Statistics 120 Good and Bad Graphsihaka/120/Lectures/lecture03.pdfStatistics 120 Good and Bad Graphs...

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Statistics 120Good and Bad Graphs


The Plan

• In this lecture we will try to set down some basic rulesfor drawing good graphs.

• We will do this by showing that violating the rulesproduces bad graphs.

• Later in the course we see that there is a solidperceptual basis for some of these rules.


Data Content

• It does not make sense to use graphs to display verysmall amounts of data.

• The human brain is quite capable of grasping one two,or even three values.


Male Female

Gender

Per

cent

age

0

10

20

30

40

50

60

Class Gender Breakdown


Data Relevance

• Graphs are only as good as the data they display.

• No amount of creativity can produce a good graph fromdubious data.


Auckland City Council:City Scene


Complexity

• Graphs should be no more complex than the data whichthey portray.

• Unnecessary complexity can be introduced by

– irrelevant decoration

– colour

– 3d effects

• These are collectively known as “chartjunk.”


Age Structure of CollegeEnrolment (1972-1976)

This graph presents five values. Ituses six colours, unnecessaryperspective and a split axis to do so.

American Education Magazine.


1972 1973 1974 1975 1976

28

29

30

31

32

33

Year

Per

cent

●

●

●

●

●

Age Structure of College EnrolmentPercent of Total Enrolment, Aged 25 and Over


1972 1973 1974 1975 1976

Year

Per

cent

0

5

10

15

20

25

30

35

Age Structure of College EnrolmentPercent of Total Enrolment, Aged 25 and Over


Share Results

The extra dimension used in thisgraph has confused even the personwho created it.

The Washington Post, 1979.


1972 1973 1974 1975 1976 1977

Earnings Per Share and Dividends

Dol

lars

1.021.08

1.16 1.16

1.281.34

1.53

1.711.63

1.721.82

1.7

EarningsDividends


Distortion

• Graphs should not provide a distorted picture of thevalues they portray.

• Distortion can be either deliberate or accidental.

• (Of course, it can be useful to know how to produce agraph which bends the truth.)


Theology

Fine Arts

Music

Medicine

Architecture

Education

Engineering

Law

Science

Commerce

Arts

0 2000 4000 6000 8000

Faculty Size


Engineering

Theology

Architecture

Commerce

Science

Medicine

Law

Fine Arts

Arts

Music

Education

0 20 40 60 80 100

Percentage of Female Students


The “Lie Factor”

• Ed Tufte of Yale University has defined a “lie factor” asa measure of the amount of distortion in a graph. (Don’ttake this too seriously – i.e don’t learn it for the exam).

• The lie factor is defined to be:

Lie Factor=size of effect shown in graphic

size of effect shown in data

• If the lie factor of a graph is greater than 1, the graph isexaggerating the size of the effect.


Data Effect=27.5−18

18= 0.53, Graph Effect=

5.3− .6.6

= 7.83,

Lie Factor= 14.8


1978 1979 1980 1981 1982 1983 1984 1985

Required Fuel Economy Standards:New Cars Built from 1978 to 1985

year

MP

G

0

5

10

15

20

25

30


Common Sources of Distortion

• The use of 3 dimensional “effects” is a common sourceof distortions in graphs.

• Another common source is the inappropriate use oflinear scaling when using area or volume to representvalues.


Lie Factor = 9.4


Is the bottom dollar note roughly half the size of the top one?


0.0

0.2

0.4

0.6

0.8

1.0$1.00

94c

83c

64c

44c

1958 1963 1968 1973 1978Eisenhower Kennedy Johnson Nixon Carter

Purchasing Power of the Diminishing Dollar


Deliberate Distortion

• Sometimes graphs contain deliberate distortions.

• Usually these are an attempt to hide some feature of thedata.


Year

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● ●●

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● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

1939 1947 1951 1955 1963 1965 1967 1970 1972 1973 1974 1975 1976

0

10,000

20,000

30,000

40,000

50,000

60,000

Median Net Incomes

Doctors

Other Professionals


Year

●● ●

● ●●

●● ● ●

● ●

●

●

●

●

●

●

●

●

●

●

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1940 1945 1950 1955 1960 1965 1970 1975

0

10,000

20,000

30,000

40,000

50,000

60,000

Median Net Incomes

Doctors

Other Professionals


Errors

• Sometimes distortions occur because of errors.

• This can be because the artist tried to be clever andsometimes because they don’t understand statistics.


Drawing Good Graphs

• If the “story” is simple, keep it simple.

• If the “story” is complex, make it look simple.

• Tell the truth – don’t distort the data.

Statistics 120 Good and Bad Graphsihaka/120/Lectures/lecture03.pdfStatistics 120 Good and Bad Graphs...

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