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

Can you trust statistics? 1

MAT2375Lecture #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.

• Before a massive vaccination program could be started it was necessary to prove the vaccine was effective.


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.


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


Experimental Results

Looks promising but is it significant?

Size Rate

Treatment 200,000 28

Control 200,000 71

Total 400,000 99


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?


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


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


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.


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.


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.


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


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


Statistical Careers

• Defense research board – data mining of surveillance data

• Ministry of Transport – analyzing accidents

• Ministry of Agriculture – forecasting

• Bank of Canada, Finance - forecasting


Statistical Careers

• Quant – modeling and forecasting markets

• Hedgie - calculating complex trading strategies like calls and puts – lots of probability

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

Documents

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