Tuesday, week 6
• Arney on Statistics and Uncertainty
• Zita on sorting wheat from chaff (Critical
thinking tools)
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–
–
–
Mammograms and “Mind tools” (Gigerenzer)
Baloney Detector Kit (Sagan)
Theory-laden “facts” (Kuhn)
Strong objectivity and situated knowledge (Harding)
• Looking ahead
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 24
by Family Income
Family Income
$90K+
$61K-$90
Series1
$35K-$61K
<$35K
0
0.1
0.2
0.3
Probability
Source: Ross Douthat, “Does Meritocracy Work?” Atlantic Monthly, November, 2005.
0.4
0.5
0.6
Obtaining a Bachelor's Degree by Age 24
by Family Income
0.6
Probability
0.5
0.4
0.3
Series1
0.2
0.1
0
<$35K
$35K-$61K
$61K-$90
Family Income
$90K+
Percent
Percentage Passing WASL
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
10th graders
4th graders
7th graders
1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05
Sophomores Passing WASL
45.0
40.0
35.0
Percent
30.0
25.0
10th graders
20.0
15.0
10.0
5.0
0.0
1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05
Percent
Sophomores Passing WASL
100.0
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
10th graders
1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05
Sophomores Passing WASL in 2005
42.8%
Current Sophomores Who Won’t
*
Graduate
57.2%
If the present situation persists.
*
19
97
19 -9 8
98
19 -9 9
99
20 -0 0
00
20 -0 1
01
20 -0 2
02
20 -0 3
03
20 -0 4
04
20 -0 5
05
20 -0 6
06
20 -0 7
07
20 -0 8
08
20 -0 9
09
-1
0
Percentage
Sophomores Passing WASL
100.0
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
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 doctor
Test 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)
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•
•
•
•
•
•
•
•
•
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 women
in 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