Looking at Statistical Graphics Rigorously
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1 Looking at Statistical Graphics Rigorously Jamie Monogan Washington University in St. Louis September 13, 2010 Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
2 Objectives By the end of this meeting, participants should be able to: Rate perceptual tasks by humans ability to perform them. Assess the clarity of a graph and whether it informs or misleads. Create graphs that present data in the clearest possible way to the reader. Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
3 Some Easy Targets (Courtesy of USA Today) Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
4 More from USA Today... Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
5 Obvious Points Graphics are an important means of conveying statistical/empirical information to increasingly impatient reviewers and editors. There is no deductive science to statistical graphics. We must focus on experimental results. Key technology: ocular reception, psychological perception, cultural interpretation. The first known graphic (a map) was on a Mesopotamian clay tablet dated 3800 BCE. Key historical figures: Halley, Playfair, Tukey, Tufte, Cleveland (see the excellent Appendix in Beniger and Robyn [1978]). Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
6 Cleveland & McGill s Elementary Perceptual Tasks Ordered by Perceptual Accuracy: position along a common scale position along non-aligned scales length, direction, angle area volume, curvature shading, color saturation Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
7 Findings From Theoretical Psychophysics (Stevens 1975) Define: p = perceived magnitude, a = actual magnitude. Then for parameters k and α: p = ka α For comparing magnitudes: Findings: p 1 p 2 = α 1 for length judgements α < 1 for area judgements α 1 for volume judgements [ ] α a1 Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20 a 2
8 Example Data: Italian Political Parties DC PCI PSI PSDI PRI PLI PR DP PdUP MS Mon Others Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
9 Italian Political Parties, Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
10 Italian Political Parties, All DC PCI PSI PSDI PRI PLI PR DP PdUP MS1 Mon Others Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
11 Italian Political Parties, Time vs. Percentage Others Mon MS1 PdUP DP PR PLI PRI PSDI PSI PCI DC Freq Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
12 Italian Political Parties, Time vs. Percentage DC DP MS1 Mon Others PCI PLI PR PRI PSDI PSI PdUP Freq Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
13 Italian Political Parties, Time vs. Percentage Percentage PCI PSDI PLI Others MS1 DP DC PSI PRI PR PdUP Mon Year Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
14 Italian Political Parties, Time vs. Percentage DC PCI PSI PSDI PRI PLI PR DP PdUP MS1 Mon Others Freq Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
15 Improving Practice #1: Breaks (Cleveland 1984) Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
16 Improving Practice #2: Scale (Cleveland 1984) Widely varying scale makes graphs look too empty, but transformations on some are confusing. When the zero point is meaningless, bar charts are encoded with numbers that make no sense. Don t use bar charts to display area or volume. For ratio comparisons use log 2 (). Why? log 2 (4) = 2 log 2 (8) = 3 log 2 (16) = = = = 16 Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
17 Improving Practice #2: Scale (Cleveland 1984) Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
18 Improving Practice #2: Interpret the Scale (Wainer 1990, average distance is 7 years) Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
19 Improving Practice #3: Boxplots Can Hide Information Histogram of b.data Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
20 Improving Practice #4: Piechart Mistakes Jamie Monogan (WUStL) Looking at Statistical Graphics Rigorously September 13, / 20
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