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

Perspective distortion Add a meaningless 3 rd dimension Tilt pie away –Edge adds to front –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 Add meaningless 3 rd dimension –Reduces differences (caps same size)

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

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 Add meaningless 3 rd dimension Tilt horizontal –Exaggerates trend

Bar vs. line: similarities Bar and line charts almost equivalent –Start with a bar chart Connect tops remove bottoms You get a line chart!

Bar vs. line: Differences Line suggests trend more strongly –Helpful with ordinal or interval variables –Misleading with nominal

Bar vs. line: Differences Line eases comparison of groups

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 )

Summary: Graphical display of distributions

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 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

Time series: don’t show distributions, show change over time

Axis distortion: start (or break) vertical above zero

Axis distortion: Squeeze vertical or stretch horizontal

Axis distortion: Squeeze horizontal or stretch vertical

Axis distortion in business 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 3 rd 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