Sociology 549, Lecture 3 Graphs by Paul von Hippel.
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Sociology 549,Lecture 3
Graphs
by Paul von Hippel
Common graphs for frequency distributions
• Pie chart
• Line chart (frequency polygon)
• Bar chart
• Histogram
Other common graphs
• Time series
• Statistical map
Common distortions
• False perspective– e.g., tilting a pie chart
• Shortening an axis; e.g.,– not starting the vertical at 0– breaking the vertical– squishing the horizontal
• Reasons– Add visual interest– Make small differences look big,– Or make big differences look small
Shapes of distributions
• Symmetric• Skewed
– Positively skewed– Negatively skewed
• Modal– unimodal– bimodal– multimodal
Pie chart
• Rare in research• Common in media• Hard to compare
wedges (different orientations)
• Can’t show order– Restrict to nominal
variables
Majors in Soc 549
Criminology35%
Psychology4%
Sociology61%
Perspective distortion
• Add a meaningless 3rd dimension
• Tilt pie away– Edge adds to front
– Perspective shrinks back
– Comparisons even harder
Sociology61%
Criminology35%
Psychology4%
Pie Charts in politics• Federal budget, from the website of the War Resisters’ League
Human Resources
32%
General Government
16%
Physical Resources
6%
Past Military20%
Current Military
26%
• Redrawn
Bar chart(column chart)
• In research,more common than pie
• Can show order– Appropriate for ordinal
and interval
– (as well as nominal)
• Easy to compare vertical distances
Majors in Soc 549
0
2
4
6
8
10
12
14
16
Sociology Criminology Psychology
Axis distortion
• Start vertical above zero– Exaggerates all
differences
• Similar distortion:– Break vertical axis
Majors in Soc 549
7
8
9
10
11
12
13
14
15
Sociology Criminology Psychology
Perspective distortion
• Add meaningless 3rd dimension– Reduces differences
(caps same size)
0
2
4
6
8
10
12
14
Psychology Criminology Sociology
Perspective distortion (continued)
• Add 3rd dimension and overlap
• Exaggerates differences– Hides side of smaller
bars
– Also hides part of top
• Rotation would make it worse
0
2
4
6
8
10
12
14
Psychology Criminology Sociology
Line chart(frequency polygon)
• Common in research• Can show order
– Appropriate for ordinal and interval variables
0
2
4
6
8
10
12
14
16
Sociology Criminology Psychology
Axis distortions
• Start vertical above zero– Or break vertical
7
8
9
10
11
12
13
14
15
Sociology Criminology Psychology
Perspective distortion
• Add meaningless 3rd dimension
• Tilt horizontal– Exaggerates trend
SociologyCriminology
Psychology
S1
0
2
4
6
8
10
12
14
Bar vs. line: similarities
• Bar and line charts almost equivalent– Start with a bar chart
• Connect tops
• remove bottoms
• You get a line chart!
Majors in Soc 549
0
2
4
6
8
10
12
14
16
Sociology Criminology Psychology
0
2
4
6
8
10
12
14
16
Sociology Criminology Psychology
Bar vs. line: Differences
• Line suggests trend more strongly– Helpful with ordinal or
interval variables
– Misleading with nominal
0
2
4
6
8
10
12
14
16
Sociology Criminology Psychology
0
2
4
6
8
10
12
14
16
Senior Junior Sophomore
Bar vs. line: Differences
0
2
4
6
8
10
12
14
16
Sociol
ogy
Crimino
logy
Psych
ology
Physic
al th
erapy
Comm
unica
tions
Biolog
y
Social statistics
Sociology of Sport
• Line eases comparison of groups
0
2
4
6
8
10
12
14
16
Socio
logy
Crimin
ology
Psych
ology
Physic
al ther
apy
Communic
ation
s
Biolog
y
Social statistics
Sociology of Sport
Histograms• Like bar chart,
except– Variable typically
continuous– Bars touch
• usually
– Horizontal can represent equal class intervals (“bins”)
• Bin shown by center value (e.g. 35.0)
• Or by ends of class interval (e.g. 33.75-36.25)
Starting salary in thousands
47.545.042.540.037.535.032.530.027.525.022.5
Starting salaries for BAs in sociology, 2000-2001
National Association of Colleges and Employers
survey of college placement off ices
30
20
10
0
Std. Dev = 4.31
Mean = 28.7
N = 96.00
Summary: Graphical display of distributions
Nominal Ordinal IntervalPie √ Book approvesBar √ √Line Book disapproves √ √Histogram if continuous
Shape of distributions: Positive or right skew
• Positive or right skew• Characteristics:
– Peak on left
– Long right tail• Stretched (Skewed)
to the right
– A few large values
• Common cause– Floor but no ceiling
Starting salary in thousands
47.545.042.540.037.535.032.530.027.525.022.5
Starting salaries for BAs in sociology, 2000-2001
National Association of Colleges and Employers
survey of college placement off ices
30
20
10
0
Std. Dev = 4.31
Mean = 28.7
N = 96.00
Negative or left skew
• Negative or left skew• Characteristics
mirror positive skew:– Peak on right– Long left tail
• Stretched (Skewed) to the left
– A few small values
• Common cause– Ceiling but no floor Assignment 1 scores
100.0
95.0
90.0
85.0
80.0
75.0
70.0
65.0
60.0
55.0
50.0
45.0
40.0
35.0
Assignment 1 scores, sociology 549, winter 200114
12
10
8
6
4
2
0
Std. Dev = 15.79
Mean = 75.4
N = 101.00
Symmetry
• Symmetry, no skew– Two tails,
or no tails
• Important example:– The normal curve
Height of adult males (inches)
82.00
80.40
78.80
77.20
75.60
74.00
72.40
70.80
69.20
67.60
66.00
64.40
62.80
61.20
59.60
58.00
Fre
qu
en
cy
200
100
0
Dummy variables
• Describe the shape of this distribution.
Sex distribution, Soc 549, winter 2003
0
5
10
15
20
25
30
0 1
Sex dummy (1=female)
Number of
students
Unimodal distributions
• Mode– peak
– most common value
• Unimodal– one peak
– e.g., starting salaries• mode around $27K
• Interpretation– the most common salaries
– are in the high $20sStarting salary in thousands
47.545.042.540.037.535.032.530.027.525.022.5
Starting salaries for BAs in sociology, 2000-2001
National Association of Colleges and Employers
survey of college placement off ices
30
20
10
0
Std. Dev = 4.31
Mean = 28.7
N = 96.00
Bimodal distributions
• Bimodal– two modes– e.g., # children
• modes at 0 and 2• Interpretation?
NUMBER OF CHILDREN
EIGHT OR MORE
7
6
5
4
3
2
1
0
Co
un
t
500
400
300
200
100
0
Multimodal distributions
• Multimodal– more than 2 modes
– e.g., hours worked by OSU sociology students
• modes at 0, 20, 40
(primary)mode
secondarymodes
Review of shape
• Shapes– Symmetric– Skewed
• Positive (right)
• Negative (left)
– Unimodal, bimodal, multimodal
Time series:don’t show distributions,show change over time
BAs in social science and history(National Center for Educational Statistics)
0%5%
10%15%20%25%30%35%40%45%50%
1970 1975 1980 1985 1990 1995
% women
Axis distortion:start (or break) vertical
above zeroBAs in social science and history
30%
32%
34%
36%
38%
40%
42%
44%
46%
1970 1975 1980 1985 1990 1995
% women
Axis distortion:Squeeze vertical
or stretch horizontal
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1970 1975 1980 1985 1990 1995
% women
Axis distortion:Squeeze horizontal or stretch vertical
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1970 1980 1990
% women
Axis distortion in business• NASDAQ stock index, reported by Yahoo!
•Redrawn
0
500
1000
1500
2000
2500
6-Jan-02 6-Jan-03
NASDAQ stock index
Graphical distortion: Summary
• Axis distortion– Squeeze one axis
• Honest aspect ratio is 3:2 (Tufte)
– Start or break vertical axis above zero
• Perspective distortion– Add disproportionate areas in a meaningless 3rd
dimension– Use blocking & tilting
Graphics: Good advice
• Keep it simple– Don’t stretch axes– Don’t start or break axes above zero– Don’t use 3-D
• If you have to use 3D, avoid abuses
– With just a few numbers,consider a table instead of a graph
Graphics: Evil advice
• Use every trick (3D, distorted axes)– Maximize differences that serve your purpose– Minimize differences that work against you
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