Picturing the uncertain world: how to understand, communicate, and control uncertainty through graphical display
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 244 S. Ill., graph. Darst., Kt. 24 cm |
| ISBN: | 9780691137599 |
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Datensatz im Suchindex
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| adam_text | Contents
Preface
and Acknowledgments
xv
I. Introduction and Overview
CHAPTER
1
THE MOST DANGEROUS EQUATION
5
In this chapter we nominate
De Moivre s1
description of the expected
variation in the arithmetic mean for the title of the most dangerous
equation. To support this conclusion we describe five separate exam¬
ples where ignorance of this equation has led to enormous wastes of
time, money, and human resources. These five examples span almost a
thousand years and areas as diverse as monetary policy, education
policy, medical practice, and the genetic basis of sex differences in
intelligence.
II. Political Issues
In this section we show how five different kinds of issues that emerged
from essentially political arguments could be illuminated with more
careful thought and a graph or two. In chapter
6,
we introduce a very
simple probabilistic model that yields surprising richness of under¬
standing, which apparently escaped the editorial writers of the New
York Times.
CHAPTER
2
CURBSTONING
IQ
AND THE
2000
PRESIDENTIAL
ELECTION
23
Sometimes, when facts are hard to come by, people who are tasked to
gather those facts simply substitute a guess. When this is done by cen¬
sus workers it is called curbstoning (as in sitting down on the curb¬
stone in front of a house and guessing how many people live there).
Curbstone estimates, although illegal and grounds for dismissal, have
shown themselves to be remarkably accurate. In this chapter we look
at a piece of political propaganda meant to highlight the intellectual
and financial differences between red and blue states. Although it was
clearly based on someone s biases and not actual data, the conclusions
we would draw from the faked data are close to actual results.
CHAPTER
3
STUMBLING ON THE PATH TOWARD THE VISUAL
COMMUNICATION OF COMPLEXITY
31
An op-ed piece in the New York Times written by former secretary of
state George
Schultz
contained a statistical graph that showed the
economic superiority of the two Bush administrations to the Clinton
administration that was sandwiched in between. We show how this
graphic distorts our perceptions by plotting rates of change instead of
the actual GDP. The result is exactly the opposite of what former Sec¬
retary
Schultz
argues.
CHAPTER
4
USING GRAPHS TO SIMPLIFY THE COMPLEX:
THE MEDICARE DRUG PLAN AS AN EXAMPLE
35
The Medicare drug plan, although passed with great fanfare, quickly
resolved itself into a complex puzzle. In this chapter we simplify one
part of the puzzle by drawing a graph that makes clear who should
sign up. The graph is not a full solution, for how the costs will be paid
remains shrouded in a deep mystery indeed.
CHAPTERS A POLITICAL STATISTIC
39
Neither graphs nor tables are guarantees of truth. Incorrect stories can
be concocted with data displays just as they can with words. In this
chapter we investigate a graph produced by the U.S. Department of
Education that vividly shows how fourth graders reading scores remain
stubbornly flat despite skyrocketing increases in federal expenditures
viii /
CONTENTS
for education. A more careful look indicates that there is a strong
positive relationship between students test scores and money spent
on education.
CHAPTER
6
A CATCH-22 IN ASSIGNING PRIMARY
DELEGATES
47
As the
2008
election loomed ever closer, states maneuvered in various
ways to try to gain increased influence. The New York Times argued
that New York s citizens were not fully enfranchised because of the
all-or-none delegate assignment rule used in the primaries. Using a
simple mathematical model, we show that exactly the opposite is true.
III. Educational Testing
In the four thousand years since its inception in ancient China, mental
testing has promised to provide an important tool toward a true merit¬
ocratic society. Replacing family connections with an individual s
ability as the key to opening the doors to economic and social success
remains a principal goal of modern societies. Progress toward this goal
has been impressive, but it has occurred in fits and starts. In this section
we examine three proposals to aid in using test scores toward making
this a more just society. The first uses a statistical method commonly
employed in other circumstances to solve a vexing problem. In chapter
8
we examine a well-meaning but, at its heart, flawed scheme aimed at
reducing intergroup differences. And finally, in chapter
9,
we look at a
recent court case involving test scoring and show that the defenses case
was based on a misunderstanding of the meaning of uncertainty.
CHAPTER
7
TESTING THE DISABLED; USING STATISTICS TO
NAVIGATE BETWEEN THE
SCYLLA
OF STANDARDS
AND THE
CHARYBDIS
OF COURT DECISIONS S5
Test companies are in a logical bind. Standards of testing require that
individual scores on tests given under
nonstandard
conditions (for in-
stance, with extra time) be so labeled, while courts mandate that ex¬
aminees with disabilities (who are often given accommodations like
extra time) not be identified. In this chapter we show a statistical
method that can provide a way to be responsive to these two seemingly
contradictory requirements.
CONTENTS
/ ix
CHAPTER
8
ETHNIC BIAS OR STATISTICAL ARTIFACT?
FREEDLE S FOLLY
63
Social scientist Roy Freedle startled the testing world in
2003
when he
showed that black examinees outperformed matched white examinees
on hard SAT items. He suggested that ethnic group differences in test
performance could be reduced dramatically and tests thus made fairer
by making the tests harder. In this chapter we look into the validity of
this remarkable conclusion.
CHAPTER
9
INSIGNIFICANT IS NOT ZERO: MUSING ON THE
COLLEGE BOARD S UNDERSTANDING OF
UNCERTAINTY
74
On October
8,2005,
NCS Pearson, Inc., under contract to the College
Entrance Examination Board, scored an administration of the SAT
Reasoning test. Subsequently it was discovered that there was a scoring
error that had affected
5,024
examinees scores. After rescoring it was
revealed that
4,411
test scores were too low and
613
were too high.
The exams that were underscored were revised upward and the revised
scores were reported to the designated colleges and universities. The
College Board decided that it would be unfair to re-report the scores
of the
613
test takers whose scores were improperly too high and hence
did not correct them. They reached this conclusion because of a misun¬
derstanding of statistical error. In this chapter we discuss their argu¬
ment and its flaws.
IV. Mostly Methodological
This section is a bit more technical than the others, focusing more ex¬
plicitly on the statistical tool, with its application being secondary. In
chapter
10
we look at the validity of linear extrapolation through unex¬
pectedly consistent improvements in the world record for men running
a mile that have occurred over the course of the twentieth century and
speculate whether it should have been predictable, and what, if any¬
thing, it means about future improvements in the twenty-first century.
The eleventh chapter looks at statistical graphics in the popular media.
Chapter
12
demonstrates how a mixture of statistical tools, statistical
thinking, and various graphic forms combine to provide us with a
guided pathway of discovery. The last two chapters are perhaps the
χ
/
CONTENTS
most narrowly focused of all, looking first at ways to show our uncer¬
tainty graphically and next at one way in which powerful computing
when combined with our desire for simplicity at all costs can be used to
mislead us.
CHAPTER
10
HOW LONG IS SHORT?
87
All functions are well approximated by a straight line for a short part
of their length. But how can we know for how long the linear approxi¬
mation is suitable? Obviously, when the entire data series is in hand it
is easy, but what about when it is not? What do we do when we wish to
extrapolate from what appears to be linear beyond the data? For a very
short extrapolation it is usually fine, but how long is short? In this
chapter we look at a century s progress in the world records in the mile
run for help in answering this question.
CHAPTER
11
IMPROVING DATA DISPLAYS
92
The communication media s stock and trade is the distillation and
communication of possibly complex information. To do this effectively
the print media use an especially broad range of graphical formats.
Sometimes they do this poorly, but sometimes they do it very well in¬
deed. In this chapter we look at some displays devised by the media
that set a standard for excellence hard to imagine given their time dead¬
lines, as well as others that were seriously flawed.
CHAPTER
12
OLD MOTHER HUBBARD AND THE UNITED
NATIONS
106
Statistical thinking and data-based graphics are two tools used together
to understand the world. This chapter tells a story of how a detective
might use them to track down and expose some surprising aspects of
poverty.
CHAPTER
13
DEPICTING ERROR
121
Communicating data without some measure of their precision can lead
to misinterpretation and incorrect inferences. In this chapter, we dc
scribe and illustrate several conventions for displaying errors along
with the data they modify. We also offer some alternatives that seem
to provide improvements in the effective communication of error as
CONTENTS
/ xi
well as increasing the ease, and hence the likelihood, of their use. These
alternatives are illustrated principally with data from the National As¬
sessment of Educational Progress.
CHAPTER
U
THE MENDEL EFFECT K8
Data are often examined after being grouped into categories. For
example, we might see a plot of income shown as a function of educa¬
tion level, in which amount of education is collapsed (binned) into
specified categories like
0-8
years,
9-11, 12, 13-15, 16
or more. A
typical summary plot shows the mean value of income as a function of
the binned education variable, and trends are interpreted. In this chap¬
ter, I demonstrate how such trends can be epiphenomenal and are the
creation of the number of bins used and their boundaries. I provide
an algorithm that can take
trendless
data and create trends in any
direction.
V. History
We understand best those things we see grow from theirvery beginnings.
—Aristotle, Metaphysics
The Science of Uncertainty has been under development for a long
time. In this section, I pay homage to our forebears by using modern
tools to investigate ancient puzzles (chapters
15
and
16),
by exploring
the origins of some of these modern tools (chapters
17
and
19),
by
defending the wisdom of the ancients from contemporary misuses
(chapter
18),
by communicating the wisdom of a modern master (chap¬
ter
20),
and finally by a heart-rending use of graphics to paint an evoca¬
tive picture of one part of what was perhaps the greatest horror in all
human history,
CHAPTER
15
TRUTH IS SLOWER THAN FICTION
161
Novelists often use the latest scientific findings as essential plot ele¬
ments in their stories. In this chapter, we follow how some of the find¬
ings of the nineteenth-century British polymath Francis Galton were
used by Arthur Conan Doyle, by Mark Twain, and by Jules Verne, and
speculate on who got there first and why.
xii /
CONTENTS
CHAPTER
16
GALTON S NORMAL
168
Francis Galton was an early adopter of the normal distribution as a
means of making inferences about the frequency of occurrence of vari¬
ous human characteristics. In his
1869
book Hereditary Genius, he
explains how to do this with a hypothetical graph showing the heights
of British men. But the graph Galton made up revealed a serious mis¬
understanding he had about the normal distribution. In this chapter,
we uncover the error and suggest its source,
CHAPTER
17
NOBODY S PERFECT
173
In
1786,
the remarkable Scot William
Playfair
published a small
book in which he invented three of the four basic graphical formats
(bar charts, line charts, and pie charts). He did not invent the scatter
plot. In this chapter we ask and try to answer the obvious question,
why not?
CHAPTER
18
WHEN FORM VIOLATES FUNCTION
179
The title of finest statistical graphic ever prepared is generally awarded
to the nineteenth-century Frenchman Charles Joseph Minard s re¬
markable six-dimensional plot showing the fate of the French army as
it trekked between the
Niemen
River on the Poland-Russia border to
Moscow and back during Napoleon
s
ill-fated
1812-1813
campaign. In
this chapter, we examine one failing attempt to usurp Minard s famous
format for another purpose.
CHAPTER
19
A GRAPHICAL LEGACY OF CHARLES JOSEPH
MINARD: TWO JEWELS FROM THE PAST
186
Not all of those who sought to emulate Minard s success with data of
their own failed. In this chapter, we show how followers of Minard
produced treasures of their own by following in the footsteps of the
master.
CHAPTER
20
LA DIFFUSION
DE QUELQUES IDÉES:
A MASTER S VOICE
193
Jacques
Bertin (1918-)
is a French semiologist, trained in Paris, whose
seminal work La
Semiologie
Graphique
(1969)
laid the groundwork for
CONTENTS
/ xiii
modern
research in graphics. Almost forty years after its publication
it still provides important lessons to all those interested in the effec¬
tive display of quantitative information. In
2002
he sent me a note
de-
tailing his most recent developments and asked that I continue to help
him in la diffusion
de quelques idées.
This chapter tries to do ex¬
actly that.
CHAPTER
21
NUMBERS AND THE REMEMBRANCE OF
THINGS PAST
199
A single death is a tragedy; a million deaths is a statistic.
-Joseph Stalin
(1879-1953)
Unquestionably cold and cruel, this epigram conveys a sentiment that
sadly captures an aspect of human psychology. The mind is limited in
its capacity to fathom cataclysmic events. Great numbers of deaths,
particularly if they are distant in time or space, typically do not elicit
the same reaction as fewer deaths nearer to us. Sponsors and designers
of memorials face the challenge of stirring emotion, memory, and un¬
derstanding. In this final chapter we show and discuss data displays
produced by the inhabitants of the Kovno Ghetto to record their own
deaths
—
so that they might transform what could have been only a
statistic into the tragedy that it undeniably was.
VI. Epilogue
Notes
211
References
215
Source Material
225
Index
229
xiv /
CONTENTS
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| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Wainer, Howard 1943- Verfasser (DE-588)1139181955 aut Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display Howard Wainer Princeton [u.a.] Princeton Univ. Press 2009 XVIII, 244 S. Ill., graph. Darst., Kt. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Geschichte gnd rswk-swf Uncertainty (Information theory) Graphic methods Communication in science Graphic methods Statistik (DE-588)4056995-0 gnd rswk-swf Unsicherheit (DE-588)4186957-6 gnd rswk-swf Visuelle Kommunikation (DE-588)4131112-7 gnd rswk-swf Grafische Darstellung (DE-588)4129552-3 gnd rswk-swf Statistik (DE-588)4056995-0 s Unsicherheit (DE-588)4186957-6 s Grafische Darstellung (DE-588)4129552-3 s Visuelle Kommunikation (DE-588)4131112-7 s Geschichte z DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017712272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wainer, Howard 1943- Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display Uncertainty (Information theory) Graphic methods Communication in science Graphic methods Statistik (DE-588)4056995-0 gnd Unsicherheit (DE-588)4186957-6 gnd Visuelle Kommunikation (DE-588)4131112-7 gnd Grafische Darstellung (DE-588)4129552-3 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4186957-6 (DE-588)4131112-7 (DE-588)4129552-3 |
| title | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display |
| title_auth | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display |
| title_exact_search | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display |
| title_full | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display Howard Wainer |
| title_fullStr | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display Howard Wainer |
| title_full_unstemmed | Picturing the uncertain world how to understand, communicate, and control uncertainty through graphical display Howard Wainer |
| title_short | Picturing the uncertain world |
| title_sort | picturing the uncertain world how to understand communicate and control uncertainty through graphical display |
| title_sub | how to understand, communicate, and control uncertainty through graphical display |
| topic | Uncertainty (Information theory) Graphic methods Communication in science Graphic methods Statistik (DE-588)4056995-0 gnd Unsicherheit (DE-588)4186957-6 gnd Visuelle Kommunikation (DE-588)4131112-7 gnd Grafische Darstellung (DE-588)4129552-3 gnd |
| topic_facet | Uncertainty (Information theory) Graphic methods Communication in science Graphic methods Statistik Unsicherheit Visuelle Kommunikation Grafische Darstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017712272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wainerhoward picturingtheuncertainworldhowtounderstandcommunicateandcontroluncertaintythroughgraphicaldisplay |