[eBook] Edward Rolf Tufte - The Visual Display of Quantitative Information (1983)
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The visual display of quantitative
information: The use of graphs in
research and manuscripts
David L. Schriger, MD, MPH
Richelle J. Cooper, MD MSHS
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For a copy of these slides and a bibliography:
e mail: [email protected]
put “graphing lecture” on the subject line
any comments about the lecture would beappreciated. Mr Mikulich will anonymously
forward these to us (yeah right).
Much of this material can be found in theJanuary, 2001 issue of Annals of Emergency
Medicine.
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Goals of the session
• Importance and advantages of graphical
data display
• Master use of basic features of graphs
• Learn advanced techniques
• Gain ability to critique graphs
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Importance of graphs:
• Exploratory Data Analysis
• Presentation of data – Values of data elements
– Relationship of data elements
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Importance of graphs:
• Exploratory data analysis
– Picture worth 978 words
– How the investigator learns about the data
– Seeing is believing
– If we only had n dimensions
– Make multiple slices
– Advanced computer methods - “Fantastic voyage”
– Can’t cover in this hour
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-1.79
-1.7-1.68
-1.57
-1.55
-1.44
-1.36-1.34
-1.29
-1.27
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-1.23-1.18
-1.12
-1.09
-.64
-.63-.63
-.59
-.59
-.57
-.55-.55
-.38
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-.33-.32
-.31
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-.23
-.22-.22
-.2
-.19
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.37
.46
.48
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.57
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.59
.64
.71
.82
.87
.87
.9
.96
1
1.081.13
1.13
1.14
1.25
1.251.26
1.27
1.53
1.62
1.851.9
1.95
1.98
-.97
-.95-.89
-.87
-.85
-.85
-.8-.8
-.78
-.76
-.75
-.75-.73
-.66
-.66
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. summ z
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
z | 100 -.0692 .9138869 -1.79 1.98
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. summ z,d
z
-------------------------------------------------------------
Percentiles Smallest
1% -1.745 -1.79
5% -1.495 -1.7
10% -1.25 -1.68 Obs 10025% -.755 -1.57 Sum of Wgt. 100
50% -.155 Mean -.0692
Largest Std. Dev. .9138869
75% .56 1.85
90% 1.195 1.9 Variance .8351893
95% 1.575 1.95 Skewness .2684074
99% 1.965 1.98 Kurtosis 2.395736
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z-1.787513 1.983905
-.155
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Stem-and-leaf plot for x
plot in units of .01
-1** | 79,70,68
-1** | 57,55,44
-1** | 36,34,29,27,23,23
-1** | 18,12,09
-0** | 97,95,89,87,85,85,80,80
-0** | 78,76,75,75,73,66,66,64,63,63
-0** | 59,59,57,55,55
-0** | 38,35,33,33,32,31,29,23,22,22,20
-0** | 19,12,10,06,04
0** | 01,05,10,14,14,15,16
0** | 20,21,24,27,28,30,31,32,33,37
0** | 46,48,52,55,57,57,59
0** | 64,710** | 82,87,87,90,96
1** | 00,08,13,13,14
1** | 25,25,26,27
1** | 53
1** | 62
1** | 85,90,95,98
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- 1 * *
| 7 9 ,
7 0 ,
6 8
- 1 * *
| 5 7 ,
5 5 ,
4 4
- 1 * *
| 3 6 ,
3 4 ,
2 9 ,
2 7 ,
2 3 ,
2 3
- 1 * *
| 1 8 ,
1 2 ,
0 9
- 0 * *
| 9 7 ,
9 5 ,
8 9 ,
8 7 ,
8 5 ,
8 5 , 8
0 ,
8 0
- 0 * *
| 7 8 ,
7 6 ,
7 5 ,
7 5 ,
7 3 ,
6 6 , 6
6 ,
6 4 ,
6 3 ,
6 3
- 0 * *
| 5 9 ,
5 9 ,
5 7 ,
5 5 ,
5 5
- 0 * *
| 3 8 ,
3 5 ,
3 3 ,
3 3 ,
3 2 ,
3 1 , 2
9 ,
2 3 ,
2 2 ,
2 2 ,
2 0
- 0 * *
| 1 9 ,
1 2 ,
1 0 ,
0 6 ,
0 4
0 * *
| 0 1 ,
0 5 ,
1 0 ,
1 4 ,
1 4 ,
1 5 , 1
6
0 * *
| 2 0 ,
2 1 ,
2 4 ,
2 7 ,
2 8 ,
3 0 , 3
1 ,
3 2 ,
3 3 ,
3 7
0 * *
| 4 6 ,
4 8 ,
5 2 ,
5 5 ,
5 7 ,
5 7 , 5
9
0 * *
| 6 4 ,
7 1
0 * *
| 8 2 ,
8 7 ,
8 7 ,
9 0 ,
9 6
1 * *
| 0 0 ,
0 8 ,
1 3 ,
1 3 ,
1 4
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| 2 5 ,
2 5 ,
2 6 ,
2 7
1 * *
| 5 3
1 * *
| 6 2
1 * *
| 8 5 ,
9 0 ,
9 5 ,
9 8
F r a c t i o n
z-1.79 1.98
0
.1
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Importance of graphs:
•Why not just use
summary statistics?
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Summary statistics for selected variables
Variable | Obs Mean Std. Dev
---------+--------------------------------
z | 100 -.0692 .9138869
a | 100 -.0692 .9136105
u | 100 -.0692 .9131416
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r a c
o n
a-1.79 1.98
0
.2
F r a c t i o n
u-1 1.04
0
.34
r a c
o n
z-1.79 1.98
0
.1
A
Z
U
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Importance of graphs:
•Why not just use
analytic statistics?
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. regress o n
Number of obs = 100
F( 1, 98) = 411.93
Prob > F = 0.0000
R-squared = 0.8078
Adj R-squared = 0.8059
Root MSE = .40336
----------------------------------------------------o | Coef. Std. Err. t P>|t|
---------+------------------------------------------
n | 2.818721 .1388798 20.296 0.000
_cons | -1.41951 .0816387 -17.388 0.000
-----------------------------------o | [95% Conf. Interval]
---------+-------------------------
n | 2.543118 3.094323
_cons | -1.581519 -1.2575
-----------------------------------.
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o
n
.005723 .984407
-2.10937
2.46622
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Principles of graphing:
• Graph the data, not statistics
• Exploit the dimensionality of thegraphic format
• Depict the unit of analysis
• Stratify on confounders• Show the trees and the forest
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77
82
75
76
77
78
79
80
81
82
M e a n V A S ( m m )
A B
Treatment Group
p< .05
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0
10
20
30
40
50
60
70
80
90
100
A B
Treatment Group
M e a n V A S ( m m )
N = 200 N = 200
p < .05
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•The mean VAS ingroup A was 77 (SD 30,
N=200) and in group Bwas 82 (SD 7 , N=200)
(p< .05).
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VAS score (mm)
N u m b e r o f s u b j e
c t s
Treatment AN = 200
Treatment BN = 200
Mean 77
Mean 82
Median 83
Median
89
50 1000
20
15
10
5
0
5
10
15
20
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11
1
2
2
1
1
2
2
3
1
1
1
2
2
2
5
1
1
1
2
2
2
2
2
2
8
12 96 5
6
62
6
7
53
7
8
4
5
8
8
3
3
5
9
2
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4
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89
2
2
3
3
4
4
67
8
3
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8
89
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5
7
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2
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44
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77
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N u
m b e r o f c a s e
s
Low pain group High pain group
4 11
VAS (mm)
71 100
VAS (mm)
Group A by treating physician
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Principles of graphing:
• Graph the data, not statistics
• Depict the unit of analysis
• Stratify on confounders
• Show the trees and the forest
77
82
75
76
77
78
79
80
81
82
M e a n V A S ( m m
A B
TreatmentGroup
p<.05
0
10
20
30
40
50
60
70
80
90
100
A B
TreatmentGroup
M e a n V A S ( m m
N= 200 N= 200
p< . 05
VAS score (mm)
N u m b e r o f s u b j e c t s
T re a tm e n t AN = 200
T re a tm e n t BN = 200
Mean77
Mean82Median83
Median89
50 1000
20
15
10
5
0
5
10
15 2
0
11
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1
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12 96 5
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üü üü
üü üü
üü
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Importance of showing data:
• No assumptions needed
• Efficiency
• Empowers readers to:
– make their own conclusions
– determine whether authors’ analyses are
appropriate
– do their own analyses
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Elements of the graph:
Title
• Title should state what is being shown or
compared.
• Focus reader on what they are about to
see
NOT - “Change in Respiratory Function”BUT - “Change in FEV1 by group and
baseline FEV1”
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Elements of the graph:
Legend
• Makes the figure self-explanatory.
• Defines abbreviations, symbols, andmethods
– any regression line, p-value, or other symbol based on calculations should be explained
• Defines sample size if not shown in graph
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Elements of the graph:
•Axes
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Elements of the graph:
Axes - scale
• Appropriate boundaries: Do not overly
compress or expand the data.• Uniformity: Distance along axis must
retain consistent interpretation
throughout graph.
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575859606162636465666768697071
7273
1 2 3 4 5 6 7 8 9
Post-op day
M e a n P a i n S c o r e ( V A S ) m m
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Elements of the graph:
Axes – tick marks and labels
• Avoid clutter
• Align ticks, labels and data points
• Consider specific label for first and last
point of the data set
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Elements of the graph:
•Data points
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b
a-.007491 3.27872
.074068
.99277
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b
a-.007491 3.27872
.074068
.99277
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b
a-.01 3.28
.07
.99
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Elements of the graph:
Data points
• Is it the pattern or the individual points
that you want readers to see?
• Consider using jitter or alter graph
dimensions to avoid clutter.
• Consider symbols to further differentiate strata in the data.
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Elements of the graph:
•Chartjunk!
•Any ink that does not
show or explain data
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77
82
75
76
77
78
79
80
81
82
M e a n V A S ( m m )
A B
Treatment Group
p< .05
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Elements of the graph:
Background and Shading• Efficiency is the key to a good
graphic.
• Avoid
- background shadings, background
grid lines, or unnecessary axes
- moiré patterns
- 3-D effects
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Elements of the graph:
Other pitfalls to avoid
• Avoid redundancy within the graphic
• Check for errors
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Elements of the graph:
Matching the graph with the text
• Avoid redundancy.
• Use a graph to provide information beyond what can be conveyed tersely in
text.
• Be sure text and figures are congruent.• Work with copy editor - get the graphic
on the same page as the relevant text.
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Choosing the type of graph
• Choice depends on the type of data
collected, number of observations, and
the message you wish to convey. – Numeric details or overall pattern?
– Number of subjects or measurements?
– Data form a distribution?
– Data paired?
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Graph type - examples• Univariate simple display - pie chart,
bar graph, point graph
• Univariate distribution – one-way,histogram, stem-and-leaf plot, box-
and-whisker, survival curve
• Bivariate display – scatterplot and itsvariations (ROC, Bland-Altman)
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Simple Univariate Display
0
10
20
30
40
50
60
70
80
90
100
A B
Treatment Group
M e a n V A S ( m m )
N = 200 N = 200
p < .0512%
10%
36%
26%
12%
4%
1
2
3
4
5
6
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Univariate distributions-1** | 79,70,68
-1** | 57,55,44
-1** | 36,34,29,27,23,23
-1** | 18,12,09
-0** | 97,95,89,87,85,85,80,80
-0** | 78,76,75,75,73,66,66,64,63,63-0** | 59,59,57,55,55
-0** | 38,35,33,33,32,31,29,23,22,22,20
-0** | 19,12,10,06,04
0** | 01,05,10,14,14,15,16
0** | 20,21,24,27,28,30,31,32,33,37
0** | 46,48,52,55,57,57,59
0** | 64,710** | 82,87,87,90,96
1** | 00,08,13,13,14
1** | 25,25,26,27
1** | 53
1** | 62
1** | 85,90,95,98
VAS score (mm)
N u m b e r o f s u b e c t s
Treatment A
N = 200
Treatment B
N = 200
Mean 77
Mean 82
Median 83
Median
89
50 1000
20
15
10
5
0
5
10
15
2
0
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Pre Post Pre Post
P E
F R
( L / m i n )
0
200
400
600
Drug S Drug N
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P E F R
( L /
m i n )
Figure 6a - Drug S
Pre Post
0
200
400
600
Figure 6b - Drug N, v.1
Pre Post
0
200
400
600
Figure 6c - Drug N, v.2
Pre Post
0
200
400
600
Figure 6d - Drug N, v.3
Pre Post
0
200
400
600
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Figure 7 - Change in PEFR by subject
P E F R
( L
/ m i n )
Not on Steroids On Steroids
Subjects N = 360
100
225
350
475
600
N=180
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C h a n g
e i n P E F R
( L / m i n )
Initial PEFR (L / min)
Not on steroids On steroids
110 200 300 400 510
-110
0
200
400
470
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Special Features
• Allow extra detail or strata to be
portrayed.
• Convey complex relationships simply
• Increase information content while
maintaining visual clarity
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Examples of special features• Illustration of pairing
• Symbolic dimensionality
• Small multiples
• Layering of two graphic types to convey
detail and summary measures (eg scatterplot
with box-and-whisker plots)
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Linear Regression Lowess Regression
P a t i e n t S a t i s f a c t i o
n
Length of ED Stay - hours
0 2 4 6 8
1
4
7
10
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P a t i e n
t S a t i s f a c t i o n
Length of ED Stay - hours
Discharged Admitted
0 2 4 6 8
1
2
4
6
8
10
.
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P a t i e n t S a t i s f a c t i o n
Length of Stay - hours
ankle injury
1
4
7
10
laceration wrist/hand fracture
back pain
1
4
7
10
bronchospasm vomiting
don't feel well
0 4 8
1
4
7
10
weakness
0 4 8
headache
0 4 8
Length of Stay (hours)
S a t i s f a
c t i o n
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For a copy of these slides and a bibliography:
e mail: [email protected]
please put “graphing lecture” on the subject line
any comments about the lecture would be appreciated. MrMikulich will anonymously forward these to us (yeah right).
Much of this material can be found in the January, 2001 issue
of Annals of Emergency Medicine.
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0
1
2
3
4
5
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7
8
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