Transcript discussing the purpose of this course

MAT2375
Lecture #1 by D. McDonald
from the Department of
Mathematics and Statistics
Can you trust Statistics?
Can you trust statistics?
1
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?
2
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?
3
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?
4
Experimental Results
Size
Rate
Treatment
200,000
28
Control
200,000
71
Total
400,000
99
Looks promising but is it significant?
Can you trust statistics?
5
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?
6
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?
7
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   400000
 
 

 x   200000  x  200000
Can you trust statistics?
8
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?
9
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?
10
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?
11
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?
12
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?
13
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?
14
Statistical Careers
• Quant – modeling and forecasting
markets
• Hedgie - calculating complex trading
strategies like calls and puts – lots of
probability
Can you trust statistics?
15