MATH 530: Statistical Methods I
Department of Applied Mathematics and Statistics, CSM
Fall 2013
Syllabus
Instructor: Dr. Amanda S. Hering
E-mail: ahering@mines.edu
Phone: 303.384.2462
Office: 235 Chauvenet Hall
Office Hours: M 10-11, T 10-11, R 10-11, F 10-11.
Grader: Brian Zaharatos
E-mail: bzaharat@mymail.mines.edu
Office: 270 Chauvenet Hall
Office Hours: TBA
Prereq: MATH 213 (Multivariable calculus, including partial derivatives, multiple integration, and vector calculus) or equivalent.
Course Schedule: MWF 9-9:50am, Location Chauvenet Hall 143
Web Page: The username and password for the class website will be given in class.
http://inside.mines.edu/~ahering/protect/math530/
Course Description: Introduction to probability, random variables, and discrete and continuous probability models. Elementary simulation and bootstrapping. Data summarization and analysis. Confidence intervals and hypothesis testing for means and
variances. Distribution-free (i.e., nonparametric) techniques.
Textbook: (Required) Tamhane, A. C. and Dunlop, D. D. (2000) Statistics and Data
Analysis: From Elementary to Intermediate. Prentice Hall: Upper Saddle River, NJ.
ISBN: 0-1374-4426-5
(Optional) Dalgaard, Peter. (2008) Introductory Statistics with R. Springer Science
and Business Media.
ISBN: 978-0-387-79053-4.
Can be accessed for free through the university at the following website:
http://www.springerlink.com/content/978-0-387-79054-1#section=215103&page=1
Computing: All statistical computing will be demonstrated with the freely available R
software, and example code and datasets will be posted on the class webpage. You
are welcome to use other packages, such as Matlab or Mathematica, but R has many
built in functions that other more general packages lack. If you choose to use another
software package, you are on your own, and be aware that many tasks may become
more time-consuming.
Course Work: Your grade for the course will be based on the following (relative weights
given in percentage):
• Homework Assignments (30%): Homework assignments will be given approximately every other week throughout the semester. Assignments will be collected
at the START of class on the due date. Late assignments will not be accepted. The very first assignment labelled “Homework 0” is optional and is a
work-through-on-your-own introduction to R. If you choose to complete and submit this assignment, its score can be used to replace your lowest score on any
other required homework assignment.
• Exams (35% each): There will be one midterm exam, tentatively scheduled for
Wednesday, October 9th. The midterm may have an out-of-class component as
well. There is a comprehensive final exam that is likely to be a take-home exam.
The following letter grades are guaranteed:
A
B
C
D
F
100-90% 89-80% 79-70% 69-60% 59-0%
Exceptions: If you are unable to take an exam or complete an assignment on time due
to illness, accident, or circumstances beyond your control, please e-mail me within
24 hours of the exam or deadline so that appropriate arrangements can be made. If
you know ahead of time that you will have a university excused absence, homework
assignments are due before you leave, and exams will be made up after you return.
Copyright: The materials used in this course are copyrighted. By materials, I mean all
materials generated for this class including syllabi, exams, course notes, computer
code, and examples. Because these materials are copyrighted, you do not have the
right to copy the handouts or distribute them, unless I expressly grant permission.
Policy on academic integrity/misconduct: The Colorado School of Mines affirms the
principle that all individuals associated with the Mines academic community have a
responsibility for establishing, maintaining an fostering an understanding and appreciation for academic integrity. In broad terms, this implies protecting the environment
of mutual trust within which scholarly exchange occurs, supporting the ability of the
faculty to fairly and effectively evaluate every students academic achievements, and
giving credence to the universitys educational mission, its scholarly objectives and the
substance of the degrees it awards. The protection of academic integrity requires there
to be clear and consistent standards, as well as confrontation and sanctions when individuals violate those standards. The Colorado School of Mines desires an environment
free of any and all forms of academic misconduct and expects students to act with
integrity at all times.
2
Academic misconduct is the intentional act of fraud, in which an individual seeks to
claim credit for the work and efforts of another without authorization, or uses unauthorized materials or fabricated information in any academic exercise. Student Academic
Misconduct arises when a student violates the principle of academic integrity. Such
behavior erodes mutual trust, distorts the fair evaluation of academic achievements,
violates the ethical code of behavior upon which education and scholarship rest, and
undermines the credibility of the university. Because of the serious institutional and individual ramifications, student misconduct arising from violations of academic integrity
is not tolerated at Mines. If a student is found to have engaged in such misconduct
sanctions such as change of a grade, loss of institutional privileges, or academic suspension or dismissal may be imposed. The complete policy is online.
Notes: A few more things...
• Check the website frequently for updates.
• I would like to know about any particular academic difficulties or personal problems that are affecting a student’s performance.
Student Learning Outcomes: At the conclusion of this class, students should be able to:
1. compute basic probabilities and be familiar with common distributions,
2. apply appropriate exploratory data analysis techniques,
3. compute and interpret confidence intervals, p-values, and hypothesis tests,
4. identify and assess assumptions of each statistical method and know when a
method is appropriate, and
5. do some simple numerical experiments such as bootstrapping and permutation
tests.
Course Outline: The list of topics on the following page are a rough outline of what will
be covered in this course:
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Topic
1. Introduction
Introduction to statistical modeling
2. Probability Theory
Probability Rules
Characterizing random variables
Joint probability models
Discrete probability models
Continuous probability models
Functions of random variables
3. Collecting Data
Observational studies
Experimental studies
4. Summarizing and Exploring Data
Quantitative and categorical variables
Numerical and visual summarization of data
5. Sampling Distributions
SD of Sample Mean
SD of Sample Proportion
SD of Sample Variance
6. Basic Estimation and Simulation
Point estimators, bias, and variance
Maximum likelihood estimation
Bayesian estimation
Bootstrap estimators
7. Confidence Intervals–Single Sample
C.I. for mean, proportion, and variance
Prediction and tolerance intervals
Multiple intervals
Bootstrap intervals
8. Testing Hypotheses–Single Sample
Type I and II errors
Power and p-values
H.T. for mean, proportion, and variance
9. CI & HT–Two Samples
Comparing 2 means,
2 proportions,
2 variances
10. Nonparametric Tests
Tests for median
Test to compare independent samples
Permutation tests
Simulation studies
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Textbook Section
1.1-1.4
2.1, 2.2
2.3, 2.4
2.5
2.7
2.8, 2.9
2.10
3.1
3.2-3.3
3.4
4.1, 4.2
4.3, 4.4
5.1, 5.3
5.1.2
5.2, 5.4
6.1
15.1
15.3
14.6
6.2
7.1.1, 7.2.1, 9.1.1, 7.3.1
7.4
NA
NA
6.3
6.3
7.1.2, 7.2.2, 9.1.2, 7.3.2
8.1, 8.2
8.3
9.2
8.4
14.1
14.2
NA
2013 Tentative Semester Schedule
Monday
Wednesday
Aug 19th
Friday
Aug 21st
Aug 23rd
Aug 28th
Aug 30th
First Day of Class
Aug 26th
Hmwk#0
Sep 2nd
Sep 4th
Sep 6th
Hmwk#1
Sep 9th
Sep 11th
Sep 13th
Sep 16th
Sep 18th
Sep 20th
Hmwk#2
Sep 23rd
Sep 25th
Sep 27th
Sep 30th
Oct 2nd
Oct 4th
Hmwk#3
Oct 7th
Oct 9th
Oct 11th
Oct 16th
Oct 18th
Midterm
Oct 14th
Fall Break
Hmwk#4
Oct 21st
Oct 23rd
Oct 25th
Oct 28th
Oct 30th
Nov 1st
Hmwk#5
Nov 4th
Nov 6th
Nov 8th
Nov 11th
Nov 13th
Nov 15th
Hmwk#6
Nov 18th
Nov 20
Nov 25th
Nov 27th
Thanksgiving
Dec 4th
Dec 6th
Dec 11th
Dec 13th
Last Class
Dec 9th
Final Exams
Nov 29th
Thanksgiving
Dec 2nd
Hmwk#7
Nov 22th
Final Exams
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