• Arney on Statistics and Uncertainty

• Zita on sorting wheat from chaff (Critical thinking tools)– Mammograms and “Mind tools” (Gigerenzer) – Baloney Detector Kit (Sagan)– Theory-laden “facts” (Kuhn)– Strong objectivity and situated knowledge

(Harding)

• Looking ahead

Tuesday, week 6

From Harper’s Index

• Number of new U.S. soldiers the Army would need in 2006 to replenish ranks abroad: 80,000

• Percentage of this goal it expects to meet: 9.9

• Percentage change since 1996 in the average recruitment cost per new U.S. soldier: +84

From Harper’s Index• Number of Palestinian communities that will be

surrounded by the new Israeli security fence on at least three sides: 53

• Chance that a German says Israel’s treatment of Palestinians is the same “in principle” as how Nazis treated Jews: 1 in 2

• Factor by which the unemployment rate among Jewish immigrants to Germany exceeds the national average: 3.5

• Percentage of Germans who say, about the Nazi era, that “one should not poke around in old wounds”: 60

From Harper’s Index• Total annual spending controlled by functionally

illiterate U.S. consumers: $414,000,000,000• Chance that a teacher in a U.S. public school is a

man: 1 in 5• Average percentage of students in N.Y. State’s

majority-white districts who graduate in four years: 79

• Average percentage who do so in districts where a majority of students are black or Latino: 40

From Harper’s Index• Ratio of the world’s reconstruction aid given to

postwar Kosovo, per capita, to that given postwar Afghanistan: 23:1

• Ratio of the number of peacekeeping troops in Kosovo, per capita, to that in Afghanistan: 24:1

***• Amount the U.S spent last year on mosquito nets

to fight malaria in Africa: $4,000,000• Amount it paid a consultancy to conduct “social

marketing” of mosquito nets: $7,900,000

From Harper’s Index• Percentage change in the average monthly price of

oil during the Carter Administration: +85• Percentage change during the presidency of

George W. Bush, before Katrina: +107

* * *• Number of consecutive years that the U.S. median

income has failed to increase: 5• Number of consecutive years that the percentage

of Americans living in poverty has increased: 4

Obtaining a Bachelor's Degree by Age 24by Family Income

0 0.1 0.2 0.3 0.4 0.5 0.6

<$35K

$35K-$61K

$61K-$90

$90K+

Fam

ily

Inco

me

Probability

Series1

Source: Ross Douthat, “Does Meritocracy Work?” Atlantic Monthly, November, 2005.

Obtaining a Bachelor's Degree by Age 24by Family Income

0

0.1

0.2

0.3

0.4

0.5

0.6

<$35K $35K-$61K $61K-$90 $90K+

Family Income

Pro

babi

lity

Series1

Percentage Passing WASL

0.0

5.0

10.0

15.0

20.0

25.030.0

35.0

40.0

45.0

50.0

1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05

Perc

ent

10th graders

4th graders

7th graders

Sophomores Passing WASL

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05

Perc

ent

10th graders

Sophomores Passing WASL

0.0

10.0

20.0

30.0

40.0

50.060.0

70.0

80.0

90.0

100.0

1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05

Perc

ent

10th graders

Sophomores Passing WASL in 2005

42.8%

Current Sophomores Who Won’t Graduate*

57.2%*If the present situation persists.

Sophomores Passing WASL

0.010.020.030.040.050.060.070.080.090.0

100.0

Perc

enta

ge 10th graders

Linear (10th graders)

John Tukey

Exploratory Data Analysis, 1977

Edward R. Tufte

Visual Display of Quantitative Information, 1983

Envisioning Information, 1990

Visual and Statistical Thinking: Displays of

Evidence for Decision Making, 1997

Visual Explanations: Images and Quantities,

Evidence and Narrative, 1997

The Cognitive Style of PowerPoint, 2003

Break time

Zita on Sorting wheat from chaff (Critical thinking tools)

• Mammograms and “Mind tools” (Gigerenzer)

• Baloney Detector Kit (Sagan)

• Theory-laden “facts” (Kuhn)

• Strong objectivity and situated knowledge (Harding)

Mammograms: Gigerenzer’s claims

Risks > benefits

Doctors tell patients that a positive mammogram means:

• she has cancer and

• she needs surgery, preferably a mastectomy

Mammogram radiation causes breast cancer.

Mammograms: ask a doctorTest results are NOT simply “positive” and “negative” but a range of categories:• Category 0 - Need additional imaging evaluation. Most category 0 findings are

shown to be benign after additional imaging is completed. • Category 1 - Negative • Category 2 - Benign finding, noncancerous • Category 3 - Probably benign finding, short-interval follow-up suggested • Category 4 - Suspicious abnormality, biopsy considered • Category 5 - Highly suggestive of malignancy, appropriate action needed

“Suspicious abnormality” probably does NOT mean you have cancer! Instead of rush to surgery, Drs recommend:

• Second, targeted mammogram (spot check)• Needle biopsy• Surgical biopsy• Lumpectomy or mastectomy

What about radiation risk?

• G’s target group is women in their 40’s• Mammogram radiation was more dangerous 35 years

ago (when target women were teenagers), and is 10 times lower now

• High radiation took ~20 years to cause cancer (p.69)• Most women in their 40’s were not getting

mammograms 20 years ago• GG says 30/100,000 women get cancer from

mammograms - or did, when radiation dose was high?

• (By the way) mammograms save 100 lives per 100,000 women

Breast cancer pamphlets: G’s claims

• Uncertainties are not acknowledged• Risks of screening are not discussed• Detection = prevention?• Mammograms can be positive or negative• Mammogram radiation causes cancer• Early detection causes more harm than good, and

usually leads to unnecessary surgery (p.58) (but about half of ductal carcinoma in situ will progress to malignancy, if untreated! p.57)

Let’s look at the doctor’s pamphlets…

http://www.cancer.gov/cancer_information/cancer_type/breast/

http://www.cancer.gov/cancertopics/pdq/screening/breast/Patient/page4

http://www.cancer.gov/cancertopics/pdq/screening/breast/Patient/page4

Breast cancer pamphlets

• Uncertainties are acknowledged

• Risks of screening are explicit

• Detection ≠ prevention

Some of Gigerenzer’s claims appear to be

• Internally inconsistent

• Inconsistent with practice and statistics

• Supportive of his bias more than “facts”

• Red flags which make his other claims suspect

Baloney Detector can help (Sagan)

• Counting the hits and forgetting the misses. Ex: “One study shows…”

• Red herrings and straw men: Emphasized: “3/10,000 (or 3/100,000?) women will develop (mammography-)

induced breast cancer (p.70)”; Underemphasized: That was when radiation levels were 10 x higher. 100/100,000 lives are saved by mammography (p.60)

• Separate variables: women in their 40’s are at very low risk of mammogram-induced cancer

• False dichotomy: “There is a trade-off between false positives and false negatives (p.70)” – But more highly skilled radiologists should minimize both of these.

Tools for skeptical thinking (Sagan.210)

• Independent confirmation of facts• Arguments from authority carry little weight• Spin multiple hypotheses• Suspect your favorite hypothesis• Quantify. Predict. Test.• Every link in the argument chain must work.• Occam’s razor: simpler explanation more likely• Untestable hypotheses carry little weight• Control experiments and double-blind studies• Separate variables

Logical Fallacies (Sagan.212)• “ad hominem” – attacking the arguer, not the

argument• Argument from adverse consequences• Appeal to ignorance (absence of evidence ≠

evidence of absence• Special pleading• Begging the question, or Assuming the answer• Counting the hits and forgetting the misses• Misunderstanding statistics• Inconsistency• “non sequitur” – it doesn’t follow

Logical Fallacies (Sagan.213)

• “post hoc, ergo propter hoc” – it happened after, so it was caused by

• Confusion of correlation with causation• False dichotomy, or excluded middle (black and

white)• Slippery slope• Short-term vs long-term• Straw men and red herrings• Suppressed evidence or half-truths• Weasel words

Theory laden facts can help (Kuhn)Facts ≠ Truth

Knowledge is CREATED, not discovered

What counts as facts? What counts as a good question to investigate?

“Facts” depend on language, beliefs, framework, …, e.g. paradigm.

Ex: “Early detection of breast cancer does more harm than good” – what counts as harm and good?

Strong objectivity can help (Harding)

Knowledge (including science) is created by humans, therefore subjective (Kuhn)

STRONG OBJECTIVITY: first, acknowledge our subjectivities:• Biases, language, culture, values, limited perspectives• Get input from people with different perspectives

GOALS: Better knowledge and understanding:• Empirically more adequate (Kuhn)• Less partial and distorted descriptions & explanations

Ex: “Early detection of breast cancer does more harm than good” – from whose perspective?

Good statistics can help (Gigerenzer)

Use natural frequencies more often than probabilities (though probabilities ARE sometimes simpler)

Use absolute risks more than relative risks

Specify your reference class

Acknowledge prevalence of false positives and false negatives

Overcome the illusion of uncertainty – “dare to know”

Take-home messages

• Use statistics honestly and clearly• Beware: facts ≠ Truth• Know the contexts and limitations of data and

knowledge-creation• Acknowledge your bias, agenda, and

standpoint, as an analyst and as an author• Avoid logical fallacies• Use tools for skeptical thinking• Encourage readers, patients, doctors, etc. to

reason, not to blindly use numbers or formulae

Looking ahead

Invitation to women interested in physics or teaching

Expanding Your Horizons for middle-school girls - GOALS:•Increase young women’s interest in mathematics, science and technology. •Provide an opportunity to meet women working in non-traditional fields. •Foster awareness of careers for womenin mathematics and science-related areas.

This Saturday 5 Nov. from 8am-noon at SPSCC

Zita will present a workshop on “Magnet Magic”

If you are interested in helping at this workshop, please see me after class or email zita@evergreen.edu

http://www.starjumper.org/aboutus.html

http://www.cdc.gov/cancer/nbccedp/info-bc.htm