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## Chapter 1 Statistical Thinking

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Title: Chapter 1 Statistical Thinking

1
Chapter 1 Statistical Thinking
• What is statistics?
• Why do we study statistics

2
Statistical Thinking
• the science of collecting, organizing, and
analyzing data
• the mathematics of the collection, organization
and interpretation of numerical data
• The branch of mathematics which is the study of
the methods of collecting and analyzing data
• a branch of applied mathematics concerned with
the collection and interpretation of quantitative
data and the use of probability theory to
estimate population parameters

3
Statistical Thinking
• Statistics is a discipline which is concerned
• with
• designing experiments and other data collection,
• summarizing information to aid understanding,
• drawing conclusions from data, and
• estimating the present or predicting the future.

4
Statistical Thinking
• "I like to think of statistics as the science of
learning from data...." Jon Kettenring, ASA
President, 1997
• Steps of statistical analysis involve
• collecting information (Data Collection)
• evaluating the information (Data Analysis)
• drawing conclusions (Statistical Inference)

5
Statistical Thinking
• What type of information?
• A test group's favorite amount of sweetness in a
blend of fruit juices
• The number of men and women hired by a city
government
• The velocity of a burning gas on the sun's
surface
• Clinical trials to investigate the effectiveness
of new treatments
• Field experiments to evaluate irrigation methods
• Measurements of water quality

6
Statistical Thinking
• Problems
• Is a new treatment for heart disease more
effective than a standard one?
• Is using a high octane gas beneficial to car
performance?
• Does reading an article in statistics improve

7
Statistical Thinking
• Is a new treatment for heart disease more
effective than a standard one?
• Pick, say, 100 heart patients
• Divide them into two groups, 50 in each group
• Group 1------------New treatment
• Group 2------------Standard treatment

8
Statistical Thinking
• Results
• 40 out of 50 of Group 1 patients improved
• 30 out of 50 of Group 2 patients improved
• Conclusion New treatment is more effective!

9
Statistical Thinking
• How do you divide the patients?
• Have you controlled other factors? (fitness
level, life style, age, etc)
• How do you decide who gets what treatment?
Ethical issues????

10
Statistical Thinking
• Comparing Test Scores
• Select 10 students and give them a journal
article in statistics.
• Test their knowledge about the article and record
their scores
• Repeat the test after they take STT 231.

11
Statistical Thinking
• Result
• 8 out of the 10 students improved their scores.
• Question Can we conclude that reading the
article has improved students knowledge about
statistics?

12
Statistical Thinking
• Look at worst case scenarios
• Under the assumption that the new
• treatment is no better than the standard one,
• what is the chance that 80 of the patients
• benefit from this treatment?
• Under the assumption that STT 231 brings
• no benefit, how likely is it that we see 80
• of the students improve their scores?

13
Statistical Thinking
• Need a model to answer these questions!!
• If STT 231 is not beneficial, then students
• scores may go up or down with 50
• chance.
• This is equivalent to flipping a coin
• 50 chance you get Head
• 50 chance you get Tail

14
Statistical Thinking
• Comparing pre and post test scores for 10
students is equivalent to
• flipping a coin 10 times and calculating the
chance of observing 8H
• Relevant Questions
• Will the chance of observing 80 of the time H
depend on the number of students involved in the
experiment?
• Will this chance go up, down or remain the same
if you repeat the experiment with 200 students?

15
Statistical Thinking
• Suppose the proportion of improvement in 10
trials is 4.4. What does this mean?
• If STT 231 is not beneficial, then there is a
4.4chance that we will observe 8 out of 10
students scores improve.
• There is little hope that 8 students scores will
improve by just by CHANCE

16
Statistical Thinking
• Suppose the proportion of improvement in 10
trials is 4.4.
• We observed 8 students scores out of 10 improve.
• What does this mean?

17
Statistical Thinking
• Course is highly effective
• Course is ineffective and we observed an unlikely
event.
• We do not know which one!

18
Statistical Thinking
• Suppose there is a small chance that an event
happens by CHANCE,
• Then this is an indication for a strong evidence
that the change that we observe did not happen by
CHANCE.
• Hence there is a strong evidence for a factor to
be responsible for this change.

19
Statistical Thinking
• The course is highly effective!!
• Reasoning What we observed is very unlikely if
the course was ineffective. Hence the course is
effective.
• The 80 score increment is unlikely to be
achieved if the course was ineffective.

20
Statistical Thinking
• Some Remarks
• For questions that involve uncertainty
• Carefully formulate the question you want to
• Collect Data
• Summarize, analyze and present data
• Draw Conclusions. Conclusions always include
uncertainty
• Support your conclusions by quantifying how

21
Chapter 2 A Design Example
• The Polio Vaccine Case
• Caused by virus
• Big problem during the first half of the 20th
Century
• Develop vaccine to fight the disease
• Jonas Salk (1950)

22
A Design Example
• Problem with vaccines
• Are they safe?
• Are they effective?
• Undertake a large scale trial to answer these
questions

23
A Design Example
• Case 1 A Simple Study
• Distribute the vaccine widely (under the
assumption it is safe)
• Decrease in the number of polio cases after the
vaccine provides evidence that the vaccine is
effective
• Problem?????

24
A Design Example
• Problems
• Lack of control group
• Is decrease in number of polio due to the vaccine
or other factors?
• How reliable is the assumption vaccine is safe?

25
A Design Example
• Case 2 Adding a Control Group
• Have two groups
• Control group-----gets salt solution
• Treatment group---gets the actual vaccine

26
A Design Example
• Example (Observed Control Study)
• Control Group---all 1st and 3rd grade children
• Assumption
• Age difference between control and treatment
group was felt to be unimportant

27
A Design Example
• Potential Problems
• Parents of 2nd graders may not agree to
vaccinating their kids
• Parents of sicker kids are most likely to accept
the vaccine
• More educated parents tend to accept the vaccine
• Parents of sick 1st and 3rd graders may object
that their kids are not getting treatment

28
A Design Example
• Difficulty in diagnosing polio
• Extreme case of polio are easy to diagnose
• Less severe cases of polio have symptoms similar
to other common illnesses

29
A Design Example
• Potential Problems
• Physicians are aware of who has received the
vaccine and who has not
• Less severe case of polio in a 2nd grader (who
has received the vaccine) may wrongly diagnosed
as another illness
• Less severe case in a 1st or 3rd grader will most
likely be diagnosed as polio

30
A Design Example
• Case 3 Randomization, Placebo Control, Double
Blindness
• Random assignment of control and treatment groups
• Select a child
• Flip a coin-------H-------Treatment Group
• T---------Control Group

31
Design Example
• Placebo Control
• Kids in the control group receive salt solution
• Double Blind
• Neither the child
• nor the parents
• nor the doctors/nurses
• who make the diagnosis of polio know whether a
• kid receives the vaccine or the placebo

32
A Design Example
• Summary
• In designing experiments
• Introduce some sort of control group
• Use randomization to avoid bias in selection and
assignment of subjects for the study
• Double blind experiments give protection against
biases, both intentional and unintentional

33
A Design Example
• Perform the experiment on a large number of
subjects (Polio case in millions of kids)
• Repeat the experiment several times before making
definitive conclusions

34
A Design Example
• Basic Principles of Experimental Designs
• Randomization
• Blocking (Treatment/Control Groups)
• Replication