Topic 8 Hypothesis Testing Mathematics & Statistics Statistics.
MAT2375 Lecture #1 by D. McDonald from the Department of Mathematics and Statistics
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Transcript of MAT2375 Lecture #1 by D. McDonald from the Department of Mathematics and Statistics
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Can you trust statistics? 1
MAT2375Lecture #1 by D. McDonald from the Department of Mathematics and Statistics
Can you trust Statistics?
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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.
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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.
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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
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Experimental Results
Looks promising but is it significant?
Size Rate
Treatment 200,000 28
Control 200,000 71
Total 400,000 99
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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?
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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
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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.
• 99 399901
200000
400000
200000x x
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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.
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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.
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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.
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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
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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
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Statistical Careers
• Defense research board – data mining of surveillance data
• Ministry of Transport – analyzing accidents
• Ministry of Agriculture – forecasting
• Bank of Canada, Finance - forecasting
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Statistical Careers
• Quant – modeling and forecasting markets
• Hedgie - calculating complex trading strategies like calls and puts – lots of probability