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Chapter 1 Statistical Thinking


Chapter 1 Statistical Thinking What is statistics? Why do we study statistics Statistical Thinking the science of collecting, organizing, and analyzing data the ... – PowerPoint PPT presentation

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Title: Chapter 1 Statistical Thinking

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

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

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.

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)

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
  • The velocity of a burning gas on the sun's
  • Clinical trials to investigate the effectiveness
    of new treatments
  • Field experiments to evaluate irrigation methods
  • Measurements of water quality

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
  • Does reading an article in statistics improve
    students statistics grade?

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

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!

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????

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.

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

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?

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

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
  • Will this chance go up, down or remain the same
    if you repeat the experiment with 200 students?

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

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?

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

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
  • Hence there is a strong evidence for a factor to
    be responsible for this change.

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

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

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

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

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
  • Problem?????

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?

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

A Design Example
  • Example (Observed Control Study)
  • Control Group---all 1st and 3rd grade children
  • Treatment group---all 2nd graders
  • Assumption
  • Age difference between control and treatment
    group was felt to be unimportant

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

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

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

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

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

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

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

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