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

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Google

History of Statistics 105

Wee Lee Loh

History of Statistics 105

Yves Chretien

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

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

MODULES

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

?

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

- 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” …

- 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?

Answer Now

?

Q: You just met someone, and areinitially 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?

ROMANCESurvey

(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

- 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?

Kidney 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 B is better, right?

WRONG!

Simpson’s Paradox

- 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?

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.

- 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.

- 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)

?

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?

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

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

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

WINE AND CHOCOLATE

If I randomly pick up one of these chocolates, what is your best guess for the probability of champagne inside?- 0
- .1
- .2
- .3
- .4
- .5
- .6
- .7
- .8
- .9

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

Let’s collect more data!

WINE AND CHOCOLATE

If I randomly pick up one of these chocolates, what is your best guess for the probability of champagne inside?- 0
- .1
- .2
- .3
- .4
- .5
- .6
- .7
- .8
- .9

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

And even more data…

WINE AND CHOCOLATE

What happens as you accumulate more data?

- 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!

“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!)

http://movies.aol.com//movie/forrest-gump/1036/video/tom-hanks-greatest-moments/1138699

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

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

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!

Thanks much!

And we welcome your feedback!

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