Lecture 21

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

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!

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Coincidences http://www.unilad.co.uk/articles/man-accidentally-shoots-mother-in-law-after-bullet-bounces-off-armadillo/

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”

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!

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”

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.

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

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

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.

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 99.9999% Forcast 70% Clinton (people were feeling ok), 30% Trump (people were scared)