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Teaching Statistics By Example

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Title: Teaching Statistics By Example


1
Teaching Statistics By Example
  • Lisa M Sullivan, PhD
  • Boston University

2
Outline
  • Statistics in the News
  • The Introductory Statistics Requirement
  • Course Content
  • Recent Efforts at Reform
  • Modifications?
  • Examples for Specific Topics

3
News Week of May 29, 2006
  • Preserve brain function with spicy foods.
  • Kicking your food up a notch with spices could
    preserve brain function and keep your brain sharp
    and strong as you age.
  • Turmeric, a spice that lends curries their
    yellow tint, can curb mental decline and even
    slow the effects of neurodegenerative diseases
    such as Alzheimers.

4
News Week of May 29, 2006
  • Education linked to better fathers study
  • U.S. data shows trend between education and time
    spent with kids
  • Well-educated men tend to make better fathers,
    according a new U.S. government report on
    fatherhood.

5
News Week of May 29, 2006
  • U.S. Releases Bird Flu Response Plan - Details
    outline containment policies focus on worst-case
    scenarios may spread fear, experts say
  • Breast Cancer Survivors Lax About Mammograms -
    Only 33 get them annually for five years after
    diagnosis, study finds

6
News Week of May 29, 2006
  • The FDA issued a long-awaited approval on a new
    human growth product.
  • Approval of Omnitrope, made by Sandoz, was
    announced Tuesday in a statement on the FDAs Web
    site.
  • Omnitrope, also known as somatropin, is a
    hormone used to treat growth disorders in
    children and adults.

7
Statistics Requirement
  • Numerical literacy
  • Provide quantitative foundations for study in
    specific disciplines
  • Understand and interpret data
  • Perform independent research

8
Careers in Statistics
  • Business and Industry (Manufacturing, Marketing,
    Engineering)
  • Health and Medicine (Public Health, Clinical
    Trials, Epidemiology, Genetics, Health
    Communication)
  • Government (Census, Surveys)
  • Academia
  • Social Sciences
  • Health Insurance
  • Demand for statisticians far exceeds supply
    today and this is expected to increase through
    2008.

9
The Introductory Statistics Course
  • Difficult and frustrating for students
  • Difficult and frustrating for instructors
  • Hundreds of thousands of undergraduates across a
    variety of majors are required to take statistics
    - most not mathematically inclined

10
Typical Course Content
  • Descriptive Statistics
  • Classification of Variables
  • Means, Standard Deviations, Medians
  • Graphical Displays
  • Principles of Probability
  • Probability Models
  • Binomial, Poisson, Normal
  • Central Limit Theorem

11
Course Content
  • Estimation
  • Point Estimates
  • Margin of Error
  • Precision
  • Hypothesis Testing
  • Hypotheses
  • Test Statistic
  • Critical Region
  • Level of Significance, P-values

12
Course Content
  • Associations Between Variables
  • Regression Analysis
  • Analysis of Variance
  • Chi-Square Tests

13
Reforms in Undergraduate Education in Statistics
  • NSF funded various projects to improve teaching
    of undergraduate statistics courses
  • May 1999 the ASAs Undergraduate Statistics
    Education Initiative (USEI) was launched

14
Focus of the Reform
  • Emphasize concepts over procedures
  • Teach students to
  • Formulate research questions
  • Collect data
  • Analyze data
  • Interpret results

15
Focus of the Reform
  • Gain experience working with real data
  • Focus on active learning
  • Build communication skills
  • MAJOR FOCUS on statistical literacy/ statistical
    thinking

16
Statistical Thinking
  • Process of using wide ranging and interacting
    data to understand processes, problems, and
    solutions. The opposite of one factor at a time,
    where ones natural born tendency is to change one
    factor and see what happens. Statistical
    thinking is the tendency to want to understand
    how several control factors may be interacting at
    once to produce an outcome. Common cause
    variation becomes your friend and special cause
    variation your enemy. Attribute judgments of good
    and bad are replaced with estimates of
    significance with given confidence.
  • ---Six Sigma http//www.isixsigma.com/dicti
    onary/Statistical_Thinking-454.htm

17
Statistical Thinking
  • Recognize and attempt to understand/explain
    variation
  • The process of asking a good question,
    collecting, analyzing and interpreting data and
    appropriately recognizing limitations
  • How do we teach statistical thinking?

18
Recommendations for Instructors
  • Provide working examples that include questions
    and processes to solve statistical problems
  • Allow students to practice using statistical
    thinking with open-ended questions and problems
  • Use technology to collect, manage and analyze data

19
Recommendations for Instructors
  • Use real data
  • Choose data and questions that are of interest to
    students
  • Reduce content to focus on key concepts in
    greater detail

20
Whats Missing
  • Study Design Issues and Implications
  • Real Data
  • Interpretation of Results
  • Practical Implications
  • Limitations of Inferences
  • Statistical Computing

21
Limitations/Interpretation
  • Association is not causation
  • Statistical significance is not practical
    importance
  • Lack of statistical significance does not imply
    no difference
  • Understand how to interpret news stories/articles
    with statistical information

22
Modifications?
  • Include design and analysis issues in curriculum
  • Sharpen skills in interpretation of results
  • Include projects with real data
  • Stress communication skills
  • Focus more on big picture

23
Big Picture
  • What is a statistical study?
  • How is sample constructed?
  • What are the key questions?
  • How is information collected analyzed
    interpreted?
  • What makes a good study?
  • A poorly analyzed study can be re-analyzed. A
    poorly designed study cannot be re-designed.

24
Biostatistics
  • A specialized branch of applied
    mathematics/statistics that deals with the
    statistical evaluation of experimental research
    or clinical trial results.
  • Statistical applications in the medical or public
    health arena.

25
Biostatistics

Mathematics/Statistics
Medicine/Public Health
Biostatistics
Computer Science
26
Examples
  • What proportion of college students drink
    alcohol, use illegal drugs?
  • Should driving age be increased?
  • Are cell phones safe for children?
  • How can we address these questions?

27
Research Teams
  • Principal Investigator (Clinicians, Scientists)
  • Statistician/Biostatistician
  • Co-Investigators
  • Project Manager
  • Statistical Programmers
  • Research Assistants

28
Statisticians Role on Team
  • Develop Study Design
  • Research question
  • Study sample
  • Sample size
  • Enrollment/Follow-up strategies
  • On-going monitoring
  • Perform Interim and Final Analysis
  • Interpret and Report Results

29
Cell Phones for Children?
  • University of Washington scientist states 70-80
    of the energy emitted from the antenna of a
    mobile phone is absorbed in the head Childrens
    skulls are thinner and their growing brains may
    be much more susceptible to radiation exposure.
  • FDA states that scientific evidence does not show
    a danger to users of wireless communication
    devices including children.

30
Study of Cell Phone Safety
  • What is the outcome?
  • What is exposure/risk factor?
  • How can we assess relationship between cell phone
    use and health outcomes?
  • Study Design
  • Data Collection and Analysis
  • Interpretation/Attribution

31
Issues for Biostatisticians
  • Children - Obesity, Immunizations, Asthma,
    Autism..
  • Adolescents Alcohol Tobacco Use, Depression,
    STDs, Traffic Accidents.
  • Adults Cancer, CVD, Substance Abuse, HIV/AIDS,
    Mental Health
  • What is 1 killer of men and women in US?
  • What are the risk factors?

32
Research Set Context
  • Framingham Heart Study
  • Pharmacologic Clinical Trials in Children with
    Autism
  • Effect of Alcohol Exposure in Pregnancy on SIDS

33
The Framingham Heart Study
  • 5000 men and women enrolled in 1948
  • Longitudinal cohort study
  • Exams every 2 years for cardiovascular risk
    factors - surveillance
  • Ancillary studies hearing, exercise, nutrition,
    neurological studies
  • 5000 offspring spouses enrolled in 1976
  • Third generation enrolled in 2002
  • http//www.nhlbi.nih.gov/about/framingham/

34
Milestones from Framingham
  • 1960 Cigarette smoking increases risk of heart
  • disease
  • 1961 Cholesterol blood pressure increase risk
    of
  • heart disease
  • 1967 Physical activity reduces risk of heart
    disease,
  • obesity increases risk of heart disease
  • 1970 High blood pressure increases risk of stroke
  • 1978 Psychosocial factors increases heart disease
  • 1988 High levels of HDL cholesterol reduces risk
    of
  • death
  • More than 1500 scientific papers published

35
Framingham Study Risk Functions
  • Risk prediction models
  • Predict likelihood that a person will have
    coronary heart disease in the next 10 years
  • Models designed to include risk factors that are
    readily available
  • Age, blood pressure, cholesterol, smoking,
    diabetes, treatment for hypertension high
    cholesterol, obesity
  • Risk Calculator
  • http//hp2010.nhlbihin.net/atpiii/calculator.asp

36
Clinical Trial in Children with Autism
  • Autism-brain disorder usually diagnosed before
    age 3 that affects communication, social
    interaction, and creative play.
  • Affects over 500,000 children in the US
  • Trial to assess the efficacy of drug treatment in
    reducing repetitive behaviors
  • Children randomized to receive study drug or
    placebo

37
Clinical Trial in Children with Autism
  • 144 children with autism aged 5-17 years followed
    every 2 weeks for 12 weeks for improvements in
    repetitive behaviors
  • Issues
  • Randomization/Blinding
  • Measurement of outcome (child, parent, teacher)
  • Safety/Ethical issues

38
Effect of Alcohol Exposure in Pregnancy on SIDS
  • SIDS Unexplained infant death before 1 year of
    life
  • Extremely high rates of SIDS among American
    Indians in Northern Plains of North and South
    Dakota and in Cape Town South Africa
  • High rates of alcohol consumption

39
Effect of Alcohol Exposure in Pregnancy on SIDS
  • SIDS 0.57/1000 in US
  • 3.4/1000 in Northern Plains
  • 3.5/1000 in Cape Town
  • In US 13 of women report drinking
  • alcohol in pregnancy
  • 58 in Northern Plains
  • 41 in Cape Town

40
Effect of Alcohol Exposure in Pregnancy on SIDS
  • Study of 12,000 pregnant women in Northern Plains
    and Cape Town
  • Assess relationship between alcohol and SIDS
  • Issues
  • Measuring alcohol exposure
  • Ethical Issues e.g., Autopsies

41
Examples for Specific Topics
  • Conditional Probability
  • Performance of screening tests for prenatal
    diagnosis, prostate cancer, breast cancer, HIV

42
Prenatal Diagnosis
  • Your family is pregnant should you have a
    screening test?
  • Standard of Care in the US is serum screen
  • 68 sensitivity
  • 5 false positive rate

43
Performance Characteristics of Screening Tests
  • Disease Disease
  • Test a b
  • Test - c d

44
Performance Characteristics
  • Sensitivity True Positive Fraction P(Test
    Disease)
  • False Positive Fraction
  • P(Test No Disease)

45
For the Patient
  • Positive Predictive Value
  • P(Disease Test )
  • Negative Predictive Value
  • P(No Disease Test -)

46
Examples for Specific Topics
  • Normal Probability Model
  • Percentiles
  • Height, Weight, BMI for age
  • http//www.cdc.gov/growthcharts/

47
Statistical Inference
  • Estimation and Hypothesis Testing
  • Clinical Trials
  • Search for clinical trials
  • Recent results (press releases and scientific
    articles)
  • http//www.clinicaltrials.gov/

48
Introductory Statistics
  • Big Picture and Make it Real!
  • Real Data
  • Relevant Examples
  • Focus on Interpretation Practical Importance
  • http//health.msn.com/

49
Academic Programs at Boston Uwww.bu.edu
  • BA in Mathematics/Statistics
  • Minor in Applied Statistics
  • Summer Institute for Training in Biostatistics
  • MA in Biostatistics
  • PhD in Biostatistics
  • Minor in Public Health(Biostatistics,
    Epidemiology, Environmental Health, International
    Health, Health Law, Maternal and Child Health,
    Health Services, Social and Behavioral Science)
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