Sociology 549, Lecture 3

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Sociology 549,Lecture 3

• Graphs
• by Paul von Hippel

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Common graphs for frequency distributions

• Pie chart
• Line chart (frequency polygon)
• Bar chart
• Histogram

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Other common graphs

• Time series
• Statistical map

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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

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Shapes of distributions

• Symmetric
• Skewed
• Positively skewed
• Negatively skewed
• Modal
• unimodal
• bimodal
• multimodal

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Pie chart

• Rare in research
• Common in media
• Hard to compare wedges (different orientations)
• Cant show order
• Restrict to nominal variables

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Perspective distortion

• Add a meaningless 3rd dimension
• Tilt pie away
• Edge adds to front
• Perspective shrinks back
• Comparisons even harder

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Pie Charts in politics

• Federal budget, from the website of the War
  Resisters League

• Redrawn

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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

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Axis distortion

• Start vertical above zero
• Exaggerates all differences
• Similar distortion
• Break vertical axis

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Perspective distortion

• Add meaningless 3rd dimension
• Reduces differences(caps same size)

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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

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Line chart(frequency polygon)

• Common in research
• Can show order
• Appropriate for ordinal and interval variables

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Axis distortions

• Start vertical above zero
• Or break vertical

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Perspective distortion

• Add meaningless 3rd dimension
• Tilt horizontal
• Exaggerates trend

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Bar vs. line similarities

• Bar and line charts almost equivalent
• Start with a bar chart
• Connect tops
• remove bottoms
• You get a line chart!

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Bar vs. line Differences

• Line suggests trend more strongly
• Helpful with ordinal or interval variables
• Misleading with nominal

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Bar vs. line Differences

• Line eases comparison of groups

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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)

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Summary Graphical display of distributions
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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

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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

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Symmetry

• Symmetry, no skew
• Two tails, or no tails
• Important example
• The normal curve

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Dummy variables

• Describe the shape of this distribution.

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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 20s

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Bimodal distributions

• Bimodal
• two modes
• e.g., children
• modes at 0 and 2
• Interpretation?

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Multimodal distributions

• Multimodal
• more than 2 modes
• e.g., hours worked by OSU sociology students
• modes at 0, 20, 40

(primary) mode
secondary modes
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Review of shape

• Shapes
• Symmetric
• Skewed
• Positive (right)
• Negative (left)
• Unimodal, bimodal, multimodal

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Time seriesdont show distributions,show
change over time
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Axis distortionstart (or break) vertical above
zero
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Axis distortionSqueeze vertical or stretch
horizontal
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Axis distortionSqueeze horizontal or stretch
vertical
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Axis distortion in business

• NASDAQ stock index, reported by Yahoo!

• Redrawn

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Graphical distortion Summary

• Axis distortion
• Squeeze one axis
• Honest aspect ratio is 32 (Tufte)
• Start or break vertical axis above zero
• Perspective distortion
• Add disproportionate areas in a meaningless 3rd
  dimension
• Use blocking tilting

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Graphics Good advice

• Keep it simple
• Dont stretch axes
• Dont start or break axes above zero
• Dont use 3-D
• If you have to use 3D, avoid abuses
• With just a few numbers,consider a table instead
  of a graph

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Graphics Evil advice

• Use every trick (3D, distorted axes)
• Maximize differences that serve your purpose
• Minimize differences that work against you