Teaching Statistics By
Example
Lisa M Sullivan, PhD
Boston University
Outline
 Statistics in the News
 The Introductory Statistics
Requirement
 Course Content
 Recent Efforts at Reform
 Modifications?
 Examples for Specific Topics
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 Alzheimer’s.
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.
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
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 FDA’s Web site.
Omnitrope, also known as somatropin, is a
hormone used to treat growth disorders in
children and adults.
Statistics Requirement
 Numerical literacy
 Provide quantitative foundations for
study in specific disciplines
 Understand and interpret data
 Perform independent research
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.
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
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
Course Content
 Estimation
 Point Estimates
 Margin of Error
 Precision
 Hypothesis Testing
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Hypotheses
Test Statistic
Critical Region
Level of Significance, P-values
Course Content
 Associations Between Variables
 Regression Analysis
 Analysis of Variance
 Chi-Square Tests
Reforms in Undergraduate
Education in Statistics
 NSF funded various projects to
improve teaching of undergraduate
statistics courses
 May 1999 the ASA’s Undergraduate
Statistics Education Initiative (USEI)
was launched
Focus of the Reform
 Emphasize concepts over procedures
 Teach students to:
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Formulate research questions
Collect data
Analyze data
Interpret results
Focus of the Reform
 Gain experience working with real
data
 Focus on active learning
 Build communication skills
 MAJOR FOCUS on statistical literacy/
statistical thinking
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/dictionary/Statistical_Thinking-454.htm
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?
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
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
What’s Missing
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Study Design Issues and Implications
Real Data
Interpretation of Results
Practical Implications
Limitations of Inferences
Statistical Computing
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
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
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?
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 A poorly analyzed study can be reanalyzed. A poorly designed study cannot
be re-designed.
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.
Biostatistics
Mathematics/Statistics
Medicine/Public Health
Biostatistics
Computer Science
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?
Research Teams
 Principal Investigator (Clinicians,
Scientists)
 Statistician/Biostatistician
 Co-Investigators
 Project Manager
 Statistical Programmers
 Research Assistants
Statistician’s Role on Team
 Develop Study Design

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Research question
Study sample
Sample size
Enrollment/Follow-up strategies
On-going monitoring
 Perform Interim and Final Analysis
 Interpret and Report Results
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: Children’s 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.
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
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?
Research – Set Context
 Framingham Heart Study
 Pharmacologic Clinical Trials in
Children with Autism
 Effect of Alcohol Exposure in
Pregnancy on SIDS
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/
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
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
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
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
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
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
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
Examples for Specific Topics
 Conditional Probability
 Performance of screening tests for
prenatal diagnosis, prostate cancer,
breast cancer, HIV
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
Performance Characteristics of
Screening Tests
Test +
Test -
Disease +
a
c
Disease –
b
d
Performance Characteristics
 Sensitivity = True Positive Fraction =
P(Test + | Disease)
 False Positive Fraction =
P(Test + | No Disease)
For the Patient
 Positive Predictive Value =
P(Disease | Test +)
 Negative Predictive Value =
P(No Disease | Test -)
Examples for Specific Topics
 Normal Probability Model
 Percentiles
Height, Weight, BMI for age
http://www.cdc.gov/growthcharts/
Statistical Inference
 Estimation and Hypothesis Testing
 Clinical Trials
 Search for clinical trials
 Recent results (press releases and scientific
articles)
http://www.clinicaltrials.gov/
Introductory Statistics
 Big Picture and Make it Real!
 Real Data
 Relevant Examples
 Focus on Interpretation – Practical
Importance
http://health.msn.com/
Academic Programs at Boston U
www.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)