Visualising Variables – Validly!

Damien JolleySchool of Public Health & Preventive

MedicineMonash University

AHMRC Posters

8 September 2010

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Motivating examples Weather information,

New York Times, September ‘08 Petrol prices, Melbourne,

Aug-Sep, 2010

Note: There are 22 x 81 = 382 data points displayed in the NY Times weather chart

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Obvious fact #1:

Graphs can communicate data:

quickly

accurately

powerfully

efficiently

Download slides from: http://www.jolley.com.au“Only 50% of American 17-year-olds can identify information in a graph”*

Source: Wainer H. Understanding graphs and tables. Educational

Researcher 1992; 21:14-23

* US National Assessment of

Educational Progress,June 1990

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Whose fault?

Source: Wainer H. Understanding graphs and tables. Educational

Researcher 1992; 21:14-23

0

20

40

60

80

1970 1980 1990 2000Year

Qua

drill

ion

BTU

s

Petroleum

Nuclear power

Natural gas

Coal

Hydropower

“Like characterising someone’s ability to read by asking questions about a passage full of spelling

and grammatical errors. What are we really testing?”

Drawn using MS Excel ‘XY-chart’

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Survival from Ovarian cancer

Image taken from www.healthlinx.com.au

Marketers of OvPlex proposed screening test for ovarian cancer

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Obvious fact #2:

Bad graphs can hinder communication

http://odtmaps.com

A new view of the world

http://www.worldmapper.org

Where in the world is diabetes?

http://www.gapminder.org

http://www.safetyandquality.gov.au/ acknowledgement: UQ PhD scholar Megan Preece

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Less obvious facts #3, #4, #5:

What characterises a “good” graph?

What are the characteristics of a “bad” graph?

What software to use? How to use it?

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Howie’s Helpful Hintsfor bad graph displays

Ten useful pointers to help you create uninformative, difficult-to-read scientific graphs

Adapted from:Wainer H. (1997) Visual Revelations. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers

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Steps for better graphs

1. Identify direction of effect In almost all cases, the cause or predictor

variable should be horizontal (X) Effect or outcome variable is best vertical

(Y)2. Identify the levels of

measurement Nominal, ordinal or quantitative are

different!3. Think of visual perception

guides Columns or dots? Lines or scatterplot?

4. Minimise guides and non-data Grid lines, tick marks, legends are non-

data

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Cause (X) and effect (Y)Figure 16

Standard deviation of batting averages for all full-time players by year for the first 100 years of professional baseball. Note the regular decline.*

Standard deviation

Tim

e

Source:Gould, Stephen Jay. Full House: The Spread of Excellence from

Plato to Darwin. Random House, 1997.cited: http://www.math.yorku.ca/SCS/Gallery/, 24 Nov 2002* My emphasis

Standard deviation

Time

Source:

Killias M. International correlations

between gun ownership and rates

of homicide and suicide.

Can Med Assoc J 1993; 148: 1721-5

% of households owning guns

Rat

e of

hom

icid

e w

ith a

gun

(per

mill

ion

per y

ear)

10 20 30 40

1

5

10

50 USA

Norway

Canada

France

FinlandBelgium

Australia

SpainSwitzerland

Netherlands

West Germany

Scotland

England & Wales

Drawn using S-plus

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Levels of Measurement The right display for a variable depends on its

level of measurement

For univariate graphs, qualitative barplot ordinal column chart quantitative boxplot or histogram

For bivariate graphs, X ordinal, Y binary

connected percents X & Y both quantitative

scatterplot X categorical, Y quant

box plots

Binary eg gender, death, pregnant

Categorical Qualitative

eg race, political party, religion Diverging

eg change (-ve to +ve) Ordinal

eg rating scale, skin type, colour Quantitative

Interval only differences matter, eg BP, IQ

Ratio absolute zero, ratios matter,

eg weight, height, volume

Source:Lewis S, Mason C, Srna J.

Carbon monoxide exposure in blast furnace workers.

Aust J Public Health. 1992 Sep;16(3):262-8.

Ordinal variable, but categories

mixed

Outcome is COHb%, but drawn on X

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An alternative display . . .

Smokers

0%

5%

10%

Blast Furnace Exposure

None Low High

Non-smokers

0%

5%

10%

Blast Furnace Exposure

CO

Lev

el in

blo

od (%

)

None Low High

Area of circles proportional to nPredictor variable

Out

com

e va

riab

le

Drawn using MS Excel ‘bubble plot’

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Principles of visual perception

WS Cleveland much work in

psycho-physics of human visual understanding

Tells us: hierarchy of visual

quantitative perception

patterns and shade can cause vibration

graphs can shrink with almost no loss of information

Source: Cleveland WS. The Elements of Graphing Data. Monterey: Wadsworth, 1985.

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Ubiquitous column charts

Source: Jamrozik K, SpencerCA, et al. Does the Mediterranean paradox extend to abdominal aortic aneurism? Int J Epidemiol 2001; 30(5): 1071

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A dotchart version…

MediterraneanNetherlands

All otherOther N Europe

AustraliaScotland

Full fat milk

50 60 70 80

Adds salt50 60 70 80

Meat 3+ weekly

50 60 70 80

Fish 1+ weekly50 60 70 80

Percent

Drawn using S-plus “Trellis” graphics

Moiré vibrationis easy with

a computer !!!

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Moiré vibration Vibration is maximised with lines of equal

separation

This is common in scientific column charts

cited in Tufte E. The Visual Display of Quantitative Information.

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Minimise non-data ink

Non-data ink includes tick marks, grid lines, background, legend

Explanation of error bars, P-values can be included in caption or in text

Mortality Risk Ratio (95% CI) derived from Cox's Proportional Hazards model amongst FHILL cohorts by ethnicity and locality

00.20.40.60.8

11.2

Greeks inGreece

Greeks inAustraliaP=0.0001

Anglo-Celtsin Australia

P=0.056

Swedes inSwedenP=0.0001

Japanese inJapan

P=0.0008

FHILL cohorts

Ris

k R

atio

(RR

)

LowerUpperRisk Ratio

Greeks in Australia

Swedes in Sweden

Japanese in Japan

Anglo-Celts in Australia

Greeks in Greece

0.10 0.25 0.50 0.75 1.00Relative mortality rate (all causes)

Note the exception for X-Y orientation: because predictor is qualitative (unordered)

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Software for scientific graphics

Dedicated programs – thousands! Prism ViSta DeltaGraph SigmaPlot

Business graphics MS Excel Visio (MS Office) many other spreadsheet programs

Graphics in statistical packages

Stata simple, powerful

R powerful, free

StatsDirect Very like Excel

SPSS interactive graphics easy, expensive

Systat good reputation

SAS expensive, powerful

Minitab Popular, powerful

Advice: Avoid “default” choice in all programs (almost always wrong).Avoid programs with “Chart Type” menus – wrong approach.

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Death by Powerpoint

Powerpoint is power-ful for editing graphs, presenting

But… Dependence on bullet points Linear thinking Presenters READING slide-after-slide

Many design gurus now reject the Powerpoint (keynote, etc) paradigm

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Graph formats Object-oriented

lines, shapes, etc can be identified within graph

each object has attributes (eg size, colour, font)

editable using selection and “grouping”

Common formats: Postscript (ps,eps) Windows metafile (wmf,emf)

Bit-mapped image exists as a

collection of pixels each pixel is light or

dark, coloured can edit only pixels not

objects often “compressed” to

save disk space, bandwidth

Common formats graphics interchange

(gif) Windows bitmap (bmp) JPEG interchange (jpg)

Advice: Use WMF format where possible. Paste WMF into PowerPoint, “ungroup”, then edit objects for publication quality.

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References, further reading

Tufte ER.

The Visual Display of Quantitative Information

Cheshire, CT: Graphics Press 2001

www.edwardtufte.com

Cleveland WS.

Visualizing Data

Summit NJ: Hobart Press, 1993

Wainer H.

Visual Revelations. Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot

Mahwah, NJ: Lawrence Erlbaum Associates, Publishers. 1997

www.erlbaum.com

Wilkinson L.

The Grammar of Graphics

New York: Springer Verlag, 1999

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Summary Howie’s Helpful Hints for bad graphs:

Don’t show the data Show the data inaccurately Obfuscate the data

Steps for better graphs: Identify direction of cause & effect Exploit levels of measurement Accommodate visual perception principles Minimise non-data ink

Don’t use Excel unless you have to And if you have to, don’t use the default

chart!

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Thank you!

Finally, on a personal note,

To all my friends at Monash & SPHPM for their continuing support and understanding

over the last 18 months,particularly Steve, John, Peter & Just