by Dr. John Snow and
`the unfortunate decision to launch the space shuttle Challenger.
`
`Edward Tvgfife
`
`Page 4 of 32
`
`

`
`Although we often hear that data speakfor themselves, their voices can he
`
`sojft and sly.
`
`Frederick Mosteller, Stephen E. Fienberg, and Robert
`E. K. Rourke, Beginning Statistics with Data Analysis
`(Reading, Massachusetts, 1983), p. 234.
`
`Negligent speech doth not only discredit the person ofthe Speaker, but it
`Jiscrediteth the opinion ofhis reason andjudgment; it discrediteth theforce
`and uniformity ofthe matter, and substance.
`
`Ben Jonson, Timber: or, Discoveries (London, 1641), first
`printed in the Folio of 1640, The Worlecs . . . , p. 12.2
`of the section beginning with Horace his Art ofPoetry.
`
`rm AssEssMERT oz= TEMPERATURE concern: on sRM~25 (51L) LAuucR
`
`«,
`
`0
`0
`
`0
`
`CALcuLATIoNs snow THAT SRM-25 0-RINGS WILL BE 20' cot.nER THAII SRM-15 D-RINGS.
`TEMPERATURE DATA NOT coNcLIIsIVE on PREDICTING PRIMARY 0-RING BLOW-BY
`
`ENGINEERING ASSESSMENT Is THAT:
`0
`CDLDER 0-RINGS WILL HAVE IMcREAsEn EFFECTIVE nuRoMETER ("HARDER")
`D
`"HARDER" 0-RINGS WILL TAKE LONGER T0 "SEAT"
`
`0
`
`Mom: GAS MAY I>Ass RRIMARII 0-RING BEFORE THE PRIMARY SEAL sEATs
`(RELATIVE TO SRM-15)
`
`0
`»
`
`DEMDNSTRATED SEALING THRESHOLD Is 3 TIMES EREATER THAN 0.038"
`ERosI~oIt EXPERIENCED on SRM-15
`
`0
`
`IF THE PRIMARY SEAL DOES NOT SEAT; THE SECONDARY SEAL WILL SEAT
`U
`PRESSURE WILL GET TO SECONDARY SEAL BEFORE THE METAL PARTS ROTATE
`0
`0*-RING PRESSURE LEAIC CHECK PLACES SECONDARY SEAL IN OUTBOARD
`POSITION WHICH MINIMIZES SEALING TIME
`
`0
`
`MTI REcoMMERns S‘l'S—5lL LAUNCH PROCEED on 28 JANUARY 1985
`0
`SRM-.25 MILL NOT BE SIGNIFICANTLY DIFFERENT FROM SRM-15
`
`!<u.MIMsTER, vIcE PRESIDENT '
`C.
`ACE BoosTER. Enoenms
`
`_ MOKTONTHIOKOLINC.
`Wasatch Diilsibn
`
`IIFOIHNVJII GI "I3 FIRE WAS PREPIIED ‘IO §.|FFfll'l’|' AN MILL PIIESHITATDII
`AND CIIINOT IE CONSIDERED COMPLETE WIYNOIJY ‘(HE DRAI. IIISCUSSKIII
`
`The final approval and rationale for the launch of the
`space shuttle Challenger, faxed by the rocket-maker to
`NASA the night before the launch. The rocket blew up
`12. hours later as a result of cold temperatures.
`
`Page 5 of 32
`
`

`
`Visual and Statistical Thinking:
`Displays ofEvidence for Making Decisions
`
`WHEN we reason about quantitative evidence, certain methods for
`displaying and analyzing data are better than others. Superior methods
`are more likely to produce truthful, credible, and precise findings. The
`difference between an excellent analysis and a faulty one can sometimes
`have momentous consequences.
`This chapter examines the statistical and graphical reasoning used in
`making two life-and-death decisions: how to stop a cholera epidemic
`in London during September 1854; and whether to launch the space
`shuttle Challenger on january 28, 1986. By creating statistical graphics
`that revealed the data, Dr. John Snow was able to discover the cause
`of the epidemic and bring it to an end. In contrast, by fooling around
`with displays that obscured the‘ data, those who decided to launch the
`space shuttle got it wrong, terribly wrong. For both cases, the conse-
`quences resulted directly from the quality of methods used in displaying
`and assessing quantitative evidence.
`
`The Cholera Epidemic in London, 1854
`
`In a classic of medical detective work, On the Mode ofCommunication of
`Cholera,‘ John Snow descr-ibed~—with an-eloquent and precise language
`of evidence, number, comparison—the severe epidemic:
`
`The most terrible outbreak of cholera which ever occurred in this kingdom, is
`probably that which took place in Broad Street, Golden Square, and adjoining
`streets, a few weeks ago. V/ithin two hundred and fifty yards of the spot where
`Cambridge Streetjoins Broad Street, there were upwards offive hundred fatal at-
`tacks of cholera i.n ten days. The mortality in this limited area probably equals any
`that was ever caused in this country, even by the plague; and it wasmuch more
`sudden, as the greater number of cases terminated in a few hours. The mortality
`would undoubtedly have been much greater had it not been for the flight of the
`population. Persons in furnished lodgings left first, then other lodgers went away,
`leaving their furniture to be sent for. . . . Many houses were closed altogether
`owing to the death ofthe proprietors; and, in a great number ofinstances, the
`tradesmen who remained had sent away their families; so that in less than six days
`from the commencement of the outbreak, the most afllicted streets were deserted
`by more than three-quarters of their inhabitants.’
`
`‘John Snow, On the Mode of Communi-
`. cation 9)’ Cholera (London, 1855). An
`acute disease of the small intestine, with
`severe watery diarrhea, vomiting, and
`rapid dehydration, cholera has a fatality
`rate of so percent or more when un-
`treated. With the rehydration therapy
`developed in the 1960s, mortality can be
`reduced to less than one percent. Epi-
`demics still occur in poor countries, as
`the bacterium Vibrio cholera: is distributed
`mainly by water and food contaminated
`with sewage. See Dhiman Barua and
`V/illiam B. Greenough ru, eds., Cholera
`(New York, 1992); and S. N. De,
`Cholera: Its Pathology and Pathogenesis
`(Edinburgh, 1961).
`
`2 Snow, Cholera, p. 38. See also Report
`on the Cholera Outbreak in the Parish
`of St. James’s, Westminster, during the
`Autumn of 1854, presented to the Vestry
`by The Cholera Inquiry Committee
`(London, 1855); and H. Harold Scott,
`Same Notable Epidemics (London, 193 4.).
`
`Page 6 of 32
`
`

`
`6
`
`VISUAL EXPLANATIONS
`
`Cholera broke out in the Broad Street area of central London on
`the evening of August 31, 1854. John Snow, who had investigated
`earlier epidemics, suspected that the water from a community pump-
`well at Broad and Cambridge Streets Was contaminated. Testing the
`water from the well on the evening of September 3, Snow saw no
`suspicious impurities, and thus he hesitated to come to a conclusion.
`This absence of evidence, however, was not evidence of absence:
`
`Further inquiry . . . showed me that there was no other circumstance or agent
`common to the circumscribed locality in which this sudden increase of cholera
`occurred, and not extending beyond it, except the water of the above mentioned
`pump. I found, moreover, that the water varied, during the next two days, in the
`amount of organic impurity, visible to the naked eye, on close inspection, in the
`form ofsmall white, flocculent [loosely clustered] particles. . . .3
`
`From the General Register Office, Snow obtained a list of 83 deaths
`from cholera. When plotted on a map, these data showed a close link
`between cholera and the Broad Street pump. Persistent house—by-house,
`case—by—case detective work had yielded quite detailed evidence about
`a possible cause-effect relationship, as Snow made a kind of streetcorner
`correlation:
`
`On proceeding to the spot, I found that nearly all ofthe deaths had taken place
`within a short distance ofthe pump. There were only ten deathssin houses situated
`decidedly nearer to another street pump. In five ofthese cases the families ofthe
`deceased persons informed me that they always sent to the pump in Broad Street, as
`they preferred the water to that ofthe pump which was nearer. In three other cases,
`the deceased were children who went to school near the pump in Broad Street.
`Two of them were known to drink the water; and the parents of the third think it
`probable that it did so. The other two deaths, beyond the district which this pump
`supplies, represent only the amount ofmortality from cholera that was occurring
`before the irruption took place.
`I
`
`With regard to the deaths occurring in the locality belonging to the pump, there
`were sixty-one instances in which I was informed that the deceased persons used to
`drink the pump-water from Broad Street, either constantly or occasionally. In six
`instances I could get no information, owing to the death or departure ofevery
`one connected with the deceased individuals; and in six cases I was informed that
`the deceased persons did not drink the purnp~water before their ilh1ess.“
`
`Thus the theory implicating the particular pump was confirmed by
`the observed covariation: in this area of London, there were few
`occurrences of cholera exceeding the normal low level, except among
`those people who drank water from the Broad Street pump. It was
`now time to act; after all, the reason we seek causal explanations is
`in order to intervene, to govern the cause soas to govern the effect:
`“Policy—thinki.ng is and must be causality-thinl<ing.”5 Snow described
`his findings to the authorities responsible for the community water
`supply, the Board of Guardians of St. _]ames’s Parish, on the evening
`of September 7, 18 54. The Board ordered that the pump-handle on the
`Broad Street well be removed immediately. The epidemic soon ended.
`
`5 Snow, Cholera, p. 39. Writing a few
`weeks after the epidemic, Snow reported
`his results in a first-person narrative, more
`like a laboratory notebook or a personal
`journal than a modern research paper
`with its pristine, reconstructed science.
`
`" Snow, Cholera, pp. 39-40.
`
`5 Robert A. Dahl, “Cause and Effect
`in the Study of Politics,” in Daniel
`Lerner, ed., Cause and Eflett (New York,
`1965), p. 88. Wold writes “A frequent
`situation is that description serves to
`maintain some modus vivendi (the control
`of an established production process,_
`the tolerance ofa limited number of
`epidemic cases), whereas explanation
`serves the purpose of reform (raising the
`agricultural yield, reducing the mortality
`rates, improving a. production process).
`In other words, description is employed
`as an aid in the human adjustment to con-
`ditions, while explanation is a vehicle
`for ascendancy over the environment.”
`Herman Wold, “Causal Inference from
`Observational Data,"_Ioumal of the Royal
`Statistical Society, A, 119 (1956), p. 29.
`
`Page 7 of 32
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`

`
`VISUAL AND STATISTICAL THINKING
`
`7
`
`Moreover, the result of this intervention (a before/ after experiment
`of sorts) was consistent with the idea that cholera was transmitted by
`impure water. Snow’s explanation replaced previously held beliefs
`that cholera spread through the air or by some other means. In those
`times many years before the discovery of bacteria, one fantastic theory
`speculated that cholera vaporously rose out of the burying grounds of
`plague victims from two centuries earlier.‘ In 1886 the discovery ofthe
`bacterium Vibrio choleraeconfirmed Snow’s theory. He is still celebrated
`for establishing the mode of cholera transmission and consequently the
`method ofprevention: keep drinking water, food, and hands clear of
`infected sewage. Today at the old site of the Broad Street pump there
`stands a public house (a bar) named after John Snow, Where one can
`presumably drink more safely than 140 years ago.
`
`WHY Was the centuries-old mystery of cholera finally solved? Most
`importantly, Snow had a good idea—~a causal theory about how the
`disease spread——-that guided the gathering and assessment of evidence.
`This theory developed from medical analysis and empirical observation;
`by mapping earlier epidemics, Snow detected a link between diiferent
`water supplies and varying rates of cholera (to the consternation of
`private Water companies who anonymously denounced SnoW’s work).
`By the 18 54 epidemic, then, the intellectual framework was in place,
`and the problem ofhow cholera spread was ripe for solution."
`Along with a good idea and a timely problem, there was a good
`method. SnoW’s scientific detective Work exhibits a shrewd intelligence
`about evidence, a clear logic of data display and analysis:
`
`1. Placing the data in an appropriate contextfor assessing cause and efllect.
`The original data listed the victims’ names and described their circum-
`stances, all in order by date of death. Such a stack of death certificates
`naturally lends itself to time-series displays, chronologies of the epi-
`demic as shown below. But descriptive narration is not causal explanation;
`the passage of time is a poor explanatory variable, practically useless in
`discovering a strategy of hoW- to intervene and stop the epidemic.
`
`" H. Harold Scott, Some Notable Epidemics
`(London. 1934), 1213- 3-4-
`
`7 Scientists are not “admired for failing
`in the attempt to solve problems that
`lie beyond [their] competence. . .
`. If
`politics is the art of the possible, re-
`search is surely the art of the soluble.
`Both are immensely practi_ca1—m.inded
`affairs. .
`.
`. The art of research .[is] the
`art of making dificult problems soluble
`by devising means of getting at them.
`Certainly good scientists study the most
`important problems they think they can
`solve. It is. after all, their professional
`business to solve problems, not merely
`to grapple with them. The spectacle of
`a scientist locked in combat with the
`forces of ignorance is not an inspiring
`one if, in the outcome, the scientist is
`routed. That is why so many of the
`most important biological problems
`have not yet appeared on the agenda
`of practical research.” Peter Medawar,
`Pluto’: Republic (New York, 1984), pp.
`253-254; 2-3-
`
`700- Cumulative deaths from cholera,
`- beginning August 19, I854; final
`total 616 deaths
`
`600
`
`- Deaths from
`- cholera, each
`day during
`the epidemic
`
`20 22 24 26 28 30
`August
`
`Page 8 of 32
`
`

`
`3
`
`vIsUiAL EXPLANATIONS
`
`Instead of plotting a time—series, which would simply report each
`day’s bad news, Snow constructed a graphical display that provided
`direct and powerful testimony about a possible cause-efiiect relation-
`ship. Recasting the original data from their one—dimensional temporal
`drderirig‘iiito a two-dimensional spatial comparison, Snow marked
`deaths from cholera (lllllll) on this map, along with locations of the
`area’s 11 community water pump-wells (Co) The notorious well is
`located amid an intense cluster of deaths, near the D in BROAD srrnnnr.
`This map reveals a strong association between cholera and proximity
`to the Broad Street pump, in a context ofsimultaneous comparison
`with other local water sources and the surrounding neighborhoods
`without cholera.
`'
`
`2. Making quantitative comparisons. The deep, fundamental question
`in statistical analysis is Compared with what? Therefore, investigating
`the experiences of the victims of cholera is only part of the search for
`credible evidence; to understand fully the cause of the epidemic also
`requires an analysis of those who escaped the disease. With great clarity,
`the map presented several intriguing clues for comparisons between the
`living and the dead, clues strikingly visible at a brewery and a work-
`house (tinted yellow here). Snow wrote in his report:
`
`-
`
`There is a brewery in Broad Street, near to the pump, and on perceiving that no
`brewer's men were registered as having died of cholera, I called on Mr. Huggins,
`the proprietor. He informed me that there were above seventy workmen employed
`in the brewery, and that none ofthem had suffered fiom cholera—at least in severe
`Eorm—-—only two having been indisposed, and that not seriously, at the time the
`disease prevailed. The men are allowed a certain quantity ofmalt liquor,
`Huggins believes they do not drink water at all; and he is quite certain
`workmen never obtained water from the pump in the street. There is a
`in the brewery, in addition to the New River water.
`42)
`
`the
`well
`
`’~
`
`Saved by the beer! And at a nearby Workhouse, the circumstances of
`non-victims of the epidemic provided important and credible evidence
`about the cause of the disease, as well as a quantitative calculation
`of an expected rate of cholera compared with the actual observed rate:
`
`The Workhouse in Poland Street is more than three-fourths surrounded by houses
`in which deaths fiom cholera occurred, yet out offlve-hundred-thirty-five inmates
`only five died ofcholera, the other deaths which took place being those ofpersons
`admitted after they were attacked. The workhouse has a pump—well on the premises,
`in addition to the supply from the Grand Junction Water Works, and the inmates
`neversent to Broad Street for water. Ifthe mortality in the workhouse had been
`equal to that in the streets immediately surrounding it on three sides, upwards of
`one hundred persons would have died. (p. 42)
`
`Such clear, lucid reasoning may seem commonsensical, obvious, insuf-
`ficiently technical. Yet we will soon see a tragic instance, the decision
`to launch the space shuttle, when this straightforward logic of statistical
`(and visual) comparison was abandoned by many engineers, managers,
`and government officials.
`
`Page 9 of 32
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`

`
`Page 10 of 32
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`

`
`10 VISUAL EXPLANATIONS
`
`3. Considering alternative explanation: and contrary cases. Sometimes it
`can be difficult for researchers—who both report and advocate their
`findings—to face up to threats to their conclusions, such as alternative
`explanations and contrary cases. Nonetheless, the credibility of a report
`is enhanced by a careful assessment of all relevant evidence, not just the
`evidence overtly consistent with explanations advanced by the report.
`The point is to get it right, not to win the case, not to sweep under
`""the rug all the assorted puzzles and inconsistencies that frequently occur
`in collections of data.‘
`
`Both Snow's map and the time—sequence of deaths Show several
`apparently contradictory instances, a number of deaths from cholera
`with no obvious link to the Broad Street pump. And yet . . .
`
`In some ofthe instances, where the deaths are scattered a little further from
`the rest on the map, the malady was probably contracted at a nearer point to
`the pump. A cabinet-maker who resided on Noel Street [some distance from
`Broad Street] Worked in Broad Street. . . . A little girl, who died inHa.m
`Yard, and another who died in Angel Court, Great \lVindmill Street, Went to
`the school in Dufour's Place, Broad Street, and were in the habit of drinlcing
`the pump-water. . . .9
`
`In a particularly unfortunate episode, one London resident made
`. a special effort to obtain Broad Street" well—water, a delicacy of taste
`with a sideéefiect that unwittingly cost two lives. Snow’s report is
`one of careful description and precise logic:
`
`Dr. Fraser also first called my attention to the following circumstances, which
`are perhaps the most conclusive ofall in proving the connexion between the
`Broad Street pump and the outbreak ofcholera. In the ‘Weekly Return of
`Births and Deaths’ of September 9th, the following death is recorded: ‘At West
`End, on and September, the widow ofa percussion—cap maker, aged 59 years,
`diarrhea two hours, cholera epidemica sixteen hours.’ I was informed by this lady’:
`son that she had not been in the neighbourhood ofBroad Street for many
`months. A cart went from Broad Street to West End every day, and it was the
`custom to take out a large bottle of the water from the pump in Broad Street,
`as she preferred it. The water was taken on Thursday, 31st August, and she drank
`ofit in the evening, and also on Friday. She was seized with cholera on the
`evening ofthe latter day, and died on Saturday. . . . A niece, who was on a
`visit to this lady, also drank ofthe water; she returned to her residence, in a high
`and healthy part oflslington, was attacked with cholera, and died also. There
`was no cholera at the time, either at West End or in the neighbourhood where
`the niece died.”
`
`Although at first glance these deaths appear unrelated to the Broad
`Street pump, they are, upon examination, strong evidence pointing-to
`that well. There is here a clarity and undeniability to the link between
`cholera and the Broad Street pump; only such a link can account for
`what would otherwise be a mystery, this seemingly random and unusual
`occurrence of cholera. And the saintly Snow, unlike some researchers,
`gives full credit to the person, Dr. Fraser, who actually found this
`crucial case.
`
`5 The distinction between science and
`advocacy is poignantly posed when
`statisticians serve as consultants and
`witnesses for lawyers. See Paul Meier,
`“Damned Liars and Expert V/itnesses,”
`and Franklin M. Fisher, "Statisticians,
`Econometricians, and Adversary Pro-
`ceedings,” journal qfthe American
`Statistical Association, 81 (1986), pp.
`269-276 and 277-286;
`
`9 Snow, Cholera, p. 47.
`
`1° Snow, Cholera, pp. 44-45.
`
`Page 11 of 32
`
`

`
`Deaths from
`
`cholera, each
`day during
`the epidemic
`
`August
`
`VISUAL AND STATISTICAL THINKING 11
`
`Handle removed from
`
`Broad Street pump,
`September 8, I854
`
`iii.‘
`[;'$§I"'$""llIll“I"l7"‘1-"l"‘1'
`17
`19 21
`23 25
`27
`29
`
`Data source: plotted from the table i.n
`Snow, Cholera, p. 49.
`
`Ironically, the most famous aspect of Snow’s work is also the most
`uncertain part of his evidence: it is not at all clear that the removal
`of the handle of the Broad Street pump had much to do with ending
`the epidemic. As shown by this time—series above, the epidemic was
`already in rapid decline by the time the handle was removed. Yet, in
`many retellings of the story of the epidemic, the pump—handle removal
`is the decisive event, the umnistakable symbol of Snow’s contribution.
`Here is the dramatic account of Benjamin Ward Richardson:
`
`On the evening ofThm-sday, September 7th, the vestrymen of St. _Iames’s were
`sitting in solemn consultation on the‘ causes of the [cholera epidemic]. They might
`well be solemn, for such a panic possibly never existed in London since the days
`of the great plague. People fled from their homes as from instant death, leaving
`behind them, in their haste, all the mere matter which before they valued most.
`Whfle, then, the vestrymen were in solemn deliberation, they were called to con-
`sider a new suggestion. A stranger had asked, in modest speech, for a brief hearing.
`Dr. Snow, the stranger in question, was admitted and in few words explained his
`view of the ‘head and front of the offending.’ He had fixed his attention on the
`Broad Street pump as the source and centre ofthe calamity. He advised removal
`ofthe pump-handle as the grand prescription. The Vestry was incredulous, but
`had the good sense to carry out the advice. The pump-handle was removed, and
`the plague was stayed.“
`
`Note the final sentence, a declaration of cause and effect.” Modern
`
`epidemiologists, however, are distinctly skeptical about the evidence
`that links this intervention to the epidemic’s end:
`
`John Snow, in the seminal act ofmodern public health epidemiology, performed
`an intervention that was non-randomized, that was appraised with historical con—
`trols, and that had major ambiguities in the equivocal time relationship between
`his removal of the handle ofthe Broad Street pump and the end of the associated
`epidemic of c.holera—but be correctly demonstrated that the disease was transmitted
`through water, not air.”
`
`“ Benjamin W. Richardson, “The Life
`ofJohn Snow, M.D.," foreword to John
`Snow, On Chlarzy’orm and Other Anaes-
`thetics: Their Action and Administration
`(London, 1858), pp. xx—xxr.
`'
`
`*3 Another example of the causal claim:
`“On September 8, at Snow’s urgent
`request, the handle of the Broad Street
`pump was removed and the incidence of
`new cases ceased almost at once,” E. W.
`Gilbert, "Pioneer Maps of Health and
`Disease in England,” The Geographical
`journal, 124. (1958), p. 174. Gilbert’s
`assertion was repeated in Edward R.
`Tufte, The Visual Display qfQuan!itative
`Izgformation (Cheshire, Connecticut,
`1983). 13- 24-
`
`13 Alvan R. Feinstcin, Clinical Epidemi-
`ology: The Architecture of Clinical Research
`(Philadelphia, 1985), pp. 4o9—41o. And
`A. Bradford Hill [“Snow—AI1 Appreci-
`ation," Proceeding: qf the Royal Society
`qfMedx’cine, 48 (1955), p. 1010} Writes:
`“Though conceivably there might have
`been a second peak in the curve, and
`though almost certainly some more
`deaths would have occurred if the pump
`handle had remained in situ, it is clear
`that the end of the epidemic was not
`dramatically determined by its removal.”
`
`Page 12 of 32
`
`

`
`" “There is no doubt that the mortality
`was much diminished, as I said before, by
`the flight of the population, which com-
`menced soon after the outbreak; but the
`attacks had so far diminished before the
`use of the water was stopped, that it is
`impossible to decide whether the Well
`still contained the cholera poison in an
`active state, or whether, from some
`cause, the water had become free from
`it." Snow, Cholera, pp. 51-52.
`
`12 VISUAL EXPLANATIONS
`
`At a minimum, removing the pump—handle prevented a recurrence
`of cholera. Snow recognized several difiiculties in evaluating the effect
`ofhis intervention; since most.people living in central London had fled,
`the disease ran out of possible victims—which happened simultaneously
`with shutting down the infected Water supply.“ The case against the
`Broad Street pump, however, was based on a diversity of additional
`evidence: the cholera map, studies of unusual instances, comparisons of
`the living and dead with their consurnption ofwell—water, and an idea
`about a mechanism of contamination (a nearby underground sewer had
`probably leaked into the infected Well). Also, the finding that cholera
`was carried by Water—a life-saving scientific discovery that showed how
`to intervene and prevent the spread ofcholera——derived not only from
`study of the Broad Street epidemic but also from Snow's mappings of
`several other cholera outbreaks in relation to the purity of community
`Water supplies.
`I
`V
`
`4. Assessment ofpossible errors in the numbers reported in graphics. Snow’s
`analysis attends to the sources and consequences of errors in gathering
`the data. In particular, the credibility of the cholera map grows out of
`supplemental details in the text—as image, word, and number combine
`to present the evidence and make the argument. Detailed comments on
`possible errors annotate both the map and the table, reassuring readers
`about the care and integrity of the statistical detective work that pro-
`duced the data graphics:
`
`The deaths which occurred during this fatal outbreak of cholera are indicated
`in the accompanying map, as far as I could ascertain them. There are necessarily
`some deficiencies, for in a. few ofthe instances of persons who died in the hos-
`pitals after their removal from the neighbourhood of Broad Street, the num-
`ber ofthe house firom which they had been removed was not registered. The
`address ofthose who died a.fi:er their removal to St. James’s Workhouse was not
`registered; and I was only able to obtain it, in a part of the cases, on application
`at the Master’s Office, for many ofthe persons were too ill, when admitted, to
`give any account ofthemselves. In the case also ofsome of the workpeople and
`others who contracted the cholera in this neighbourhood, and died in different
`parts ofLondon, the precise house from which they had removed is not stated
`in the retum of deaths. I have heard ofsonic persons who died in the country
`shortly after removing from the neighbourhood ofBroad Street; and there must,
`no doubt, be several cases of this kind that Ihave not heard of. Indeed, the full
`extent of the calamity will probably never be known. The deficiencies I have i
`mentioned, however, probably do not detract from the correctness of the map
`as a
`ofthe topography ofthe outbreak; for, ifthe locality of the few
`additional cases could be ascertained, they would probably be distributed over
`the district of the outbreak in the same proportion as the large number which
`are known.“
`
`The deaths in the above table [the time-series of daily deaths] are compiled from
`the sources mentioned above in describing the map; but some deaths which were
`omitted fi:om the map on account of the number ofthe house not being known,
`are included in the table. . . .1‘
`
`‘5 Snow, Cholera, pp. 45-46.
`
`1‘ Snow, Cholera, p. 50.
`
`Page 13 of 32
`
`

`
`VISUAL AND STATISTICAL THINKING 13
`
`Snow drew a dot map, marking each individual death. This design
`has statistical costs and benefits: death rates are not shown, and such
`maps may become cluttered with excessive detail; on the other hand,
`the sometimes deceptive effects of aggregation are avoided. And of
`course dot maps aid in the identification and analysis of individual
`cases, evidence essential to Snow’s argument.
`.
`The big problem is that dot maps fail to take into account the num—
`.
`.
`.
`.
`.
`..
`her ofpeople living in an area and at risk to get a disease: an area
`of the map may be free of cases merely because it is not populated.””
`3I10W’S map does not fully answer the question Compared with what?
`For example, if the population as a Whole in central London had been
`distributedjust as the deaths were, then the cholera map would have
`merely repeated the unimportant fact that more people lived near the
`Broad Street pump than elsewhere. This was not the case; the entire
`area shown on the map—with and without cholera—was thickly
`populated. Still, Snow’s dot map does not assess varying densities of
`population in the area around the pump. Ideally, the cholera data
`should be displayed on both a dot and a rate map, with population-
`based rates calculated for rather small and homogeneous geographic
`units. In the text of his report, however, Snow did present rates for
`a few different areas Surrounding the Pump.
`Aggregations by area can sometimes mask and even distort the true
`story of the data. For two of the three examples at right, constructed
`by Mark Monmonier from SnoW’s individual-level data, the intense
`cluster around the Broad Street pump entirely vanishes in the process
`of geographically aggregating the data (the greater the number of
`cholera deaths, the darker the area).‘3
`In describing the discovery of how cholera is transmitted, various
`histories of medicine discuss the famous map and Snow’s analysis. The
`cholera map, as Snow drew it, is difficult to reproduce on a single
`page; the full size of the original is awkward (a square, 40 cm or 16
`inches on the side), and ifreduced in size, the cholera symbols become
`murky and the type too small. Some facsimile editions of On the Mode
`qfCommunication ofCholera have given up, reprinting only Snow’s
`text and not t