[ebook] edward rolf tufte - the visual display of quantitative information (1983)

7/16/2019 [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



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.



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



Importance of graphs:

• Exploratory Data Analysis

• Presentation of data – Values of data elements

– Relationship of data elements




• 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



-1.79

-1.7-1.68

-1.57

-1.55

-1.44

-1.36-1.34

-1.29

-1.27

-1.23

-1.23-1.18

-1.12

-1.09

-.64

-.63-.63

-.59

-.59

-.57

-.55-.55

-.38

-.35

-.33

-.33-.32

-.31

-.29

-.23

-.22-.22

-.2

-.19

-.12

-.1-.06

-.04

.01

.05

.1

.14

.14

.15

.16

.2

.21

.24

.27

.28

.3

.31

.32

.33

.37

.46

.48

.52

.55

.57

.57

.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



. summ z

Variable | Obs Mean Std. Dev. Min Max

---------+-----------------------------------------------------

z | 100 -.0692 .9138869 -1.79 1.98



. 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



z-1.787513 1.983905

-.155



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



- 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

1 * *

| 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




•Why not just use

summary statistics?



Summary statistics for selected variables

Variable | Obs Mean Std. Dev

---------+--------------------------------

z | 100 -.0692 .9138869

a | 100 -.0692 .9136105

u | 100 -.0692 .9131416



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




•Why not just use

analytic statistics?



. 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

-----------------------------------.



o

n

.005723 .984407

-2.10937

2.46622



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



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



0

10

20

30

40

50

60

70

80

90

100

A B

Treatment Group


N = 200 N = 200

p < .05



•The mean VAS ingroup A was 77 (SD 30,

N=200) and in group Bwas 82 (SD 7 , N=200)

(p< .05).



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



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

3

4

4

7

8

4

6

6

7

7

8

3

3

5

6

7

8

1

2

3

3

5

7

9

3

3

3

5

7

7

89

2

2

3

3

4

4

67

8

3

5

6

7

8

8

89

3

3

3

4

5

7

78

2

2

3

3

3

3

44

5

6

6

77

9

2

3

3

3

3

6

77

8

8

9

2

3

3

5

5

6

66

6

7

8

8

2

4

4

5

5

6

66

7

8

8

89

2

3

5

5

5

7

77

7

3

3

4

5

6

8

4

5

6

9

9

3

3

9

9

2

3

5

6

7

1

5

7

7

8

9

2

2

2

3

7

7

78

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



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

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

3

4

4

7

8

4

6

6

7

7

8

3

3

5

6

7

8

1

2

3

3

5

7

9

3

3

3

5

7

7

8

9

2

2

3

3

4

4

6

7

8

3

5

6

7

8

8

8

9

3

3

3

4

5

7

7

8

2

2

3

3

3

3

4

4

5

6

6

7

7

9

2

3

3

3

3

6

7

7

8

8

9

2

3

3

5

5

6

6

6

6

7

8

8

2

4

4

5

5

6

6

6

7

8

8

8

9

2

3

5

5

5

7

7

7

7

3

3

4

5

6

8

4

5

6

9

9

3

3

9

9

2

3

5

6

7

1

5

7

7

8

9

2

2

2

3

7

7

7

8

üü üü

üü üü

üü



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



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”




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




•Axes




Axes - scale

• Appropriate boundaries: Do not overly

compress or expand the data.• Uniformity: Distance along axis must

retain consistent interpretation

throughout graph.



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




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




•Data points



b

a-.007491 3.27872

.074068

.99277



b

a-.01 3.28

.07

.99




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.




•Chartjunk!

•Any ink that does not

show or explain data



77

82

75

76

77

78

79

80

81

82


A B

Treatment Group

p< .05




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




Other pitfalls to avoid

• Avoid redundancy within the graphic

• Check for errors




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.



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?



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)



Simple Univariate Display

0

10

20

30

40

50

60

70

80

90

100

A B

Treatment Group


N = 200 N = 200

p < .0512%

10%

36%

26%

12%

4%

1

2

3

4

5

6



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



Pre Post Pre Post

P E

F R

( L / m i n )

0

200

400

600

Drug S Drug N



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



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



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



Special Features

• Allow extra detail or strata to be

portrayed.

• Convey complex relationships simply

• Increase information content while

maintaining visual clarity



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)



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



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

.



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



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.



0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

[ebook] edward rolf tufte - the visual display of quantitative information (1983)

Documents

graphsimportance of

azuimportance of graphs

use of graphs inresearch

summ zvariable obs

usesummary statistics

selected variablesvariable

useanalytic statistics

regress o nnumber of