2008-11.ppt

1
STAT 105
Real-Life Statistics:
Your Chance for Happiness
(or Misery)
?

© 2008 Department of Statistics, Harvard University
2
History of Statistics 105
Wee Lee Loh

3
Linjuan Qian Reetu Kumra

4
Yves Chretien

5

6
Pedagogical Motivation
 To fill in the gap between intro-level
courses and higher-level courses
 Intro “service” courses jam-packed with tools
 Higher-level courses require advanced maths
 To provide more depth and intuition
 Useful for Masters and PhD students as well
 Gen-Ed introduction to statistics
 Unforeseen side benefit: The Happy Team

7
Outcomes (so far)
 Positive mid-term feedback
 Every student would recommend it to future students
 The process of developing the course
 Graduate School Dean is recommending an
institutionalized graduate seminars on designing new
courses based on our model
 Attention to the subject and department
 Media
 Gazette
 Crimson
 Students
 Administration

8

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FINANCE
•What do you want to
learn from this data?
• How do you
summarize the data?
• How do you visualize
the signal behind the
noise?

10
FINANCE
• Would the
“twistogram” idea
work for the S&P
500 index over this
extended time
period?

11
• The dating world is full of questions we would
all love answers to:
• When you meet someone, should you play
hard-to-get or make your attraction obvious?
• Where should you go on a first date?
• What is the best thing to do on the first date
to impress your date?
• What are the important factors that make
two people “click” …
ROMANCE

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• Suppose you have been hired by a U.S. online
dating company, and they want you to find out
people’s opinions here in the US about these
questions.
• How would you go about collecting the
information?
ROMANCE

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ROMANCE
Survey
Q: You just met someone, and are
initially interested. Are you more likely to
maintain/increase interest in the person if
he/she plays hard-to-get, or if he/she is
obvious about being into you?
(
a
)
H
A
R
D
T
O
G
E
T
(
I
p
.
.
.
(
b
)
C
L
E
A
R
L
Y
I
N
T
O
M
E
.
.
.
79%
21%
(a) HARD TO GET (I prefer a
person who initially plays
hard-to-get)
(b) CLEARLY INTO ME (I prefer
someone who makes it clear
he/she is very into me)

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• Suppose during your survey you fell in love
with a Chinese person, and subsequently moved
to China and now work for a Chinese online
dating company.
• You want to impress your new boss (and your
new love), so you decide to repeat your U.S.
survey, which had 1000 subjects, in China
ROMANCE

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America has a population of about
304 million but China has a
population of about 1.3 billion.
How many people would you need
to survey in China to get just as
reliable results as in the U.S.?
1
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
>
4
0
0
0
28%
9%
43%
11%
8%
ROMANCE
1. 1000
2. 2000
3. 3000
4. 4000
5. > 4000

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• How do you test whether a new drug is
effective?
• Ideally, we perform a controlled clinical trial, by
randomly assign one group of people to take the
drug, and another group to take a placebo.
• It needs to be double blinded.
• When such an experiment is not possible due to
practical or ethical issues, what can go wrong?
MEDICAL

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MEDICAL
Kidney stone treatment
C. R. Charig, D. R. Webb, S. R. Payne, O. E. Wickham (March 1986)
Br Med J (Clin Res Ed) 292 (6524): 879–882.
Treatment A Treatment B
78%
(273/350)
83%
(289/350)
Treatment A Treatment B
Small
Stone
93%
(81/87)
87%
(234/270)
Large
Stone
73%
(192/263)
69%
(55/80)
Treatment B is better, right?
WRONG!
Simpson’s Paradox

18

19
Small Stones
Treatment
A
Treatment
B
Successful 81 (93%) 234 (87%)
Unsuccessful 6 36
Slope = # successful / # unsuccessful = odds

20
Large Stones
Treatment
A
Treatment
B
Successful 192 (73%) 55 (69%)
Unsuccessful 71 25
Slope = # successful / # unsuccessful = odds

21
Combined
Treatment
A
Treatment
B
Successful
81+192=27
3
289
Unsuccessful 6+71=77 61

22
Combined
Treatment
A
Treatment
B
Successful 273 (78%) 289 (83%)
Unsuccessful 77 61

23
Combined
Treatment
A
Treatment
B
Successful 273 (78%) 289 (83%)
Unsuccessful 77 61

24

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• When and why does Simpson’s
paradox occur?
• How do we deal with it?
MEDICAL

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• How is statistics an important part of our legal
system?
• How might we use a statistic or probability as
evidence in a trial?
• How are statistics often misinterpreted by
lawyers and juries?
LEGAL

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LEGAL
You have just been selected for jury duty. In 1996 in
England, Denis Adams was suspect in a rape trial.
Listen closely to the details of the case and the
arguments presented before deciding your verdict.
(We have simplified the actual case/arguments for the
purpose of this illustration.)

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• Adams’ DNA profile matches that of evidence found
at the scene of the crime
•If Adams is innocent, there is only a 1 in 20 million
chance that his DNA would match that found at the
crime
• Therefore, the probability Adams is innocent is only
.00000005, hence the probability he is guilty is 1
minus that, .9999995. Thus Adams is guilty beyond
the shadow of a doubt.
LEGAL
Prosecution Argument

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• If the odds of a DNA match for any person is
1/ 20,000,000, since there are 60 million people in
England, there are on average 3 other people with this
DNA type (in 1996).
•Since it is equally likely to be any of these others, the
probability of Adams’ guilt is 1/3 = .33, which is not
enough certainty to convict.
LEGAL
Defense Argument

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• In an identity line up, victim failed to pick out Adams
• Victim describes an attacker in his 20’s
• Adams is 37
• Victim guessed Adams to be about 40
• Adams had an alibi for the night of the crime (he
spent the night with his girlfriend)
LEGAL
Defense Argument

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LEGAL
Would you convict
Adams?
Y
e
s
N
o
47%
53%
1. Yes
2. No

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1) What is the probability that you drive into a
tree given that you are drunk?
2) What is the probability that you are drunk
given that you drive into a tree?
Why is it important to distinguish them?
LEGAL

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WINE AND CHOCOLATE
If I randomly pick
up one of these
chocolates, what do
you think is the
probability there is
champagne inside? (
a
)
0
-
.
2
(
b
)
.
2
1
-
.
4
(
c
)
.
4
1
-
.
6
(
d
)
.
6
1
-
.
8
(
e
)
.
8
1
-
1
53%
30%
0%
2%
14%
(a) 0 - .2
(b) .21 - .4
(c) .41 - .6
(d) .61 - .8
(e) .81 - 1

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WINE AND CHOCOLATE
If I randomly pick
up one of these
chocolates, what do
you think is the
probability there is
champagne inside? (
a
)
0
-
.
2
(
b
)
.
2
1
-
.
4
(
c
)
.
4
1
-
.
6
(
d
)
.
6
1
-
.
8
(
e
)
.
8
1
-
1
29%
14%
21%
0%
36%
(a) 0 - .2
(b) .21 - .4
(c) .41 - .6
(d) .61 - .8
(e) .81 - 1

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WINE AND CHOCOLATE
How certain are
you about your
estimate? If you
were to give an
interval that you
are fairly confident
contains the truth,
how wide would
this interval be?
.
0
5
.
1
.
3
5
.
6
.
7
5
1
9%
12% 12%
9%
24%
35%
1. .05
2. .1
3. .35
4. .6
5. .75
6. 1

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WINE AND CHOCOLATE
Let’s collect some data!

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WINE AND CHOCOLATE
Did your chocolate
have champagne in it?
Y
e
s
N
o
100%
0%
(a) Yes
(b) No

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WINE AND CHOCOLATE
If I randomly pick
up one of these
chocolates, what is
your best guess for
the probability of
champagne inside?
(a) 0
(b) .1
(c) .2
(d) .3
(e) .4
(f) .5
(g) .6
(h) .7
(i) .8
(j) .9

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WINE AND CHOCOLATE
How certain are
you about your
estimate? If you
were to give an
interval that you
contains the truth,
how wide would
this interval be?
.
0
5
.
1
.
3
5
.
6
.
7
5
1
14%
24%
10%
21%
10%
21%
1. .05
2. .1
3. .35
4. .6
5. .75
6. 1
Let’s collect more data!

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WINE AND CHOCOLATE
Did your chocolate
Y
e
s
N
o
89%
11%
(a) Yes
(b) No

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WINE AND CHOCOLATE
If I randomly pick
up one of these
chocolates, what is
your best guess for
the probability of
champagne inside?
(a) 0
(b) .1
(c) .2
(d) .3
(e) .4
(f) .5
(g) .6
(h) .7
(i) .8
(j) .9

42
WINE AND CHOCOLATE
How certain are
you about your
estimate? If you
were to give an
interval that you
contains the truth,
how wide would
this interval be?
.
0
5
.
1
.
3
5
.
6
.
7
5
1
22%
17%
4%
26%
9%
22%
1. .05
2. .1
3. .35
4. .6
5. .75
6. 1
And even more data…

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WINE AND CHOCOLATE
Did your chocolate
Y
e
s
N
o
83%
17%
(a) Yes
(b) No

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WINE AND CHOCOLATE
What happens as you accumulate more data?
1) Your estimates become more accurate
2) You can narrow in on your interval prediction
(your uncertainty decreases)
3) In this case, you get to enjoy chocolate! 

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http://movies.aol.com//movie/forrest-gump/1036/video/tom-hanks-greatest-moments/1138699
“Life is like a box of
chocolates… you
never know what
you’re going to get.”
BUT YOU CAN ESTIMATE IT!
(especially after you take STAT 105!)

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Things We Do Differently …
 Student/Faculty course design collaboration
 Modules, allowing “out of sequence”
teaching in terms of technical material
 The use of “Clickers” (Personal Response
Devices)
 Module-based team projects and project
presentations
 Module-based guest lecturers
 Assessment
 Peer evaluation
 Assignments, projects, no traditional exams

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Challenges
 Time management
 Structured material vs “improvised” discussions
 So much material, so little time
 Student team dynamics
 Prerequisites
 Can we offer stat105 without prerequisites?
 Funding for course material
 e.g. wine and chocolate
 Outside speaker expenses
 Scaling to a (much) larger class size in the
future

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Future Happiness …
 Developing more modules
 Sports
 Nutrition
 ……
 Prepare a multimedia-based teaching package
 Text book
 Website
 Similar courses aimed at different levels
 More advanced
 Less advanced
 Build more Happy Teams!

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Thanks much!
And we welcome your
feedback!

2008-11.ppt

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