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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) Can’t show order –Restrict to nominal variables

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Perspective distortion Add a meaningless 3 rd 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 3 rd dimension –Reduces differences (caps same size)

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Perspective distortion (continued) Add 3 rd 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 3 rd 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 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 series: don’t show distributions, show change over time

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Axis distortion: start (or break) vertical above zero

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Axis distortion: Squeeze vertical or stretch horizontal

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Axis distortion: Squeeze 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 3:2 (Tufte) –Start or break vertical axis above zero Perspective distortion –Add disproportionate areas in a meaningless 3 rd dimension –Use blocking & tilting

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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

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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

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Copyright 2011 by W. H. Freeman and Company. All rights reserved.1 Introductory Statistics: A Problem-Solving Approach by Stephen Kokoska Chapter 2 Tables.

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