stat 105 real-life statistics: your chance for happiness (or misery)

11

STAT 105 STAT 105 Real-Life Statistics:Real-Life Statistics:

Your Chance for Your Chance for Happiness Happiness (or Misery)(or Misery)

?

22

© 2008 Department of Statistics, Harvard © 2008 Department of Statistics, Harvard UniversityUniversity

History of Statistics 105History of Statistics 105

Wee Lee Loh

33


Linjuan Qian Reetu Kumra


44



Yves Chretien

55


66


Pedagogical MotivationPedagogical Motivation

To fill in the gap between intro-level To fill in the gap between intro-level courses and higher-level coursescourses and higher-level coursesIntro “service” courses jam-packed with toolsIntro “service” courses jam-packed with toolsHigher-level courses require advanced mathsHigher-level courses require advanced maths

To provide more depth and intuitionTo provide more depth and intuitionUseful for Masters and PhD students as wellUseful for Masters and PhD students as well

Gen-Ed introduction to statisticsGen-Ed introduction to statisticsUnforeseen side benefit: The Happy Team Unforeseen side benefit: The Happy Team

77


Outcomes (so far)Outcomes (so far)

Positive mid-term feedbackPositive mid-term feedback Every student would recommend it to future Every student would recommend it to future

studentsstudents The process of developing the courseThe process of developing the course

Graduate School Dean is recommending an Graduate School Dean is recommending an institutionalized graduate seminars on institutionalized graduate seminars on designing new courses based on our model designing new courses based on our model

Attention to the subject and departmentAttention to the subject and department MediaMedia

GazetteGazetteCrimsonCrimson

StudentsStudents AdministrationAdministration


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?


FINANCE

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

Google


• 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


• 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


ROMANCESurvey

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) HARD TO GET (I p... (b) CLEARLY INTO ME...

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)


• 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


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.?

1000 2000 3000 4000 > 4000

28%

9%

43%

11%8%

ROMANCE

1. 1000

2. 2000

3. 3000

4. 4000

5. > 4000


• 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


MEDICALKidney stone treatmentC. 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

SmallStone

93% (81/87)

87% (234/270)

Large Stone

73% (192/263)

69% (55/80)

Treatment B is better, right?

WRONG!

Simpson’s Paradox

http://en.wikipedia.org/w/index.php?title=Br_Med_J_%28Clin_Res_Ed%29&action=edit




Small Stones

Treatment A

Treatment B

Successful 81 (93%) 234 (87%)

Unsuccessful

6 36

Slope = # successful / # unsuccessful = odds


Large Stones

Treatment A

Treatment B

Successful 192 (73%) 55 (69%)

Unsuccessful

71 25

Slope = # successful / # unsuccessful = odds


CombinedTreatment

ATreatment

B

Successful81+192=2

73289

Unsuccessful

6+71=77 61


CombinedTreatment

ATreatment

B

Successful 273 (78%) 289 (83%)

Unsuccessful

77 61


• When and why does Simpson’s paradox occur?

• How do we deal with it?

MEDICAL


• 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


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.)


• 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.

LEGALProsecution Argument


• 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.

LEGALDefense Argument


• 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)

LEGALDefense Argument


LEGAL

Would you convict Adams?

Yes No

47%

53%

1. Yes

2. No


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


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) .21 - .4 (c) .41 - .6 (d) .61 - .8 (e) .81 - 1

53%

30%

0%2%

14%

(a) 0 - .2

(b) .21 - .4

(c) .41 - .6

(d) .61 - .8

(e) .81 - 1


WINE AND CHOCOLATE


chocolates, what do you think is the

probability there is champagne inside?

(a) 0 - .2 (b) .21 - .4 (c) .41 - .6 (d) .61 - .8 (e) .81 - 1

29%

14%

21%

0%

36%

(a) 0 - .2

(b) .21 - .4

(c) .41 - .6

(d) .61 - .8

(e) .81 - 1


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? .05 .1 .35 .6 .75

1

9%

12% 12%

9%

24%

35%

1. .05

2. .1

3. .35

4. .6

5. .75

6. 1


WINE AND CHOCOLATE

Let’s collect some data!


WINE AND CHOCOLATE

Did your chocolate have champagne in it?

Yes No

100%

0%

(a) Yes

(b) No


WINE AND CHOCOLATE


chocolates, what is your best guess for

the probability of champagne inside?

0 .1 .2 .3 .4 .5 .6 .7 .8

55%

39%

6%

0% 0%0%0%0%0%0%

(a) 0(b) .1(c) .2(d) .3(e) .4(f) .5(g) .6(h) .7(i) .8(j) .9


WINE AND CHOCOLATE




1

14%

24%

10%

21%

10%

21%1. .05

2. .1

3. .35

4. .6

5. .75

6. 1

Let’s collect more data!


WINE AND CHOCOLATE


Yes No

89%

11%(a) Yes

(b) No


WINE AND CHOCOLATE


chocolates, what is your best guess for

the probability of champagne inside?

0 .1 .2 .3 .4 .5 .6 .7 .8

17%

75%

8%

0% 0%0%0%0%0%0%

(a) 0(b) .1(c) .2(d) .3(e) .4(f) .5(g) .6(h) .7(i) .8(j) .9


WINE AND CHOCOLATE




1

22%

17%

4%

26%

9%

22%

1. .05

2. .1

3. .35

4. .6

5. .75

6. 1

And even more data…


WINE AND CHOCOLATE


Yes No

83%

17%(a) Yes

(b) No


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!


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!)

4646


Things We Do Differently …Things We Do Differently …Student/Faculty course design Student/Faculty course design

collaborationcollaborationModules, allowing “out of sequence” Modules, allowing “out of sequence”

teaching in terms of technical material teaching in terms of technical material The use of “Clickers” (Personal Response The use of “Clickers” (Personal Response

Devices)Devices)Module-based team projects and project Module-based team projects and project

presentationspresentationsModule-based guest lecturers Module-based guest lecturers AssessmentAssessment

Peer evaluationPeer evaluationAssignments, projects, no traditional examsAssignments, projects, no traditional exams

4747

Module-Based Approach Module-Based Approach (MBA)(MBA)

Statistical Topics Finance Romance Medical Legal Wine/ChocolateProbability Random variables/Probability Distributions

Rules of probabilityBayes's RuleDescriptive Statistics

Statistical Inference Hypothesis TestingPosterior probabilities and p-valuesDecision Theory

Advanced Statistics Linear RegressionANOVATime Series ModelsLogistic RegressionStatistical InteractionModel/Variable SelectionSimpson's ParadoxMultiple Hypothesis Testing

Study Design Survey MethodsExperimental DesignObservational StudiesSelection BiasResponse BiasPublication Bias

4848


ChallengesChallengesTime managementTime management

Structured material vs “improvised” Structured material vs “improvised” discussionsdiscussions

So much material, so little timeSo much material, so little timeStudent team dynamicsStudent team dynamicsPrerequisitesPrerequisites

Can we offer stat105 without prerequisites?Can we offer stat105 without prerequisites?Funding for course materialFunding for course material

e.g. wine and chocolate e.g. wine and chocolate Outside speaker expenses Outside speaker expenses

Scaling to a (much) larger class size in Scaling to a (much) larger class size in the futurethe future

4949


Future Happiness …Future Happiness … Developing more modulesDeveloping more modules

SportsSports NutritionNutrition …………

Prepare a multimedia-based teaching packagePrepare a multimedia-based teaching package Text bookText book WebsiteWebsite

Similar courses aimed at different levelsSimilar courses aimed at different levels More advancedMore advanced Less advancedLess advanced

Build more Happy Teams! Build more Happy Teams!

5050


Thanks much!Thanks much!

And we welcome your And we welcome your feedback!feedback!

stat 105 real-life statistics: your chance for happiness (or misery)

Documents

department of statistics

reallife statistics

harvard universityoutcomes

harvard universityamerica

harvard universityfinancewhat

harvard universityq

harvard university ho

new courses