Research Experience for Undergraduates (REU) in Statistics at Miami University Vasant B. Waikar,...

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

Vasant B. Waikar,Miami UniversityOxford, OH, USA [email protected]

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

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

SUMSRI Faculty & Students-2008

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

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

Programs that Make a Difference

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

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)

PersonnelDirectors: Dennis Davenport and Vasant Waikar

Patrick Dowling (Real Analysis) & Bonita Porter, Program Coordinator

Research Seminar Directors: Edray Goins, Vasant Waikar & Reza

Akhtar

Not pictured: Dennis Keeler, Algebraic Topology, & Dennis Davenport: GRE Prep

Thomas Farmer, Mathematical Writing

List of Personnel—2006

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.

Organization

Director(s)

Coordinator

4 Short Course Instructors

3 Research Seminar Directors

3 graduate assistants

Statistical Research Seminar

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

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

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

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

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 A&M University Mary Cunnigham, James Madison University Cheryl Gerde, Morehead State University

2003

A Multivariate Statistical Analysis of Stock Trends April Kerby, Alma College James Lawrence, Miami University

A Multivariate Statistical Analysis of the NBA Lori Hoffman, University of Wisconsin,

River Falls Maria Joseph, Kentucky State University

2004

Educating the States: A Multivariate Statistical Analysis of EducationNick Imholte, Xavier University, Cincinnati Sara Blight, University of Arizona, Tucson

A Multivariate Statistical Analysis of Crime Rate in US CitiesKendall Williams, Howard University Ralph Gedeon, University of Florida

2005

A Multivariate Statistical Analysis of Substance Abuse in the United StatesJoshua Svenson, Baldwin-Wallace CollegeMonique Owens, Central State University

A Multivariate Statistical Analysis of Female EmpowermentJanelle Jones, Spelman CollegeAdriAnne Demski, Clarion University

2006

Reckless or Responsible: A Multivariate Statistical Analysis of Consumer Spending

Emilola Abayomi, Albany State UniversityErin Esp, Montana TechShannon Grant, University of Idaho

Education By Nation: A Multivariate Statistical Analysis

Ashley Brooks, Winston Salem State UniversityAmber Shoecraft, Johnson C. Smith UniversityAnthony Franklin, Coastal Carolina University

2007 College Desirability: A Multivariate

Statistical Analysis Andrea M. Austin, St. Michael's CollegeTerrell A. Felder, North Carolina A & TLindsay 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

ABSTRACTS

Multivariate Statistics 1999

Rebecca Dann and Lynn Holmes give their final presentations.

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.

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.

Multivariate Statistics Group2000

Multivariate Classification Methods: The Prevalence of Sexually Transmitted Diseases

By Candace Porter, Albany State University; Michael Sotelo, California Polytechnic—Pomona; 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.

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.

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.

Multivariate Analysis of Vehicle Safety

By Leigh Cobbs, Texas A&M 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.

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 team’s 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.

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 company’s 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 company’s 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.

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.

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.

A Multivariate Statistical Analysis of

Substance Abuse in the United States Joshua Svenson, Baldwin-Wallace College

and 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.

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.

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

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.

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

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 Control’s 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.

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

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

Results for Minority Students

64 minority participants

51 now hold bachelor degrees

44 in graduate school or have graduate degree

Results for Women

99 female participants

82 have graduated

69 in graduate programs or hold graduate degree

Women of SUMSRI 2007

References

[1] Alderete, J.F., February 16, 1998. Absence of Minorities from Research Fields Will Result in Grave Consequences in U.S., The Scientist 12[4]:8.

[2] Davenport, D.E. and, B. Porter 2004. Starting and Running an REU for Minorities and Women. Accepted for publication in Primus.

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