Teaching Statistics By Example

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Teaching Statistics By Example

• Lisa M Sullivan, PhD
• Boston University

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Outline

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

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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.

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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.

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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

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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.

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Statistics Requirement

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

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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.

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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

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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

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Course Content

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

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Course Content

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

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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

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Focus of the Reform

• Emphasize concepts over procedures
• Teach students to
• Formulate research questions
• Collect data
• Analyze data
• Interpret results

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Focus of the Reform

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

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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

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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?

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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

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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

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Whats Missing

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

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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

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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

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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.

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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.

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Biostatistics

Mathematics/Statistics
Medicine/Public Health
Biostatistics
Computer Science
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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?

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Research Teams

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

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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

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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.

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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

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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?

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Research Set Context

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

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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/

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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

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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

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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

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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

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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

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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

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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

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Examples for Specific Topics

• Conditional Probability
• Performance of screening tests for prenatal
  diagnosis, prostate cancer, breast cancer, HIV

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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

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Performance Characteristics of Screening Tests

• Disease Disease
• Test a b
• Test - c d

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Performance Characteristics

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

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For the Patient

• Positive Predictive Value
• P(Disease Test )
• Negative Predictive Value
• P(No Disease Test -)

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Examples for Specific Topics

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

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Statistical Inference

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

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Introductory Statistics

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

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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)