Research Experience for Undergraduates (REU) in Statistics at Miami University

1
Research Experience for Undergraduates (REU) in
Statistics at Miami University

• Vasant B. Waikar,
• Miami University
• Oxford, OH, USA
• waikarvb_at_muohio.edu

2
REU (Research Experience for Undergraduates) in
Statistics at Miami University

• In this paper I will describe the working of this
  REU named the Summer Undergraduate Mathematical
  Sciences Research Institute or SUMSRI that I have
  directed for the last nine summers at Miami
  University. SUMSRI is funded by the National
  Security Agency (NSA) and the National Science
  Foundation (NSF). I will also discuss the nature
  and content of the research papers written by the
  undergraduates at this REU under my supervision.
  Some of these papers have won awards in the
  student paper competition sponsored by the
  American Statistical Association (ASA).
• Keywords Research Experience for Undergraduates,
  Statistics

3
SUMSRI Faculty Students-2008

• SUMSRI-Summer Undergraduate Mathematical Sciences
  Institute at Miami University, Oxford, OH
  (1999-present)
• Supported by the NSF, NSA and Miami Univ.
• Seven weeks (June-July)
• Underrepresented minority students women

4
Statistics on Mathematical Scientists

• In Spring 2006, 1245 Ph.D.s in Mathematical
  Sciences
• 522 Math Ph.D.s to US citizens
• 17 Math Ph.D.s to African Americans
• 17 Math Ph.D.s to Hispanics
• 143 Math Ph.D.s to women

5
Objectives of SUMSRI

• To encourage 12-15 US participants to get Ph.D in
  math or related area
• To smooth the transition between undergraduate
  and graduate school
• To provide information on graduate school
  applications and finances
• To provide mentors and role models

6
Programs that Make a Difference

• SUMSRI won the Programs that Make a Difference
  Award from the American Mathematical Society in
  2008.

7
What SUMSRI Offers

• Short courses in Analysis and Algebra
• Mathematical Writing course
• GRE Preparation course
• Research seminars in Math and Statistics
• Two colloquia per week by minority and female
  mathematicians and statisticians
• Graduate school panel discussion
• Students present their work to the department and
  submit a paper. (See their papers at
  http//www.users.muohio.edu/porterbm/sumj/
• Journal.html)

8
Personnel
Directors Dennis Davenport and Vasant Waikar
Thomas Farmer, Mathematical Writing
Not pictured Dennis Keeler, Algebraic Topology,
Dennis Davenport GRE Prep
Patrick Dowling (Real Analysis) Bonita Porter,
Program Coordinator
Research Seminar Directors Edray Goins, Vasant
Waikar Reza Akhtar
9

• List of Personnel2006
• Program Co-directors Dr. Dennis Davenport
• Dr. Vasant Waikar
• Program Coordinator Ms. Bonita Porter
• Algebra Short Course Dr. Dennis Keeler
• Analysis Short Course Dr. Patrick Dowling
• GRE Instruction Dr. Dennis Davenport
• Mathematical Writing Dr. Thomas Farmer
• Computer Expert Dr. Dennis Burke
• Research Seminar Directors
• Algebra Dr. Reza Akhtar
• Number Theory Dr. Edray Goins
• Statistics Dr. Vasant Waikar
• With the exception of the Number Theory seminar
  director, Dr. Goins, who came from Purdue,
  everyone else is from Miami University, Math and
  Statistics Department.

10
Organization
11
Statistical Research Seminar

• Pre-requisites
• Instruction
• Locating data set
• Analyzing data writing paper
• Presenting research

12
Past Statistical Research Papers

• 1999
• Do Students in Mathematics and the Sciences at
  Miami University Cheat on Exams Using Graphing
  Calculators?  An Unrelated-Question Randomized
  Response Experiment             Lynn Holmes,
  Fayetteville State University            
  Bethany Lyles, Fort Lewis College
• The Change in the Number of Four-letter Words in
  the English Language             Rachel
  Kahlenberg, Ohio Northern University            
  Rebekkah Dann,  Messiah College

13
2000

• Multivariate Classification Methods The
  Prevalence of Sexually Transmitted Diseases
             Candace Porter, Albany State
  University             Michael Sotelo,
  California Polytechnic Pomona            
  Brandon McKenzie,  Centre College            
  Lindsay Kellam, Queens College

14
2001

• A Multivariate Statistical Analysis of State
  Desirability             Jennifer Everson,
  Carthage College             Melissa Hildt,
  College of Notre Dame of Maryland            
  Jason Popovic, Baldwin-Wallace College
              Sarah Zimmermann, Bemidji State
  University

15
2002

• A Multivariate Statistical Analysis of the Free
  World             David Friedenberg, Miami
  University             Shenek Heyward, Francis
  Marion University
• Multivariate Analysis of Vehicle Safety
              Leigh Cobbs, Texas AM University
              Mary Cunnigham, James Madison
  University             Cheryl Gerde, Morehead
  State University

16
2003

• A Multivariate Statistical Analysis of Stock
  Trends            April Kerby, Alma College   
          James Lawrence, Miami UniversityA
  Multivariate Statistical Analysis of the NBA   
          Lori Hoffman, University of Wisconsin,
  River Falls            Maria Joseph, Kentucky
  State University

17
2004

• Educating the States A Multivariate Statistical
  Analysis of Education
• Nick Imholte, Xavier University, Cincinnati
• Sara Blight, University of Arizona, Tucson
• A Multivariate Statistical Analysis of Crime Rate
  in US Cities
• Kendall Williams, Howard University
• Ralph Gedeon, University of Florida

18
2005

• A Multivariate Statistical Analysis of Substance
  Abuse in the United States
• Joshua Svenson, Baldwin-Wallace College
• Monique Owens, Central State University
• A Multivariate Statistical Analysis of Female
  Empowerment
• Janelle Jones, Spelman College
• AdriAnne Demski, Clarion University

19
2006

• Reckless or Responsible A Multivariate
  Statistical Analysis of Consumer Spending
• Emilola Abayomi, Albany State University
• Erin Esp, Montana Tech
• Shannon Grant, University of Idaho
• Education By Nation A Multivariate Statistical
  Analysis
• Ashley Brooks, Winston Salem State University
• Amber Shoecraft, Johnson C. Smith University
• Anthony Franklin, Coastal Carolina University

20
2007

• College Desirability  A Multivariate Statistical
  Analysis
• Andrea M. Austin, St. Michael's College
• Terrell A. Felder, North Carolina A T
• Lindsay M. Moomaw, Baldwin-Wallace College
• Risky Behavior A Multivariate Statistical
  Analysis of the United States Based on Health
  Risk Factors Christina McIntosh, Spelman
  CollegeAlicia Smith, Winston-Salem State
  UniversityAshley Swandby, Longwood University

21

• ABSTRACTS

22
Multivariate Statistics 1999
Rebecca Dann and Lynn Holmes give their final
presentations.
23
Do Students in Mathematics and the Sciences at
Miami University Cheat on Exams Using Graphing
Calculators?  An Unrelated-Question Randomized
Response Experiment

• By Lynn Holmes, Fayetteville State University and
  Bethany Lyles, Fort Lewis College
• We used the randomized response method to look at
  how many students might cheat on tests using
  graphing calculators. Graphing calculators allow
  students to perform tedious mathematical
  calculations with great ease and considerably
  shorten the amount of time needed to work some
  difficult problems. However, it is possible to
  store information, such as formulas or
  definitions, in graphing calculators and use this
  information to cheat on exams. In order to
  address this issue, an unrelated-question
  randomized response experiment was conducted at
  Miami University in Oxford, Ohio. To compare the
  percentages of students that have cheated on
  exams using graphing calculators among different
  departments, samples were taken from among
  mathematics, chemistry, and physics students. The
  unrelated-question randomized response method
  applies to this situation because some people may
  feel uncomfortable responding truthfully to
  direct statements regarding sensitive issues,
  such as cheating on exams. Relative to standard
  randomized response, this method yields a smaller
  variance. The smaller variance given by the
  unrelated-question randomized response method
  allows a shorter confidence interval to be
  constructed.

24
The Change in the Number of Four-letter Words in
the English Language

• By Rachel Kahlenberg, Ohio Northern University
  and Rebekkah Dann, Messiah College
• Abstract The English language is constantly
  changing, but it is almost impossible to detect
  all of those changes without choosing a specific
  area of study. Because four letter words are an
  integral and sometimes interesting part of the
  English language, it is worthwhile to contemplate
  whether their use has changed over the past few
  decades. However, the task of counting the
  number of four-letter words would be very time
  consuming, but through the use of statistical
  sampling, the time this takes is considerably
  reduced.

25
Multivariate Statistics Group2000
26
Multivariate Classification Methods The
Prevalence of Sexually Transmitted Diseases

• By Candace Porter, Albany State University
  Michael Sotelo, California PolytechnicPomona
  Brandon McKenzie, Centre College and Lindsay
  Kellam, Queens College
• Abstract We took a statistical look at the
  spread of sexually transmitted diseases.   Each
  year, thousands of federal and state dollars are
  allocated for STD education programs, medical
  treatments, and preventative measures. We used
  the STD situation to illustrate how multivariate
  classification methods can be used. First, we
  used principal component analysis to simplify the
  interpretation and summary of those variables
  which aid in predicting STD rates. Principal
  component analysis allowed us to depict a set of
  data using a number of descriptive factors that
  was less than the number of variables. We began
  with measurements of ten racial, ethnic,
  socioeconomic, and educational variables for each
  case and were able to combine them into four
  components that provide a clearer picture of the
  factors that predict the rate of STDs. Second,
  using discriminant analysis, we created a model
  that consisted of two groups a group with a high
  rate of STDs and another with a low rate of STDs.
  Members (cases) in each group share similar
  racial, ethnic, socioeconomic, and educational
  variables. Using this discriminant model, we can
  predict an unknown observation's group
  classification.

27
Multivariate Statistics Group2001
28
A Multivariate Statistical Analysis of State
Desirability

• By Jennifer Everson, Carthage College Melissa
  Hildt, College of Notre Dame of Maryland Jason
  Popovic, Baldwin-Wallace College and Sarah
  Zimmermann, Bemidji State University
• Abstract We determined the desirability of
  living in any state by using a set of several
  different variables.  The multivariate
  statistical methods of factor analysis and
  discriminant analysis lend themselves to this
  issue.  We used factor analysis to reduce a large
  number of variables to a smaller set of common
  factors which describe state desirability.  We
  then used discriminant analysis to classify
  states according to their desirability level
  based on a set of measured variables.

29
Multivariate Statistics Group2002
30
A Multivariate Statistical Analysis of the Free
World

• By David Friedenberg, Miami University and Shenek
  Heyward, Francis Marion University
• Abstract Is a democracy more than just
  competitive multiparty elections in which all
  participants have a legitimate chance of
  attaining power? Using such statistical analyses
  processes such as discriminant analysis and
  factor analysis, we hope to determine a rule for
  classifying countries from a sample into one of
  two groups, democratic or non-democratic. We
  also hope to reduce our data from 11 variables to
  a smaller set of underlying factors that can be
  used to explain the dynamics surrounding each
  country.

31
Multivariate Analysis of Vehicle Safety

• By Leigh Cobbs, Texas AM University Mary
  Cunningham, James Madison University and Cheryl
  Gerde, Morehead State University
• Abstract Vehicle safety affects our lives daily.
  To measure safety, we took a large sample of
  popular vehicles and set out to create a vehicle
  safety rating system. To do this, we used two
  multivariate techniques, Principal Components
  Analysis and Discriminant Analysis. Principal
  Components Analysis reduced our set of variables
  to a smaller set of principal components. We
  then used Discriminant Analysis to classify
  vehicles by safety rating using principal
  components scores.

32
Multivariate Statistics Group2003
33
A Multivariate Statistical Analysis of the NBA

• By Lori Hoffman, University of Wisconsin River
  Falls and Maria Joseph, Kentucky State University
• Abstract Will your favorite National Basketball
  Association (NBA) team make it to the playoffs
  this year? What variables affect a teams
  postseason outcome? In an attempt to determine
  which teams will make the NBA playoffs, we will
  collect and analyze team data using multivariate
  statistical methods including Principal
  Components Analysis and Discriminant Analysis.

34
A Multivariate Statistical Analysis of Stock
Trends

• By April Kerby, Alma College and James
  Lawrence, Miami University
• Abstract Is there a method to predict the stock
  market? What factors determine if a companys
  stock value will rise or fall in a given year?
  Using the multivariate statistical methods of
  principal component analysis and discriminant
  analysis, we aim to determine an accurate method
  for classifying a companys stock as a good or a
  poor investment choice. Additionally, we will
  explore the possibilities for reducing the
  dimensionality of a complex financial and
  economic dataset while maintaining the ability to
  account for a high percentage of the overall
  variation in the data.

35
Multivariate Statistics Group2004
36
Educating the States A Multivariate Statistical
Analysis of Education

• By Nick Imholte, Xavier University, Cincinnati
  and Sara Blight, University of Arizona, Tucson
• Abstract Educating the population is important
  in every state. To measure the quality of
  education in a state, we examine average
  Scholastic Aptitude Test scores. We create a
  model to predict future scores based on variable
  that affect education. First, we use the
  multivariate statistical methods of Principal
  Component Analysis and Factor Analysis to reduce
  the number of variables. Second, we use both of
  these methods in conjunction with Discriminant
  Analysis to create a model that predicts future
  scores. Finally, we use the results of
  Discriminant Analysis to conjecture how to
  improve the quality of education.

37
A Multivariate Statistical Analysis of Crime Rate
in US Cities

• By Kendall Williams, Howard University and Ralph
  Gedeon, University of Florida
• We classify a city as safe or unsafe by using
  multivariate methods of Principal Components,
  Factor Analysis, and Discriminant Analysis. In
  addition, we discover which variables have
  salience in the identification of a city being
  safe or dangerous. The fore mentioned analytical
  techniques can assist city governments in finding
  out what variables they need to change to improve
  their state or city and make it a better place to
  live.

38
Multivariate Statistics Group2005
39
A Multivariate Statistical Analysis of Substance
Abuse in the United States

• Joshua Svenson, Baldwin-Wallace Collegeand
  Monique Owens, Central State University
• Where do the major drug problems occur in this
  country among the states?  How are social and
  economic factors related to substance abuse in
  the states?  We approach these questions with
  multivariate statistics.  By using factor
  analysis, we distinguish the underlying factors
  of a collection of variables related to substance
  abuse.  With discriminant analysis, we design a
  rule for classifying states as either having a
  major drug problem or minor drug problem. 

40
A Multivariate Statistical Analysis of Female
Empowerment

• Janelle Jones, Spelman Collegeand AdriAnne
  Demski, Clarion University
• As women of the world struggle for equality there
  is a need for ways of measuring progress.  We
  explore the empowerment of women using
  multivariate statistical techniques such as
  factor analysis and discriminant analysis. We
  hope to classify countries into two populations,
  one where women are empowered and the other where
  women are not.  We simplify this process by
  reducing the dimensionality of the data from 13
  variables to a smaller collection of underlying
  factors.

41
Multivariate Statistics Group2006
42
Education By Nation A Multivariate Statistical
Analysis

• Ashley Brooks, Winston Salem State University,
  Amber Shoecraft, Johnson C. Smith University, and
  Anthony Franklin, Coastal Carolina University
• We analyze education systems of 64 countries
  using multivariate statistical techniques such as
  principal component analysis, factor analysis,
  and discriminant analysis. Our goal is to
  classify countries into two populations, one
  where the educational system of the country is
  exceptional and the other where the educational
  system is fair. Reducing the dimensionality of
  the data set simplifies this process.
• Education is our passport to the future, for
  tomorrow belongs to the people who prepare for it
  today.-- Malcolm X

43
Reckless or Responsible A Multivariate
Statistical Analysis of Consumer Spending

• Emilola Abayomi, Albany State University, Erin
  Esp, Montana Tech and Shannon Grant, University
  of Idaho
• As Americans spend more and save less, there is a
  need to evaluate variables which influence
  spending habits. First, we reduce the number of
  variables with Principal Components analysis and
  identify underlying factors by grouping
  correlated variables in Factor Analysis.
  Finally, we use Discriminant Analysis to develop
  a rule for classifying individual consumers as
  either reckless or responsible spenders.

44
Multivariate Statistics Group2007
45
College Desirability  A Multivariate Statistical
Analysis

•             By Andrea M. Austin, Terrell A.
  Felder, Lindsay M. Moomaw
• The colleges and universities across the United
  States are all unique. To quantify how
  institutions of all sizes measure up,
  multivariate techniques of Principal Component
  Analysis, Factor Analysis, and Discriminant
  Analysis are used fittingly and effectively,
  producing a valid, unbiased evaluation of each
  school, and also a model to gauge any chosen
  seminary. The method of Principal Components
  reduces the number of variables, focusing on
  those with efficacy while Factor Analysis
  provides a data reduction to explain the
  variability of the college or university
  statistics. Finally, a Discriminant Analysis of
  the data classifies the schools and establishes a
  method of accurate prediction.
• Directed by Dr. Vasant Waikar, with graduate
  assistant, Kevin Tolliver

46
Risky Behavior A Multivariate Statistical
Analysis of the United States Based on Health
Risk Factors

• By Christina McIntosh, Alicia Smith, Ashley
  Swandby
• Under the direction of Dr. Vasant Waikar and
  graduate assistant, Kevin Tolliver, Christina,
  Alicia and Ashley studied a number of variables
  associated with health risk factors in the United
  States.  They used the 2006 Centers for Disease
  Controls Behavioral Risk Factor Surveillance
  System survey data to analyze each state based on
  these variables. They used Principal Component
  Analysis, Factor Analysis, and Discriminant
  Analysis in order to analyze the multivariate
  data. Furthermore, they provided a ranking of
  relative health for some of the states based on
  the analysis.

47
Outcomes and Conclusions

• 129 total participants
• 18.5 are still undergraduates
• 70 are either in grad school or hold graduate
  degree
• Remainder are in education, government and
  private business, including banking, insurance,
  cancer research and defense research

48
Awards

• Several papers received awards at the American
  Mathematical Society Annual Meetings
• One statistical paper won a student award at the
  Joint Statistical Meetings in competition with
  Ph.D. students

Shenek Heyward works on her award winning paper
with David Friedenberg
49
Results for Minority Students

• 64 minority participants
• 51 now hold bachelor degrees
• 44 in graduate school or have graduate degree

50
Results for Women

• 99 female participants
• 82 have graduated
• 69 in graduate programs or hold graduate degree

Women of SUMSRI 2007
51
References

• 1 Alderete, J.F., February 16, 1998. Absence
  of Minorities from Research Fields Will Result in
  Grave Consequences in U.S., The Scientist
  1248.
• 2 Davenport, D.E. and, B. Porter 2004.
  Starting and Running an REU for Minorities and
  Women. Accepted for publication in Primus.

52
Questions?