1. Lecture 21

2. Final Project Design your own survey!
Find an interesting question and population
Design your sampling plan
Collect Data
Analyze using R
Write 5 page paper on your results
Due December 1

3. Final presentation All are required to give a short presentation
Last two classes (December 1 and 6)
Select one of the three projects
Make a powerpoint presentation (no more than 3-5 slides)
Present your results to the class
Need 10 volunteers to present on Thursday!

4. Fill your evaluations!
It is helpful!!!!

5. Coincidences

6. In statistics
We want to believe in unlikely events (coincidences) only if other explanations are not possible
Are there some ”laws” for alternative explanations? Author (David Hand) coins the following cool
“Law of Inevitability”
“Law of Truly Large numbers”
“Law of Selection”
“Law of Probability Lever”
“Law of Near enough”

7. Law of inevitability
Something must happen. If we consider all possible outcomes in a setting of interest, one of them has to happen.
1990: Virginia State lottery.
Genoese style 6 out of 44 balls, $1 to play
Chance of winning for a single ticket 1:7,059,052
In Feb 1992 jackpot was $27 million.
A group “International Lotto fund” collected around 2500 small investors(mainly from Australia but also US, Europe, NZ) raised $7 million and bought all possible tickets! “Surprisingly” they won!

8. Law of inevitability 1024 monkeys are managing mutual funds
Each week half of them predicts up and the other down.
The half that was wrong gets fired and the game continues.
After 10 weeks there is one winning monkey that got it right 10 straight in the row! The monkey goes on a TV tour giving stock tips.
Some say this principle is behind the most of the successes of “miracle investors”

9. Law of truly large numbers
Every day filled with innumerable number of events. Something unusual will happen.
Chance of being struck by lightening in a year: 1/300,000. SMALL!
However 7 billion people on earth! Chance that no one gets struck = (1 – 1/300000)7 billion =1/ 10101,333! So we would expect every year there have to be people being killed by lightening.
Estimates: 24,000 deaths.

11. Law of Selection
Example: Remember all the times we seem to hit every possible red light? Think the universe is conspiring against us? Remember only those days. Do not remember all the times everything went fine.
How our brain works: Typical example: dream something which then happens few days later. In fact have 4-6 periods of dreams most which we forget. Much more likely to remember dream if something related happens next day.
Brain connects/categorizes things trying to find patterns.
Murphy’s law, Anecdotal evidence

12. Probability lever (wrong model)
Basic point: small errors in our model/assumptions in the world can result in major differences in probability predictions leading to several orders of magnitude difference in probabilities of events.
The big crash:
People were using models that underestimated the chance that many mortgages would go bad at the same time
Based on this model the big crash of 2008 was ”impossible”…
Roy Sullivan – Virginia park ranger struck by lightening 7 times!
Chance of that (1/300000)7 – virtually impossible!
Park ranger – much higher chance of being struck by a lightning

13. Law of Near Enough
Outcomes that are merely similar are regarded as identical
Charles Dickens: “And we are both widows too!” said Barbara’s mother. ”We must be made for each other” … tracing things back from effects to causes they neturally reverted to their husbands, respecting whose lives deaths and burials, they compared notes, and discovered sundry circumstances that tallied with wonderful exactnes; such as Barbara’s father having been exactly 4 years and 10 months older than Kit’s father, and one of them died on a Wdnesday and the other on Thursday, and both of them having been a very fine make and remakably good-looking, with other extraordinary conincidences.

14. Understanding of probability
Outcomes are uncertain
A good way to think is frequencies and bets
Consider 50%, 66%, 75%, 95%, 99.99%
Odds 1:1, 2:1, 3:1, 19:1, 9999:1
Probability scale could be a bit misleading
99.99% looks like %
Forcast 70% Clinton (people were feeling ok), 30% Trump (people were scared)