Undergraduate Statistical Science
Statistics is the science of
uncertainty, the key to making inference in scientific inquiry and to balancing
the risks and benefits that every decision-maker faces. Early 21st
century statistical science is a mature, mathematical model-based computational
science with a philosophical and theoretical foundation in probabilistic
reasoning and far-reaching application across all social, policy, natural and
biomedical sciences. The concurrent emergence in the 1990's of unprecedented
desktop computational power and the rediscovery of simulation-based
computational algorithms led to a revolution in statistical science, enabling
advances in natural and social sciences based on statistical modeling of
increasing realism and complexity. This has led us to a position in scientific
modeling and inference where we can address scientific questions that were
scarcely conceivable only two decades ago.�
Modern statistical science lies at the heart of contemporary research in
areas of genomics, environmental science, telecommunications, neurobiology,
finance, and many other fields.� Duke's
Department of Statistical Science is at the forefront of this intellectual
revolution and since inception has been a leader in the development of
statistical science in inter-disciplinary applications across many fields.
The Department of Statistical
Science at
The mission of the
undergraduate program in statistics at
Service Courses
The goals for undergraduate
service education in statistics at
�
4.
� Foster active learning in the classroom;
5.
� Use technology for developing conceptual
understanding and analyzing data;
STA10, STA101, STA102,
STA102b, STA103, and STA113 each incorporate these GAISE outlines.
Major/Minor
Students receiving either a
major or minor in statistics are given a rigorous, comprehensive,
research-based learning experience. A distinctive feature of our major program
is the completion of a two-semester supervised research project under the
direction of a member of the
Goals/Objectives
The goals for undergraduate education in statistics at
Goal 1: Mastery of Intellectual Foundations
Students will develop a
strong intellectual foundation in mathematical and computational statistics.
Students learn about the basic mathematical principles, computational tools,
and research approaches through foundation courses STA104, STA114, STA121 and
STA122.�
Goal 2: Mastery of Core Skills of the Discipline
Including Study Design, Data Analysis, and Computational Skills
Students will acquire
knowledge of a wide range of methodologies and computing skills related to the
statistical science.�� Applications of
these skills and core knowledge will occur in many courses including STA121,
STA122, STA130, STA135, STA140, STA175, STA180.
Goal 3: Mastery of Research and Critical Thinking
Skills
Students will develop
competence in the conducting research in statistical science.� All majors will engage in a two-semester
sequence of statistical research STA190A,B.�
Further research experience may be gained though independent study
courses.�
Goal 4: Development of Professional Communication
Skills
Students will gain experience
in professional communication though statistical consulting, STA145S. Expertise
in oral and written communication is developed via oral and written
presentations on collaborations with scientists from other fields.
Goal 5: Career Preparation
Students seeking careers in
statistics will be prepared in two paths.�
Preparation for graduate school.
For those students aspiring
to graduate education, additional mathematics and computer science is highly
desirable.� STA104 and STA114, the
probability and mathematical statistics sequence is minimal, and we encourage
these students to take further math including linear algebra and real analysis
as well as higher-level programming courses.�
We encourage these students to serve as teaching assistants and take
statistical consulting (STA145S) to improve their communication skills
Preparation for employment.
For those students aspiring
to a professional career, skills that prepare for work in industry, clinical
trials, business management, and government are desirable.� We encourage these students to take further
courses in multivariate analysis, design of surveys and experiments, and
statistical consulting.� Both data
analysis and communication skills are key for these individuals.
Assessment
Service Courses
Teaching statistics to
students from other disciplines is a contentious topic, because statistics is
often viewed as a toolbox of methods to be memorized and applied in a template
fashion.� A survey of course structures
at many universities and discussions with students of AP courses quickly
uncovers that most courses are taught in this way, rather than with an
appreciation that statistics is a discipline, a method of critical thinking, a
field for which methods depend on data structure and research question rather
than discipline, and a set of methods that when applied in a template manner
often leads to wrong conclusions.
Because of this, our
undergraduate service courses attempt to teach statistics conceptually.� Rather than focusing on teaching template
methods, students are taught underlying fundamental principles that underlie
all methods.� Instead of focusing on the
calculation of various test statistics and p values, courses focus on what is
it that a test statistic measures and what probability is it that a p value
represents.� This is a level of abstract
reasoning that is new and challenging to many undergraduates and that is often
poorly understood by those trained in a template manner.� All undergraduate service courses, except
STA10 a quantitative literacy course that prepares students for our 100-level
courses, have a computing lab in which students get hands on experience with
real data and statistical software.� In
these labs, students learn application of the conceptual ideas to the analysis
of real data arising from sociology, psychology, public policy, education,
environmental studies, political science, and other fields.� It is a course after which students
understand interdisciplinary collaboration with the field of statistics.
Assessment in our service
courses is comprised of a placement exam that channels students into the course
for which their prerequisite math skills are appropriate, frequent in-class warm-up
exercises, in-class exams covering conceptual topics of the text and lecture,
and data-analysis projects or exams in which students show that they can apply
these conceptual ideas to real data.�
Because statistics is such a cumulative subject, students are given
feedback on a regular and frequent basis, so that falling behind is signaled
quickly.� Because of the large
enrollments in these courses, exams are a mixture of multiple choice,
true/false, short answer, and problem solving.
Questions include
comprehension, calculation and interpretation.�
Professors are encouraged to include questions on the final exam that
include the statistical results of published research reports. Students must
demonstrate understanding of the results and an ability to critique the
correctness of the argument the authors make.�
Questions are designed as a mixture of easy, moderate, and difficult, so
that we understand comprehension levels at both ends of the spectrum.
Typically, a student must score at least 70% to attain a C or better in the
course. To assess proficiency in data analysis some professors choose in-class
data analysis exams, some require written data analysis projects, and others
prefer poster session formats.� Finally,
on a biennial basis the DUS of Statistical Science meets with DUS of the
departments of the majors we serve to get feedback on whether students in these
fields are demonstrating statistical mastery at a level sufficient for
follow-up courses taught by these departments.
Major and Minor
The major and minor are new
at Duke starting in 2007.� As a student
begins the program, each meets individually with the Director of Undergraduate
Studies to discuss the student�s mathematical and statistical background, their
long-range plan of study, and their expectations for the major or minor.� After this time, students meet each semester
with their assigned advisor and at least once per semester with the DUS and
other majors.� Throughout the student�s
course of study, the department uses frequent homework assignments, in and
out-of-class exams, data analysis projects, and written research reports to
keep track of student progress through the curriculum.� Each semester the faculty discusses progress
of all students.� The department
anticipates that within 5 years (2012), 50% of undergraduate majors will
complete an honors thesis. As majors and minors graduate, we will track job and
graduate school placements.� Below are
examples of assessment that are used in our courses designed for the major and
minor.
STA104 and 114 focus on Goal
1: Mastery of Intellectual Foundations.
The primary assessment of reaching this goal is from problem sets and
exams.� Upon completion of STA104
students must be able to perform combinatorial analyses, use axioms of
probability to assess chance events, understand conditional probability and
independence, understand random variables, transformations of random variables
and joint distributions of random variables, and demonstrate basic proofs of
limit theorems. Upon completion of STA114 students must be able to demonstrate
properties of sampling including sums of random variables and convergence
concepts and properties of sample statistics.�
They must understand principles of data reduction including sufficiency,
the likelihood principle, and invariance.�
The student must master methods of point and interval estimation from
Bayesian and Classical perspectives.�
Finally students must understand hypothesis testing from a decision
theoretic framework covering methods of finding tests as well as evaluating
these tests.� While primary assessment of
students will be through problem sets and exams, because these topics are
prerequisite knowledge for most other courses, instructors of follow-on classes
will also assess how well students have mastered this prerequisite material and
provide feedback to instructors of STA104 and STA114.� This assessment will occur during the first
two weeks of each semester via assignments over prerequisite material.� Feedback will occur in a faculty meeting held
during the third week of each semester.
STA121 and 122 focus on three
goals: Mastery of Core Skills of the
Discipline Including Study Design, Data Analysis, and Computational Skills;
Mastery of Research and Critical Thinking Skills; and Development of Professional
Communication Skills.� In STA121 and
STA122 students learn about multivariate statistical analysis including linear
regression, logistic regression, and time-series analysis, implement these
methods, and write and present undergraduate thesis-quality papers
incorporating these methods in the exploration of a research question.� Throughout the semester students present
their updated projects to the class and critique each other�s work. Their
presentations and papers are evaluated by peers and the instructor for: 1)
appropriateness and accuracy of statistical analysis, 2) awareness of
limitations in design and analysis, and 3) clarity and completeness of the
statistical argument pertaining to the research question. All students must
complete this project at a satisfactory level to pass the course. Examples of
projects from recent semesters include:
�
Unpacking the
National Election Survey 2004: Does Foreign Policy Approval Matter?
�
The Role of
Adolescence, Anxiety, Novelty Seeking, and Stress Hormones in Cocaine
Addictions
�
Teacher Turnover
in North Carolina Public Schools
�
Changes in
Political Donors� Tolerance Following September 11th
STA130 and STA135 focus on goal 2:� Mastery of Core Skills of the Discipline
Including Study Design, Data Analysis, and Computational Skills.� STA130 covers statistical analysis in causal
research questions, while STA135 covers statistical analysis in the design and
analysis of complex sample surveys. STA135 topics include the design-based
(randomization-based) and model-based paradigms, survey weights, typical one
stage and multi-stage sampling designs and their relative merits, missing data
methods, and accounting for complex sampling designs when estimating
regressions. Students must be proficient at analyzing basic complex
probability samples, understand the trade offs (e.g., cost versus accuracy) in
selecting different basic sampling designs, and deriving statistical properties
of estimators using first principles. Students
receive feedback on weekly projects analyzing complex survey data and weekly
methods assignments that require proving properties of estimators. Students
must also pass a written exam for which they must get 70% to pass the course.
In STA130 students make presentations on the statistical analysis used to
answer a causal research question.� They
are assessed on their level of understanding of the design and analysis and
their ability to point out strengths and limitations of the design that
threaten internal and external validity of the study. Examples of presentations
from recent semesters of STA130 include:
� Causal Effects of Alcohol and Tobacco on Birth Weight
� The Role of Handguns on Murder Rates
� The Effect of Gender on Service Time in Coffee Bars
STA145S focuses on goals four
and five: Development of Professional
Communication Skills and Career
Preparation.� In all statistical
work, the ability to communicate statistical methodologies to lay persons is
essential. In this course, students are not expected to come out with increased
knowledge about a specific set of statistical methodologies or statistical
knowledge but rather improved communication skills and experience in
communicating the ideas of statistics to others.� Undergraduates are paired with a more senior consultant to work with clients on a
research project. Beyond meeting with clients, students participate in
weekly meetings in which projects with all clients are presented and
discussed.� Students are assessed on
their ability to ask probing questions, critique alternative methods, and
explain and justify choice of the most appropriate methodologies to help answer
the client�s research question.� Students
are expected to gain a greater comprehensive grasp of alternative statistical
methods and their appropriateness for particular research questions and an
appreciation of the diverse range of methods that statisticians use.
STA190 focuses on goal 3: Mastery of Research and Critical Thinking
Skills. �In STA190 students work
one-on-one with a faculty member on a particular research project.� Students are assessed on their research
progress based on weekly discussions, progress reports and research papers. STA
190 continues for two semesters and the end assessment of the goal is based on
a paper expected to pass standards for publication.� In Fall 2007, students worked on the
following research topics
�
Statistical
models for studying exposure disease relationships
�
Statistical
dynamic graphical models in financial mutual funds portfolio studies
Finally,
upon graduation with a statistics degree, all graduates will be given an exit
interview in which they may give feedback to the department on advising,
particular courses, the synchronization between courses, their experiences on
the job market, and anything else they would like to discuss pertaining to our
major.
In
recognition of the need to closely assess learning goals while developing the
major and minor, over the next five years the department will
1) Collect systematic data on student mastery and
progress related to each of the learning goals
a. Intellectual Foundations
b. Core Skills of the Discipline Including Study Design,
Data Analysis, and Computational Skills
c. Research and Critical Thinking Skills
d. Development of Professional Communication Skills
e. Career Preparation
2) Develop and apply consistent standards of scoring for
all honors projects
3) Develop a process by which the Chair and DUS evaluate
whether each graduate has met the learning objectives of the program
4) Implement methods by which feedback from each of the
above leads to constant improvement in the training our undergraduate majors
and minors
Plans for assessing the learning experiences of statistical science majors