STAT1010 cautions on graphics

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Cornelius Franklin
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3.4 Cautions with Graphics Graphics can be misleading. How do we perceive the graphic? Is the graphic portrayed honestly? Are they comparing apples to apples? Or apples to oranges?

1 3.4 Cautions with Graphics Graphics can be misleading. How do we perceive the graphic? Is the graphic portrayed honestly? Are they comparing apples to apples? Or apples to oranges? Is it a percentage change or an absolute change they are presenting? Is there SO MUCH in the graphic that we are distracted? 1 Perceptual Distortions Presenting area (2-Dimensional) changes to represent a length (1-Dimensional) change. Example (LA Times, Aug. 5, 1979): Percentage of doctors devoted solely to family practice: % 12% A little less than half 2 4 feet 2 feet Though the height comparisons are OK, our eyes are drawn to the area comparisons (which suggest docs are down a whole lot more than 50%). 3 1

Perceptual Distortions The lengths of the bars represent the data, but our eyes tend to focus on the areas of the bars Dollar value: 1980 2006 $1.00 $0.

2 Perceptual Distortions The lengths of the bars represent the data, but our eyes tend to focus on the areas of the bars Dollar value: $1.00 $0.41 A little less than half 4 Perceptual Distortions If volume is used (rather than area), the distortion is even greater. Houses with cable TV: million 73 million 4 times larger Multiplying height, width, and length by 4 multiplies volume by 4 3 =64. 5 Choice of values for the vertical axis can change the perception. Women as a Percentage of All College Students Same data, different vertical axes. 6 2

When comparing groups, axes should be the same (in most cases). The spreads look similar below for the three groups, but in reality, they are not. 7 Choice of scaling (units, units 2, log-scale, etc.

3 When comparing groups, axes should be the same (in most cases). The spreads look similar below for the three groups, but in reality, they are not. 7 Choice of scaling (units, units 2, log-scale, etc.) can affect perception. Exponential scaling Same data, different scaling on vertical axes. 8 Horizontal axis can also affect perception. If using years, keep the scale uniform even if missing data on some years. Potentially misleading Rate of homeownership Percentage of Americans who own their own home Year Percentage of Americans who own their own home Better Rate of homeownership Year 9 3

4 Too much white space is not a good thing in a graphic, but don t be misleading in your quest to get rid of white space. If zero is not in the observed values, you don t necessarily have to show it on the axis (zooming-in can provide more resolution), but again, don t be misleading. Use good judgment. 10 Should Zero Be Included? Vs. General Rule: Axes should span range of the data unless excluding zero creates false impressions. Taken from: Design of Scientific Graphics, Cornell Center for Materials Research. 11 Percentage Change Graphs Graphs that show percentage change are very common, particularly with economic data. Although they are perfectly honest, you can be easily misled unless you interpret them with great care. Always be careful when interpreting percentage changes. 12 4

A percentage change graph showing a flat line constant increase.

increase, but smaller than the previous year increase.

13 Pictographs Sensory overload, distractions.

26 yrs 123 yrs Horizontal axis is not uniform in years.

5 A percentage change graph showing a flat line constant increase. A percentage change graph showing a decreasing trend but still above 0 still an increase, but smaller than the previous year increase. Actual costs can be easier to interpret (obviously cost has always been rising). 13 Pictographs Sensory overload, distractions. The people are completely decorative here, population will not be going down. 26 yrs 123 yrs Horizontal axis is not uniform in years. Suggests a linear trend (it s not, population is exponentially increasing). 14 Pie Charts why not? Which provides better visual information below? Taken from: Wikipedia Pie Chart. 15 5

Pie Charts why not? Meaningful? Taken from: boingboing.net/2006.

com. 17 Misleading? Problem 7, Chapter Quiz (chapter 3).

6 Pie Charts why not? Meaningful? Taken from: boingboing.net/ Choosing between graphics Same data, different graphics. Taken from: junkcharts.typepad.com. 17 Misleading? Problem 7, Chapter Quiz (chapter 3). In what way is this graph misleading? Number of Twin births in US Number of twin births (thousands) year 18 6

7 Problem? 19 7

Lecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 2.1- #

Lecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 2.1- # Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola Chapter 2 Summarizing and Graphing Data 2-1 Review and Preview 2-2 Frequency Distributions 2-3 Histograms