# Statistics

Statistics is a branch of mathematics that deals with the gathering, organizing, analyzing and drawing conclusions from data.

## Program Overview

Statistics is used in most of the professions, in most sectors of the economy, and in a great many academic areas.

Courses in the Department of Mathematics and Statistics are designed to:

• teach the language of the mathematical sciences
• provide a command of powerful mathematical tools
• develop problem-solving skills
• foster the ability to ask questions and make independent discoveries
• encourage the experience of mathematics as a distinctively rigorous way of knowing.

In addition, especially through the statistics offering, the rich interplay between an applied context and mathematical models in working with numerical data is an area of particular emphasis.

Each year some of our students enter graduate programs in statistics, or in allied fields (business, economics, education, or psychology). Many enter the job market and later pursue advanced degrees.

Community Voices

## Spotlight on Math and Statistics students and alums

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Kylee Miller ’24

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Lupe Antonio Lopez ’23

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## Learning Goals

We welcome all students into the Statistics major, and we aim to create an inclusive, supportive environment for everyone. Statistics majors have the following learning goals:

• Communicate statistical concepts and their interpretation, with statistical colleagues and with a wider audience

• Describe key statistical methods and the reasoning behind them

• Use appropriate statistical and computational methods to explore data and draw conclusions

• Ask questions about new methods and applications, learn new techniques, and make new discoveries

• Incorporate “big picture” reasoning, including ethics, practicality, and creativity, into statistical practice

• Develop the independence to approach new problems, and the ability to collaborate effectively.

## Requirements for the Major

A minimum of 36 credits:

As a prerequisite for MATH-203:
MATH-101
Calculus I
MATH-102
Calculus II
MATH-203Calculus III4
MATH-211Linear Algebra4
As a prerequisite for STAT-242:
STAT-140
Introduction to the Ideas and Applications of Statistics
STAT-242Intermediate Statistics4
STAT-340Applied Regression Methods4
MATH-342Probability4
STAT-343Mathematical Statistics4
12 additional credits in mathematics or statistics at the 200-level or above 112
Total Credits36
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.

Students considering developing a special major in statistics and economics should consult the Special Major chapter.

## Requirements for the Minor

A minimum of 16 credits:

At least one 200-level course in statistics4
At least one 300-level course in statistics4
Two additional courses in mathematics or statistics at the 200 level or above8
Total Credits16

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.

### 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.

Many students with these interests design a special major in mathematics and economics or a 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).

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 abstract algebra 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
T. Day, M. Ozanne
Advisory: 2 years of high school algebra

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
I. Beaudry, C. Hosman
Prereq: STAT-140 or equivalent.

STAT-244 Intermediate Topics in Statistics

STAT-244MP Intermediate Topics in Statistics: 'Survey Sampling'

Fall. 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, estimation, poststratification, imputation, and survey error. We will also apply these methods by frequently using real (and often messy) survey data through assignments and projects. The analysis of the data will be performed through R programming. Background should include estimation, confidence intervals and hypothesis testing.

Applies to requirement(s): Math Sciences
I. Beaudry
Prereq: STAT-140.
Notes: No prior knowledge of the statistical software R is required.

STAT-244NF Intermediate Topics in Statistics: 'Infectious Disease Modeling'

Spring. Credits: 4

Infectious disease has plagued humanity since time immemorial. Statistical models serve a critical role in improving understanding of the progression and proliferation of infection in a population, as well as the impact of interventions in stopping the spread of disease. In this course, we will explore regression and compartmental model-based approaches, which will be motivated by some of the most impactful epidemics and pandemics in recent history, including HIV/AIDS, Ebola, Zika, and COVID-19. R statistical software will be used.

Applies to requirement(s): Math Sciences
M. Ozanne
Prereq: STAT-140.

STAT-244NP Intermediate Topics in Statistics: 'Nonparametric Statistics'

Not Scheduled for This Year. Credits: 4

The methods taught in traditional statistics courses are based on assumptions that are often not satisfied by real data sets. In this course we will learn about approaches that require fewer assumptions, known as nonparametric methods. After taking this course, students will be able to examine assumptions for different approaches to statistical inference, compare nonparametric statistical tests such as sign and Wilcoxon tests to their parametric equivalents, and implement non-parametric approaches using R. In addition, the course will incorporate computational techniques for statistical analysis, including simulation, permutation tests, and bootstrapping.

Applies to requirement(s): Math Sciences
The department
Prereq: STAT-140.
Advisory: Students should have experience with the programming language R.

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-331 Design of Experiments

Not Scheduled for This Year. Credits: 4

How do you get informative research results? By doing the right experiment in the first place. We'll look at the techniques used to plan experiments that are both efficient and statistically sound, the analysis of the resulting data, and the conclusions we can draw from that analysis. Using a framework of optimal design, we'll examine the theory both of classical designs and of alternatives when those designs aren't appropriate. On the applied side, we'll use R to explore real-world experimental data from science, industry, and everyday life; and we'll discuss key principles for working with expert (and not-so-expert) collaborators to help them set up the experiments they need.

Applies to requirement(s): Math Sciences
The department
Prereq: STAT-242.

STAT-340 Applied Regression Methods

Fall and Spring. 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
I. Beaudry, L. Tupper
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
L. Tupper
Prereq: MATH-102 and MATH-342.

STAT-344 Seminar in Statistics and Scientific Research

STAT-344TM Seminar in Statistics and Scientific Research: 'Time Series Analysis'

Spring. Credits: 4

Time series -- data collected across time -- show up in a vast range of application areas, from climate to economics to music. But they can have special behaviors, like seasonality, memory, and directionality, that require some special treatment! We'll look at tools for describing, modeling, and predicting time series behavior. Topics include decomposition, ARIMA, exponential smoothing, dynamic regression, and a foray into the frequency domain. We'll apply these concepts using real datasets in R.

Applies to requirement(s): Math Sciences
L. Tupper
Prereq: STAT-242 and MATH-211.
Advisory: Previous or concurrent registration in STAT-340 (or other multiple regression experience) is recommended.

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.

The Department of Mathematics and Statistics strives to teach the language of the mathematical sciences, provide a command of mathematical tools, develop problem-solving skills, foster an ability to ask questions and make independent discoveries.