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
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. 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 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
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