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Statistics 120Good and Bad Graphs
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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.
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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.
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Male Female
Gender
Per
cent
age
0
10
20
30
40
50
60
Class Gender Breakdown
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Data Relevance
• Graphs are only as good as the data they display.
• No amount of creativity can produce a good graph fromdubious data.
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Auckland City Council:City Scene
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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.”
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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.
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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
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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
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Share Results
The extra dimension used in thisgraph has confused even the personwho created it.
The Washington Post, 1979.
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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
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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.)
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Theology
Fine Arts
Music
Medicine
Architecture
Education
Engineering
Law
Science
Commerce
Arts
0 2000 4000 6000 8000
Faculty Size
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Engineering
Theology
Architecture
Commerce
Science
Medicine
Law
Fine Arts
Arts
Music
Education
0 20 40 60 80 100
Percentage of Female Students
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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.
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Data Effect=27.5−18
18= 0.53, Graph Effect=
5.3− .6.6
= 7.83,
Lie Factor= 14.8
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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
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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.
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Lie Factor = 9.4
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Is the bottom dollar note roughly half the size of the top one?
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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
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Deliberate Distortion
• Sometimes graphs contain deliberate distortions.
• Usually these are an attempt to hide some feature of thedata.
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Year
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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
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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
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Errors
• Sometimes distortions occur because of errors.
• This can be because the artist tried to be clever andsometimes because they don’t understand statistics.
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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.
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