# Statistics

**Andrea Foulkes, Chair**

**Lindsay Woloszyn, Academic Department Coordinator**

415A Clapp Laboratory

413-538-2162

https://www.mtholyoke.edu/acad/math

## Overview and Contact Information

Courses in the Department of Mathematics and Statistics are designed with several goals in mind: to teach the language of the mathematical sciences, to provide a command of powerful mathematical tools, to develop problem-solving skills, and to foster the ability to ask questions and make independent discoveries. Statistics courses, in addition, emphasize the interplay between applied context and mathematical models in working with numerical data.

## Faculty

#### This area of study is administered by the Department of Mathematics and Statistics:

Giuliana Davidoff, Robert L. Rooke Professor of Mathematics

Andrea Foulkes, Professor of Mathematics and Statistics

Janice Gifford, Professor of Statistics

Mark Peterson, Professor of Physics and Mathematics on the Alumnae Foundation

Margaret Robinson, Julia and Sarah Ann Adams Professor of Mathematics, Teaching Fall Only

Jessica Sidman, Professor of Mathematics on the John Stewart Kennedy Foundation

Dylan Shepardson, Associate Professor of Mathematics, On Leave 2018-2019

Timothy Chumley, Assistant Professor of Mathematics

Alanna Hoyer-Leitzel, Kennedy-Schelkunoff Assistant Professor of Mathematics

Evan Ray, Assistant Professor of Statistics

Peter Rosnick, Visiting Professor of Mathematics

Nathan Gray, Visiting Lecturer in Mathematics

Carrie Hosman, Visiting Lecturer in Statistics

Daniel Kelleher, Visiting Lecturer in Mathematics and Statistics

Jordan Tirrell, Visiting Lecturer in Mathematics and Statistics

Rebecca Tramel, Visiting Lecturer in Mathematics

Ashley Wheeler, Visiting Lecturer in Mathematics

## Requirements for the Major

A minimum of 36 credits:

Code | Title | Credits |
---|---|---|

As a prerequisite for MATH-203: | ||

Calculus I | ||

Calculus II | ||

MATH-203 | Calculus III | 4 |

MATH-211 | Linear Algebra | 4 |

As a prerequisite for STAT-242: | ||

Introduction to the Ideas and Applications of Statistics | ||

STAT-242 | Intermediate Statistics | 4 |

STAT-340 | Applied Regression Methods | 4 |

MATH-342 | Probability | 4 |

STAT-343 | Mathematical Statistics | 4 |

12 additional credits in mathematics or statistics at the 200-level or above ^{1} | 12 | |

Total Credits | 36 |

^{1} | A 300-level course that contains substantial mathematical or statistical content in another discipline may be used to fulfill at most 4 credits toward the major with prior departmental approval. |

## Requirements for the Minor

A minimum of 16 credits:

Code | Title | Credits |
---|---|---|

At least one 200-level course in statistics | 4 | |

At least one 300-level course in statistics | 4 | |

Two additional courses in mathematics or statistics at the 200 level or above | 8 | |

Total Credits | 16 |

### Additional Specifications

Substitutions are possible with the permission of the department. Students planning a minor in statistics should consult one of the statistics advisors.

With departmental permission, students who have already completed one 100-level exploration course may elect to enroll in a second exploration course at the 200-level so that it may be counted toward the minor.

## Course Advice

### Beginning the Study of Statistics

A natural way to begin if you have not studied statistics is with STAT-140, Introduction to the Ideas and Applications of Statistics.

A 200-level course in statistics is a good choice if you have taken an advanced placement statistics course or have taken the equivalent of a 100-level statistics course.

### Advice to Students with Special Interests

#### Actuarial science

Students interested in this area should plan to cover the material that is included in the first two actuarial exams as part of their undergraduate program. This material is included in Calculus I (MATH-101), Calculus II (MATH-102), Calculus III (MATH-203), Probability (MATH-342), and Mathematical Statistics (STAT-343), along with Macroeconomic Theory (ECON-211), Microeconomic Theory (ECON-212), and Economics of Corporate Finance (ECON-215). Students are also encouraged to obtain experience through an internship.

#### Biostatistics, public health, or natural resources

Students interested in these areas should include substantial work in biology, chemistry, geology, and/or environmental studies in their programs.

#### Economics or business

Many students with these interests choose the special major in mathematics and economics or the special major in statistics and economics.

#### Engineering

Students interested in engineering often double-major in mathematics and physics and/or participate in one of the College’s five-year, dual-degree programs with Dartmouth’s Thayer School of Engineering, or California Institute of Technology, or the University of Massachusetts (see the Other Degree and Certificate Programs chapter).

#### Graduate school

Students preparing for graduate school in statistics or mathematics often participate in an undergraduate research program in the summer after the junior year and continue with an honors thesis in the senior year. Students considering graduate work in statistics at the level of a Ph.D. are encouraged to include MATH-311 and especially MATH-301.

#### Teaching certification

Students interested in pursuing certification for middle school or secondary school should major in mathematics rather than statistics. However, there is increasing emphasis on statistics in secondary school, and any of the applied courses would provide good preparation.

## Course Offerings

**STAT-140 Introduction to the Ideas and Applications of Statistics**

*Fall and Spring. **Credits: 4*

This course provides an overview of statistical methods, their conceptual underpinnings, and their use in various settings taken from current news, as well as from the physical, biological, and social sciences. Topics will include exploring distributions and relationships, planning for data production, sampling distributions, basic ideas of inference (confidence intervals and hypothesis tests), inference for distributions, and inference for relationships, including chi-square methods for two-way tables and regression.

*Applies to requirement(s): Math Sciences**A. Foulkes, D. Kelleher, S. Nunez, E. Ray, J. Tirrell**Advisory: 2 years of high school algebra*

**STAT-240 Elementary Data Analysis and Experimental Design**

*Spring. **Credits: 4*

A fundamental fact of science is that repeated measurements exhibit variability. The course presents ways to design experiments that will reveal systematic patterns while 'controlling' the effects of variability and methods for the statistical analysis of data from well-designed experiments. Topics include completely randomized, randomized complete block, Latin Square and factorial designs, and their analysis of variance. The course emphasizes applications, with examples drawn principally from biology, psychology, and medicine.

*Applies to requirement(s): Math Sciences**J. Gifford**Prereq: Any 100-level mathematics or statistics course. *

**STAT-241 Methods in Data Science**

*Spring. **Credits: 4*

This course introduces methods in data science, including exploring problems, developing and implementing possible data analytic solutions and interpreting findings. Statistical programming and computational reasoning are emphasized. Topics include data visualization, data manipulation, data analysis and presentation. Reproducible research methods are explored and case studies are emphasized.

*Applies to requirement(s): Math Sciences**A. Foulkes**Prereq: STAT-140 and MATH-101. *

**STAT-242 Intermediate Statistics**

*Fall and Spring. **Credits: 4*

In this course, students will learn how to analyze data arising from a broad array of observational and experimental studies. Topics covered will include exploratory graphics, description techniques, the fitting and assessment of statistical models, hypothesis testing, and communication of results. Specific topics may include multiple regression, ANOVA, and non-linear regression. Statistical software will be used.

*Applies to requirement(s): Math Sciences**J. Gifford, C. Hosman, E. Ray**Prereq: STAT-140 or equivalent. *

**STAT-295 Independent Study**

*Fall and Spring. **Credits: 1 - 4*

*The department**Instructor permission required.**Advisory: The permission of the department is required for independent work to count toward the major or minor.*

**STAT-340 Applied Regression Methods**

*Fall. **Credits: 4*

This course includes methods for choosing, fitting, evaluating, and comparing statistical models; introduces statistical inference; and analyzes data sets taken from research projects in the natural, physical, and social sciences.

*Applies to requirement(s): Math Sciences**E. Ray**Prereq: MATH-211 and STAT-242. *

**STAT-343 Mathematical Statistics**

*Spring. **Credits: 4*

This course is an introduction to the mathematical theory of statistics and to the application of that theory to the real world. Topics include probability, random variables, special distributions, introduction to estimation of parameters, and hypothesis testing.

*Applies to requirement(s): Math Sciences**E. Ray**Prereq: MATH-102 and MATH-342. *

**STAT-344 Seminar in Statistics and Scientific Research**

**STAT-344SM Seminar in Statistics and Scientific Research: 'Survey Sampling'**

*Spring. **Credits: 4*

In this course, students will explore statistical techniques for designing and analyzing complex survey designs. Sample surveys are used to obtain data on demography, health, and development; to measure attitudes and beliefs; to estimate natural resources; to evaluate the impact of social programs; along with many other uses. The proper design and analysis of these surveys is crucial to their utility. We will cover topics including survey design, ratio estimation, regression estimation, poststratification, imputation, and survey error. We will also make frequent use of real (and often messy) survey data through assignments and projects. Background should include hypothesis testing, regression modeling, and estimation.

*Applies to requirement(s): Math Sciences**C. Hosman**Prereq: STAT-340. *

**STAT-344SP Seminar in Statistics and Scientific Research: 'Stochastic Processes'**

*Spring. **Credits: 4*

A stochastic process is a collection of random variables. For example, the daily prices of a particular stock are a stochastic process. Topics of this course will include Markov chains, queueing theory, the Poisson process, and Brownian motion. In addition to theory, the course will investigate applications of stochastic processes, including models of call centers and models of stock prices. Simulations of stochastic processes will also be used to compare with the theory.

*Crosslisted as: MATH-339SP**Applies to requirement(s): Math Sciences**T. Chumley**Prereq: MATH-211 and MATH-342. *

**STAT-395 Independent Study**

*Fall and Spring. **Credits: 1 - 8*

*The department**Instructor permission required.**Advisory: The permission of the department is required for independent work to count toward the major or minor.*