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Graphic Discovery: A Trout in the Milk and Other Visual Adventures
Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, from a key seventeenth-century precursor--England's plague-driven initiative to register vital statistics--right up to the latest advances. In a highly readable, richly illustrated story of invention and inventor that mixes science and politics, intrigue and scandal, revolution and shopping, Howard Wainer validates Thoreau's observation that circumstantial evidence can be quite convincing, as when you find a trout in the milk.
The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures.
Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world.
The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures.
Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world.
208 pages, Hardcover
First published October 26, 2004
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December 11, 2024This was a fascinating read, albeit a bit dry. Definitely something to read in sips rather than trying to power through it all at once.
Pull quotes/notes
"Let me begin with a few kind words about the bubonic plague." (1) what a first sentence
"This material is classed in the 'collection' category of the British Library with the entry, 'A collection of engraved sheets of squared paper, whereon are traced in pencil or ink the curves or sweeps of the hulls of sundry men-of-war.'" (11) sundry
"Figure 1.7. A translated and computer-enhanced reproduction of perhaps the earliest statistical graphic yet uncovered. It was apparently constructed about 1400 B.C. and was preserved in a sealed ceramic container in the Qumran caves. It was purchased by the author from Moishe the mapman at his Dead Sea antiquities stall in 1991." (18) we are assuming this is real and not a forgery because...
"In this graph we see the number of private elementary schools meandering along at about ten thousand until the start of the era of school integration, when the number of schools increased more than 50 percent. The decade of shenanigans whose goal it was to try to subvert the spirit of Brown seems to come to a crashing end with the passage of the 1964 Civil Rights Act." (31) A-plus deployment of "shenanigans" here
"[Bill Cleveland] then goes on to amplify this advice in several wise ways, including the directive that when the goal of the graph is to display change, the ratio of the vertical and horizontal axes (the aspect ratio) should be chosen so that the slope of the data is about 45 degrees." (34)
"It is important to remember that the sin of using too small a scale is venial; the viewer can correct it. The sin of using too large a scale cannot be corrected without access to the original data; it can be mortal." (38) sinful data
"Dubourg's chronographie is marvelous not just for its form but also for its content. In addition to providing the names of various principal characters in the march of history, he includes a symbol that denotes character (martyr, usurper, tyrant, just, bigot, cruel, debaucher, slothful, fool, noble, majestic, blessed, heretic, impious, upright, unfortunate, rebel) as well as profession (savant, painter, theologian, botanist, physician, musician, monk, soldier, astronomer)." (49-50)
Chapter 11: Order in the Court
Chapter 12: No Order in the Court
"If we observed a score x, midway between the means of the two groups, the best estimate of the true score of the individual who generated that score depends on which group that person belongs to. If that person came from Group 1, we should regress the score downward; if from Group 2, we should regress it upward.
The regression effect occurs because we know that there is some error in the score. The average error is defined to be zero, and so some errors will be positive and some negative. Thus, if someone from a low-scoring group has a high score, we can believe that to some extent that person is the recipient of some positive error, which is not likely to reappear upon retesting, and so we regress that score downward. Similarly, if someone from a high-scoring group has an unusually low score, We regress that score upward." (69) this is the clearest explanation of regression to the mean that I've read and is a good example of how statistics and intuitive understanding of the way the world works (or the way we want it to work) don't always go hand in hand
"The format of table 11.1 surely is a better
storage medium, allowing us to find details about specific countries easily, but it provides no glimpse of the deep structure that is so readily visible in the reformatted version (table 11.2)." (77) the concept of data storage vs deep structure as main purposes for tables makes a lot of sense to me
"The starting point determines the scale. If we start earlier today, the scale is hourly. If we start last year, the scale is monthly, and if we start in 1910, the scale is annual. The starting point and hence the scale are determined by the questions that we expect the graph to answer." (86) this is a good point for this scale but I am very distracted by the graph title font being Comic Sans
Graph labels, for car prices from lowest to highest:
"Regular convertibles
Luxury convertibles
Exotic convertibles
Penis substitutes" (94)
"Taking the next step (inverses) in this ladder of transformation does the trick.*
*Traditional statistical summaries, like the mean, work best when the distribution of data being summarized is symmetric. Anyone who has gone to a restaurant and eaten a cheeseburger when everyone else had the lobster understands that dividing the bill equally (averaging) does not yield a satisfying result." (95) also goes for teetotalers at a table of drinkers
"It was my goal here to help my beloved Times remember the past so that it does not repeat it quite so often—at least not so often on the same page. I really don't much care what the Washington Post does." (101)
"Returning to the title question, 'How
quickly are women gaining?' it appears that we must respond, 'They aren't.' Indeed, according to this measure, the gains women have shown over the past decade or two in track performances have served only to prevent them from falling farther behind." (108) in track and field and salary
"A good legend can transform a weakly
good graph into a strongly good one. We ought to make this transformation when possible. A legend should do more than merely label the components of the plot. Instead it should tell us what is important, what the point of the graph is. This serves two purposes. First, it informs the viewer, transforming what might be a weakly good graph into a strongly good one. But second, and of at least equal importance, it forces the grapher to think about why this graph is being prepared." (123)
"Because these engines are specifically designed to operate within a highly interactive environment, they are different from traditional EDA tools, which will surely remain valuable." (126) surely
"Most students can easily concoct a situation in which it is important to know how many children are in the average family. But how would we find out the answer? When this question is posed, several blasé hands inevitably go up or someone shouts out, 'Do a survey.' 'Good,' I respond, drawing them into my net, 'what do we ask in the survey?' The happy reply emerges quickly, 'How many children were in your family?' When I get this response, I immediately ask everyone in the class to respond to this question. We then collect the results, add them up and calculate the average. This is never very far from 3.5. Inwardly smirking, I say, 'The usual figure that the Census Bureau gets is about 2.5. Why are we so far off?' At this point, I am treated to explanations of random fluctuations, small samples, old data, governmental incompetence, and bad luck.
But are those indeed the answer? I ask, 'Do any of you know of any families of your parents generation that had no children?' Clearly, such families would have no representatives in my class. In the same way, a family that had six children would have six times the chance to be represented than a family with only one child. Slowly the answer dawns: the bigger the family, the greater the chance that they will be represented in the sample. This yields a response bias toward a larger-than-correct answer.* If getting the right answer to such a simple question requires subtle thinking, how can we learn the answers to more difficult questions, such as "Does mammography reduce the likelihood of death from breast cancer?' To answer such questions one must know a considerable amount about statistical thinking, for in this arena at least, a little ignorance is a dangerous thing." (142-143) again, one of the clearest explanations/illustrations of a statistical concept I've seen in a while
"Gathering data, like making love, is one of those activities that almost everyone thinks can be done well without instruction. The results are usually disastrous. Let me elaborate." (143) yes, please do
"We cannot know for sure the longevity of those who are still alive or the SAT scores for those who did not take the test. Any inferences that involve such information are doomed to be equivocal. What can we do? One approach is to make up data that might plausibly have come from the unsampled population (i.e., from some hypothesized selection model) and include them with our sample as if they were real. Then see what inferences we would draw. Next, make up some other data and see what inferences are suggested. Continue making up data until all plausible possibilities are covered. When this is done, see how stable were the inferences drawn over the entire range of these data imputations. The multiple imputations may not give a good answer, but they can provide an estimate of how sensitive inferences are to the unknown. If you do not do this, you have not dealt with possible selection biases, you have only ignored them." (149) this was hard to wrap my head around but ultimately another helpful explanation
"Bertin, Jacques (1916-) French semiologist, trained in Paris, whose seminal work La Semiologie graphique (1969) laid the groundwork for modern research in graphics. Until his retirement in 1984, he was professor at the Laboratoire graphique in the Ecole des Hautes Études in Paris." (152) haute etudes seem like they'd all be in the highest octave of a piano
Pull quotes/notes
"Let me begin with a few kind words about the bubonic plague." (1) what a first sentence
"This material is classed in the 'collection' category of the British Library with the entry, 'A collection of engraved sheets of squared paper, whereon are traced in pencil or ink the curves or sweeps of the hulls of sundry men-of-war.'" (11) sundry
"Figure 1.7. A translated and computer-enhanced reproduction of perhaps the earliest statistical graphic yet uncovered. It was apparently constructed about 1400 B.C. and was preserved in a sealed ceramic container in the Qumran caves. It was purchased by the author from Moishe the mapman at his Dead Sea antiquities stall in 1991." (18) we are assuming this is real and not a forgery because...
"In this graph we see the number of private elementary schools meandering along at about ten thousand until the start of the era of school integration, when the number of schools increased more than 50 percent. The decade of shenanigans whose goal it was to try to subvert the spirit of Brown seems to come to a crashing end with the passage of the 1964 Civil Rights Act." (31) A-plus deployment of "shenanigans" here
"[Bill Cleveland] then goes on to amplify this advice in several wise ways, including the directive that when the goal of the graph is to display change, the ratio of the vertical and horizontal axes (the aspect ratio) should be chosen so that the slope of the data is about 45 degrees." (34)
"It is important to remember that the sin of using too small a scale is venial; the viewer can correct it. The sin of using too large a scale cannot be corrected without access to the original data; it can be mortal." (38) sinful data
"Dubourg's chronographie is marvelous not just for its form but also for its content. In addition to providing the names of various principal characters in the march of history, he includes a symbol that denotes character (martyr, usurper, tyrant, just, bigot, cruel, debaucher, slothful, fool, noble, majestic, blessed, heretic, impious, upright, unfortunate, rebel) as well as profession (savant, painter, theologian, botanist, physician, musician, monk, soldier, astronomer)." (49-50)
Chapter 11: Order in the Court
Chapter 12: No Order in the Court
"If we observed a score x, midway between the means of the two groups, the best estimate of the true score of the individual who generated that score depends on which group that person belongs to. If that person came from Group 1, we should regress the score downward; if from Group 2, we should regress it upward.
The regression effect occurs because we know that there is some error in the score. The average error is defined to be zero, and so some errors will be positive and some negative. Thus, if someone from a low-scoring group has a high score, we can believe that to some extent that person is the recipient of some positive error, which is not likely to reappear upon retesting, and so we regress that score downward. Similarly, if someone from a high-scoring group has an unusually low score, We regress that score upward." (69) this is the clearest explanation of regression to the mean that I've read and is a good example of how statistics and intuitive understanding of the way the world works (or the way we want it to work) don't always go hand in hand
"The format of table 11.1 surely is a better
storage medium, allowing us to find details about specific countries easily, but it provides no glimpse of the deep structure that is so readily visible in the reformatted version (table 11.2)." (77) the concept of data storage vs deep structure as main purposes for tables makes a lot of sense to me
"The starting point determines the scale. If we start earlier today, the scale is hourly. If we start last year, the scale is monthly, and if we start in 1910, the scale is annual. The starting point and hence the scale are determined by the questions that we expect the graph to answer." (86) this is a good point for this scale but I am very distracted by the graph title font being Comic Sans
Graph labels, for car prices from lowest to highest:
"Regular convertibles
Luxury convertibles
Exotic convertibles
Penis substitutes" (94)
"Taking the next step (inverses) in this ladder of transformation does the trick.*
*Traditional statistical summaries, like the mean, work best when the distribution of data being summarized is symmetric. Anyone who has gone to a restaurant and eaten a cheeseburger when everyone else had the lobster understands that dividing the bill equally (averaging) does not yield a satisfying result." (95) also goes for teetotalers at a table of drinkers
"It was my goal here to help my beloved Times remember the past so that it does not repeat it quite so often—at least not so often on the same page. I really don't much care what the Washington Post does." (101)
"Returning to the title question, 'How
quickly are women gaining?' it appears that we must respond, 'They aren't.' Indeed, according to this measure, the gains women have shown over the past decade or two in track performances have served only to prevent them from falling farther behind." (108) in track and field and salary
"A good legend can transform a weakly
good graph into a strongly good one. We ought to make this transformation when possible. A legend should do more than merely label the components of the plot. Instead it should tell us what is important, what the point of the graph is. This serves two purposes. First, it informs the viewer, transforming what might be a weakly good graph into a strongly good one. But second, and of at least equal importance, it forces the grapher to think about why this graph is being prepared." (123)
"Because these engines are specifically designed to operate within a highly interactive environment, they are different from traditional EDA tools, which will surely remain valuable." (126) surely
"Most students can easily concoct a situation in which it is important to know how many children are in the average family. But how would we find out the answer? When this question is posed, several blasé hands inevitably go up or someone shouts out, 'Do a survey.' 'Good,' I respond, drawing them into my net, 'what do we ask in the survey?' The happy reply emerges quickly, 'How many children were in your family?' When I get this response, I immediately ask everyone in the class to respond to this question. We then collect the results, add them up and calculate the average. This is never very far from 3.5. Inwardly smirking, I say, 'The usual figure that the Census Bureau gets is about 2.5. Why are we so far off?' At this point, I am treated to explanations of random fluctuations, small samples, old data, governmental incompetence, and bad luck.
But are those indeed the answer? I ask, 'Do any of you know of any families of your parents generation that had no children?' Clearly, such families would have no representatives in my class. In the same way, a family that had six children would have six times the chance to be represented than a family with only one child. Slowly the answer dawns: the bigger the family, the greater the chance that they will be represented in the sample. This yields a response bias toward a larger-than-correct answer.* If getting the right answer to such a simple question requires subtle thinking, how can we learn the answers to more difficult questions, such as "Does mammography reduce the likelihood of death from breast cancer?' To answer such questions one must know a considerable amount about statistical thinking, for in this arena at least, a little ignorance is a dangerous thing." (142-143) again, one of the clearest explanations/illustrations of a statistical concept I've seen in a while
"Gathering data, like making love, is one of those activities that almost everyone thinks can be done well without instruction. The results are usually disastrous. Let me elaborate." (143) yes, please do
"We cannot know for sure the longevity of those who are still alive or the SAT scores for those who did not take the test. Any inferences that involve such information are doomed to be equivocal. What can we do? One approach is to make up data that might plausibly have come from the unsampled population (i.e., from some hypothesized selection model) and include them with our sample as if they were real. Then see what inferences we would draw. Next, make up some other data and see what inferences are suggested. Continue making up data until all plausible possibilities are covered. When this is done, see how stable were the inferences drawn over the entire range of these data imputations. The multiple imputations may not give a good answer, but they can provide an estimate of how sensitive inferences are to the unknown. If you do not do this, you have not dealt with possible selection biases, you have only ignored them." (149) this was hard to wrap my head around but ultimately another helpful explanation
"Bertin, Jacques (1916-) French semiologist, trained in Paris, whose seminal work La Semiologie graphique (1969) laid the groundwork for modern research in graphics. Until his retirement in 1984, he was professor at the Laboratoire graphique in the Ecole des Hautes Études in Paris." (152) haute etudes seem like they'd all be in the highest octave of a piano
August 28, 2008
This is a well-written and extremely well-illustrated book which offers both theoretical and practical guidance to making and using "infographics." It differs from Edward Tufte's better-known work in that each chapter of Wainer's book succinctly tackles a different historical or contemporary example of information display and thinking. Wainer isn't afraid to crunch some numbers to make some arguments of his own, making this book both fun and useful.
Want to read
November 11, 2008More on graphical excellence.
October 22, 2009
Clever and inspiring. Useful for statistics. i.e. showing the meaning of the numbers.
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