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MAT2375 Lecture #1 by D. McDonald from the Department of Mathematics and Statistics

MAT2375 Lecture #1 by D. McDonald from the Department of Mathematics and Statistics. Can you trust Statistics?. In 1953: 60,000 victims of polio in the USA. In the early 1950’s Dr. Jonas Salk developed a vaccination against polio.

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MAT2375 Lecture #1 by D. McDonald from the Department of Mathematics and Statistics

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  1. MAT2375Lecture #1 by D. McDonald from the Department of Mathematics and Statistics Can you trust Statistics? Can you trust statistics?

  2. In 1953: 60,000 victims of polio in the USA • In the early 1950’s Dr. Jonas Salk developed a vaccination against polio. • Before a massive vaccination program could be started it was necessary to prove the vaccine was effective. Can you trust statistics?

  3. A Randomized, Controlled Experiment • 400,000 elementary school students participated in the experiment. • 200,000 chosen at random from 400.000 in the treatment group got the vaccine. • The remaining 200,000 in the control group did not get the vaccine. Can you trust statistics?

  4. A Randomized, Controlled Double-Blind Experiment • The 200,000 children in the control got a fake vaccination called a placebo. • The children and their parents were not told if they got the real vaccine or not. • Even the doctors and nurses didn’t know; only the statisticians knew Can you trust statistics?

  5. Experimental Results Looks promising but is it significant? Can you trust statistics?

  6. Analysis: The Devil’s Advocate • Let’s play the devil’s advocate. Let’s assume the vaccine has no effect. • Then the 99 cases of polio were split into the two groups purely at random. • Is it very likely only 25 fall in the treatment group? Can you trust statistics?

  7. A Probability Model • Put 400,000 balls in an urn with 99 black and the rest white. • Draw 200,000 (for the treatment group) and count the number of black balls. • What is the chance of a split as extreme or more extreme than 28 in the treatment group and 71 in the control group. • About one in a billion Can you trust statistics?

  8. Calculating Probabilities • A statistician relies on the theory of probability to calculate probabilities. • The number of black balls X in the treatment group follows the hypergeometric distribution. Can you trust statistics?

  9. Conclusion: Get vaccinated! • We must reject the hypothesis that the treatment has no effect; otherwise we must believe we are incredibly unlucky. • We can therefore recommend mass vaccination. • We also note a vaccination does not prevent polio. Your best protection is to get vaccinated and encourage everyone to be vaccinated. Can you trust statistics?

  10. A Statistician’s Job • Understand the problem. This requires an interaction with subject specialists and often a basic understanding of their science. • Design experiments so something can be proved. Statistics is huge so somebody may already have a design. Surprisingly often you have to find a new approach. Can you trust statistics?

  11. A Statistician’s Job • Ensure the data is collected according to the design. • Use probability and computers to calculate the significance of the results. • Draw a conclusion and explain it. Can you trust statistics?

  12. Statistical Careers • SOA Society of actuaries http://www.soa.org/ • CAS Casualty Actuarial Society http://www.casact.org/ • Examination:1/P: essentially MAT2371 • Qualify for VEE-Applied Statistical Methods: essentially MAT2375 Can you trust statistics?

  13. Statistical Careers • Statistics Canada methodologist: Our courses in statistics are accredited by the Canadian Statistical Society so if you take the recommended courses you are ready to take the civil service examination Can you trust statistics?

  14. Statistical Careers • Defense research board – data mining of surveillance data • Ministry of Transport – analyzing accidents • Ministry of Agriculture – forecasting • Bank of Canada, Finance - forecasting Can you trust statistics?

  15. Statistical Careers • Quant – modeling and forecasting markets • Hedgie - calculating complex trading strategies like calls and puts – lots of probability Can you trust statistics?

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