STAT1010 – cautions on graphics

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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?  Is it a percentage change or an absolute

change they are presenting?  Is there SO MUCH in the graphic that we are

distracted?

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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: 1964 1990 27% 12%

A little less than half

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≈ 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%).

STAT1010 – cautions on graphics

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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 $0.41

A little less than half

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Perceptual Distortions

  If volume is used (rather than area), the distortion is even greater.

 Houses with cable TV: 1980 2005 18 million 73 million

4 times larger

Multiplying height, width, and length by 4 multiplies volume by 43=64.

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Axis Scaling

 Choice of values for the vertical axis can change the perception.

Women as a Percentage of All College Students

Same data, different vertical axes.

STAT1010 – cautions on graphics

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Axis Scaling  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.

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Axis Scaling  Choice of scaling (units, units2, log-scale, etc.)

can affect perception.

Same data, different scaling on vertical axes.

Exponential scaling

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Axis Scaling  Horizontal axis can also affect perception.

 If using years, keep the scale uniform even if missing data on some years.

1970 1975 1980 1985 2000 2005

Percentage of Americans who own their own home

Year

Rat

e of

hom

eow

ners

hip

020

60

1970 1975 1980 1985 2000 2005

Percentage of Americans who own their own home

Year

Rat

e of

hom

eow

ners

hip

020

60

Better

Potentially misleading

STAT1010 – cautions on graphics

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Axis Scaling

 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.

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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.

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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.

STAT1010 – cautions on graphics

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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).

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Pictographs

 Sensory overload, distractions.

The people are completely decorative here, population will not be going down.

Horizontal axis is not uniform in years. Suggests a linear trend (it’s not, population is exponentially increasing).

123 yrs

26 yrs

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Pie Charts… why not?  Which provides better visual information below?

Taken from: Wikipedia ‘Pie Chart’.

STAT1010 – cautions on graphics

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Pie Charts… why not?

 Meaningful?

Taken from: boingboing.net/2006.

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Choosing between graphics

Same data, different graphics.

Taken from: junkcharts.typepad.com.

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

 In what way is this graph misleading?

2000 2004

Number of Twin births in US

year

Num

ber o

f tw

in b

irths

(tho

usan

ds)

100

105

110

115

120

125

130

135

STAT1010 – cautions on graphics

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Problem?