Thinking in Data Workshop

Thinking About Your Data

David Weisman, Ph.D.

[email protected]

LATEX compile time: November 9, 2014, 07:47

© 2014 David Weisman. All rights reserved.

If you’d like to use this material for any purpose,please contact [email protected].

All names and stories are fictitious unless otherwise noted.

[email protected]

Story #1: Best-Burgers moves up-market

Dissect the data in this story:

Best-Burgers Attracts Upper-Income Diners

San Francisco – November 9, 2014 – It’s no secret thatBest-Burgers has been courting upper-income diners, and it lookslike their campaign is working. At lunch yesterday, I visited aBest-Burgers near our downtown office and chatted with customersenjoying the daily special: bountiful lobster salads with earthypommes frites, paired with a perfect Pouilly-Fume.

From my 14 conversations with these happy diners, the averageyearly income was $164k, far above the old stereotype ofbudget-conscious fast-food customers.

Here are some problems with the Best-Burgers story

Tiny sample Only 14 customerschance greatly affects the average

Sample bias Downtown San Francisco at lunchtime doesnot represent USA.

Selection bias Journalist picked lobster eaters

Interviewer bias Journalist may have coached participants:You look like an upper-income customer,may I ask you a quick question?

Response bias Low-income customers might be embarrassedand not answer.

























Here are counties with the lowest cancer ratesPropose a hypothesis

Wainer, H, et al. Phi Delta Kappan, 300–303, 2006

Check this out: Counties with highest cancer ratesWhat’s going on?


Small samples produce high varianceFIGURE 3.

Age-adjusted

can

cer rate (per hundred thousand) 20-

15-

10-

5-

0-

100 1,000 10,000 100,000 1,000,000 10,000,000

Population


Story #2: Stock portfolios are doing great


No Sad Faces as Dow Smashes Record

New York – November 9, 2014 – After Friday’s record stockmarket close, analysis of 5000 random investor accounts found thatthe average account balance worth was over $10 million. “Neverbefore have so many people made so much money,” beamed ajubilant Ann Smith as crisp $100 bills spilled out of her pockets.

Simple histogram reveals the underlying data

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

$0 $10 $20 $30 $40 $50

Account value in billions of dollars

Num

ber

of in

vest

ors

Average Balance = $10,000,000What could causethis data?

Outliers skewed average to $10 million

I Most account balances are small

I One is huge

I Average balance = total of all account balances5000 accounts = $10 million

I Outlier points are either:I Correct but unusual dataI Bad data (errors, typos very common)

I Takeaway: Outliers skew results

I Takeaway: Always look for outliers●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

$0 $10 $20 $30 $40 $50


Num

ber

of in

vest

ors

Takeaway: Always understand outliers

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●

Bill Gates

$0 $10 $20 $30 $40 $50


Num

ber

of in

vest

ors

Zoom in to remove outlier

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$0 $250,000 $500,000 $750,000 $1,000,000

Account value in dollars

Num

ber

of in

vest

ors

I Note horizontal axisI Average account $50k

Takeaway: Zooming revealsinteresting details

Zoom in to remove outlier

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$0 $250,000 $500,000 $750,000 $1,000,000

Account value in dollars

Num

ber

of in

vest

ors

I Note horizontal axisI Average account $50k

Takeaway: Zooming revealsinteresting details

Median finds the middle item1. Rank the account balances from smallest to biggest

2. Pick the middle position

3. This is the median

4. Median much less sensitiveto outliers than average

Rank Balance1 $02 $143 $241... ...

→ 2500 → $50,251... ...

4998 $341,0324999 $965,8645000 $50,231,754,642

Takeaway: Median tolerates outliers

Median finds the middle item1. Rank the account balances from smallest to biggest

2. Pick the middle position

3. This is the median

4. Median much less sensitiveto outliers than average

Rank Balance1 $02 $143 $241... ...

→ 2500 → $50,251... ...

4998 $341,0324999 $965,8645000 $50,231,754,642

Takeaway: Median tolerates outliers

Story #3: Refrigerator prices in deep freeze


Refrigerator Prices Stuck in Deep Freeze

Chicago – November 9, 2014 – Median refrigerator prices havebeen flat for the past ten years, despite a flood of new high-endproducts with luxury styling, celebrity endorsements, andhigh-efficiency green technology.

What are some possibilities here?

Median condenses complex data into single number

Median = 808

Median = 808

0

100

200

300

400

500

0

100

200

300

400

500

10 years agocurrent year

0 1000 2000 3000 4000 5000

Unit price (dollars)

Ref

riger

ator

s so

ld

Graphing told much more of a story than numbers

Takeaway: Summary statistics often hide interesting data

We’ve seen limitations with:I average (mean)I median

You’ll see limitations with other summary statistics:I standard deviationI correlationI regression

Takeaway: Graphing tells a much better story than numbers

Story #4: Taller children read better


Lanky Bookworms in Spotlight

Washington – November 9, 2014 – The U.S. Department ofEducation reported yesterday that reading comprehension forstudents in grades 3–8 dramatically corresponded with thestudents’ heights.

Scatter plot shows relationship of two variables

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I Just summarystatistics:slope, intersect

You’ll often see regression lines in scatter plots

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90

100

100 120 140 160 180

Height (cm)

Rea

ding

sco

re

I Single line thatbest fits points

I Regression linesoversimplifycomplexrelationships

I Just summarystatistics:slope, intersect

Why is reading score related to height?


Age Observed

Not observed Reading

Height

causes

causes


Age Observed

Not observed Reading

Height

causes

causes

Takeaway: Non-observed factors are common.Always look for underlying causes

We also measure correlation (r) between variables

1 0.8 0.4 0 -0.4 -0.8 -1

1 1 1 -1 -1 -1

0 0 0 0 0 0 0

Correlation measures strength of linear relationship:+1 Perfectly correlated (rare)

Example: Height in inches & Height in cm

-1 Perfectly inversely correlated (rare)Example: Hours sleeping & Hours awake

0 Non-correlated – no relationshipExample: Favorite food & Purchases of postagestamps

−1 < r < +1 Common – some relationship Image credit: wikipedia.org

Correlation non-helpful with complex relationships

1 0.8 0.4 0 -0.4 -0.8 -1

1 1 1 -1 -1 -1

0 0 0 0 0 0 0

wikipedia.org

Correlation does not imply causality35

30

25

20

10

5

15

0

0 5 10 15

Chocolate Consumption (kg/yr/capita)

Nob

el Lau

reate

s p

er

10 M

illion

Pop

ula

tion

Poland

SwitzerlandSweden

Norway

China Brazil

GreecePortugal

United States

Germany

France

Finland

Italy

Australia

The Netherlands

CanadaBelgium

United Kingdom

Ireland

Spain

Austria

Denmark

r=0.791P<0.0001

Japan

Messerli, FH. N Engl J Med, 367(16):1562, 2012

Big Data produces spurious correlations

Marriage rate correlates with electrocutions

24,000 automatically discovered correlations at http://www.tylervigen.com/

http://www.tylervigen.com/


Marijuana arrests inversely correlate with honey bee population




Marijuana arrests inversely correlate with honey bee population

Takeaway: Correlation does not imply causality



Be skeptical about correlations

http://xkcd.com/552/

http://xkcd.com/552/

Think about direction of causality

Cigarettes cause−−−−→ Cancer

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Cigarettes smoked per week

Can

cer

seve

rity

Think about direction of causality: Same data

Cancer causes−−−−→ Cigarettes

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100

120

140

160

180

70 80 90 100

Cancer severity

Cig

aret

tes

smok

ed p

er w

eek

Story #5: Happy colors make happy patients


Bright colors cheer up hospital patients

Topeka – November 9, 2014 – In a groundbreaking experiment,Central Hospital has shown that warm, happy colors improvepatients’ moods.

Using two identical general medicine wards, researchers splashedone with bright perky colors, and slathered the other in a viscous,dreary, Soviet-era gray. One month later, Dr. Vargas interviewed100 patients exposed to bright colors, while Dr. Mira interviewed100 patients surrounded in gloom.

The patients exposed to bright colors were 68% happier than thosefrom the other ward.

Find some possible biases here?

Vargas

Mira

Brightpaint

Patients

Gloomypaint

Patients

Story #6: Marketing manger sues firm


Fired sales manager James Smith demands compensation

Cambridge, MA – November 9, 2014 – James Smith argued inFederal Court today that sales increased by 400% while he led theInternational Marketing Division, and that he should have beenrewarded rather than terminated.

“Increasing sales by 400% is way beyond superstar performance,”roared his attorney.

Relative change hides quantity

Sales increased 400% = sales this year – last yearlast year

Sales increased 400% = 5 – 11

Sales increased 400% = 5,000,000 – 1,000,0001,000,000

True story: Contraceptive Pill Scare of 1995

U.K. Committee on Safety of Medicines (1995):Old contraceptive: 1/7,000 had severe blood clotNew contraceptive: 2/7,000 had severe blood clot

“New drugdoubles risk”

Patientsabandoned drug

Takeaway: Relative change hides quantityGigerenzer, G, et al. Psychological science in the public interest, 8(2):53, 2007

Recap: Visualization tells story better than numbers

All: y = 7.5, S = 2, r = 0.82Anscombe, FJ. The American Statistician, 27(1):17, 1973

We can visualize 3-D and 4-D datasets

Extend to 5-D and 6-D:

I Point size: O O O OI Point shape: + � l X

http://www.advsofteng.com/doc/cdperldoc/threedscatter.htm

http://www.advsofteng.com/doc/cdperldoc/threedscatter.htm

Datasets are often high-dimensional

Visualize and compare numeric data by category

VolkswagenToyota

SubaruPontiacNissan

MercuryLincoln

Land roverJeep

HyundaiHonda

FordDodge

ChevroletAudi

0 10 20 30

Highway mileage

Man

ufac

ture

r

Takeaway: Alphabetic ordering obscures story

Visualize and compare numeric data by category

VolkswagenToyota

SubaruPontiacNissan

MercuryLincoln

Land roverJeep

HyundaiHonda

FordDodge

ChevroletAudi

0 10 20 30

Highway mileage

Man

ufac

ture

r

Takeaway: Alphabetic ordering obscures story

Reordering & simplifying greatly clarifies the story

●

●

●

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●

●

Land roverLincoln

JeepDodge

MercuryFord

ChevroletNissanToyota

SubaruPontiac

AudiHyundai

VolkswagenHonda

20 25 30

Highway mileage

Man

ufac

ture

r

Takeaway: Small visualization changes add great clarity to a story

Reordering & simplifying greatly clarifies the story

●

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Land roverLincoln

JeepDodge

MercuryFord

ChevroletNissanToyota

SubaruPontiac

AudiHyundai

VolkswagenHonda

20 25 30

Highway mileage

Man

ufac

ture

r

Takeaway: Small visualization changes add great clarity to a story

Visualize and compare histograms by category

0

200

400

600

0

30

60

90

120

Cats (1000)

Dogs (1000)

0 5 10 15 20

Number of tricks

Num

ber

of p

ets

Visualized cross-tabulated dataStudent Admissions at UC Berkeley in 1973

Gender Admitted RejectedMale 1198 1493Female 557 1278

Admitted RejectedM

ale

Fem

ale

Let’s summarizeOur broad philosophy:I Always think carefully about data (brain � software)

I Always explore data

I Visualizing data is extremely valuable

I Data often contains noise and bias

I Summary statistics (mean, median, correlation, . . . )obscure important details

I Correlation does not imply causeBig Data increases spurious correlations

Thinking in Data Workshop

Data & Analytics

selection bias journalist

bestburgers story tiny

upperincome customer

coached participants

average yearly income

quick question

conscious fastfood customers

downtown oce