Sociology 549, Lecture 3

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# Sociology 549, Lecture 3 - PowerPoint PPT Presentation

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

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## Sociology 549, Lecture 3

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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
• 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
Perspective distortion
• Add a meaningless 3rd dimension
• Tilt pie away
• Perspective shrinks back
• Comparisons even harder
Pie Charts in politics
• Federal budget, from the website of the War Resisters’ League
• 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
Axis distortion
• Start vertical above zero
• Exaggerates all differences
• Similar distortion:
• Break vertical axis
Perspective distortion
• Reduces differences(caps same size)
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
Line chart(frequency polygon)
• Common in research
• Can show order
• Appropriate for ordinal and interval variables
Axis distortions
• Start vertical above zero
• Or break vertical
Perspective distortion
• Tilt horizontal
• Exaggerates trend
Bar vs. line: similarities
• Bar and line charts almost equivalent
• Connect tops
• remove bottoms
• You get a line chart!
Bar vs. line: Differences
• Line suggests trend more strongly
• Helpful with ordinal or interval variables
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)
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
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
Symmetry
• Symmetry, no skew
• Two tails, or no tails
• Important example:
• The normal curve
Dummy variables
• Describe the shape of this distribution.
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
Bimodal distributions
• Bimodal
• two modes
• e.g., # children
• modes at 0 and 2
• Interpretation?
Multimodal distributions
• Multimodal
• more than 2 modes
• e.g., hours worked by OSU sociology students
• modes at 0, 20, 40

(primary)

mode

secondary

modes

Review of shape
• Shapes
• Symmetric
• Skewed
• Positive (right)
• Negative (left)
• Unimodal, bimodal, multimodal
• NASDAQ stock index, reported by Yahoo!
• Redrawn
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