George Mason University
Volgenau School of Information Technology and Engineering
Department of Statistics
STAT 657: Nonparametric Statistics
Fall Semester, 2018
Thursdays from 7:20 to 10:00 PM (starting Aug. 30, with other dates given below)
Location: room B203 of
Robinson Hall
Contact Information (phone, fax,
e-mail, etc.)
Office Hours: 6:15-7:00 & 10:00-10:30 PM
on class nights
(more information)
(This book should be considered as required, as some of the
homework problems will come straight from this book, and my lectures will be based heavily on the book.)
(Read the bottom portion of this
web page in order to learn how you can obtain a copy of the
required software at a very low price. This software should be considered as required, as I think it will
be very hard to do a lot of the homework and pass the course without having access to StatXact.)
Description:
This course is a graduate-level course on nonparametric statistics for students who already have a decent knowledge of
basic statistics and probability. The
focus is on standard nonparametric procedures useful for the
analysis of experimental data. One-sample, two-sample, matched pairs,
one-way layout, and two-way layout procedures are covered.
Tests for lack of independence, tests of randomness, and
goodness-of-fit tests are also covered.
Applications are emphasized, but theory
is not completely neglected. State-of-the-art software for exact
nonparametric inferences is to be used throughout the semester.
(Note: Nonparametric density estimation, nonparametric methods for classification, nonparametric regression, nonparametric
methods for survival analysis, and computer-intensive nonparametric methods
such as bootstrapping are not covered. These are topics that should be covered in other courses, and there isn't enough time to
cover them adequately in this course. Also, additional prerequisites would make sense for some of these topics.)
Basically, the course will cover, in order, most of the first 13 chapters of the text book (except parts of Ch.1 will be skipped,
and material from Ch. 13 will be moved up and inserted sooner). Additional material related to StatXact will supplement
the material from the text book. (Note: Ch. 14 of the text book will not be covered since it is material that should be covered
in GMU's graduate-level course on categorical data anlysis.)
(Approximate) Class-by-Class Content:
(I think that during the first portion of the semester we'll be behind the pace indicated below, but then we'll catch up and for most
of the semester we'll be ahead of the pace indicated below.)
- [1] Aug. 30:
- introduction (class policies, strengths and limitations of nonparametric
procedures); review of some basic probability concepts with an emphasis on order statistics (including distributions of order statistics)
[the first portion of Ch. 1 of the text and the first portion of Ch. 2 of the text]
- [2] Sep. 6:
- more on order statistics (with an emphasis on asymptotic results); tolerance limits
[the second portion of Ch. 2 of the text]
- [3] Sep. 13:
- tests about randomness (tests based on runs for lack of independence, tests for trend)
[the first portion of Ch. 3 of the text]
- [4] Sep. 20:
- more varieties of tests about randomness
[the second portion of Ch. 3 of the text]
- [5] Sep. 27:
- goodness-of-fit tests
[the first portion of Ch. 4 of the text]
- [6] Oct. 4:
- more varieties of goodness-of-fit tests
[the second portion of Ch. 4 of the text and some supplementary material]
- [7] Oct. 11:
- one-sample and paired-samples procedures (inferences about quantiles, the sign test,
rank-order statistics, the signed-rank test)
[Ch. 5 of the text]
- [8] Oct. 18:
- more on one-sample and paired-samples procedures
(the one-sample normal-scores test, Fisher's permutation test, and StatXact's handling of ties), locally most powerful tests and ARE
[part of Ch. 13 of the text and some supplementary material]
- [9] Oct. 25:
- the general two-sample problem (with an emphasis on omnibus tests)
[Ch. 6 of the text]
- [10] Nov. 1:
- linear rank statistics based on two samples; linear rank tests for the two-sample location problem
[Ch. 7 and Ch. 8 of the text]
- [11] Nov. 8:
- tests for the two-sample scale problem
[Ch. 9 of the text]
- [12] Nov. 15:
- tests for the general k-sample problem (tests about the equality of 3 or more distributions),
more procedures for 3 or more samples (tests based on pairwise comparisons, comparisons with a control,
tests against monotone alternatives)
[Ch. 10 of the text and some supplementary material]
- [**] Nov. 22:
- (No class due to
Thanksgiving
Break)
- [13] Nov. 29:
- measures of association for bivariate samples and tests about the independence of two variables
(Kendall's tau coefficient, Spearman's coefficient of rank correlation, associated tests for lack of independence)
[Ch. 11 of the text]
- [14] Dec. 6:
- nonparametric procedures for two-way layouts (Friedman's test, Page's test, coefficients of concordance)
[Ch. 12 of the text]
- [**] Dec. 13:
- Final Exam (note: exam period is
from 7:30 to 10:15 PM)
Learning Outcomes:
- Understand the null and alternative hypotheses for a wide variety of nonparametric tests.
- Be able to derive the null sampling distributions for a wide variety of nonparametric tests, and be familiar with their approximate large-sample distributions.
- Know about the power characteristics of a wide variety of nonparametric tests.
Grading:
Additional Comments:
- be sure to note that there is no class on November 22
due to GMU's Thanksgiving Break
- I can possibly make arrangements to meet with you outside of my
scheduled office hours, with Friday afternoons between 1:30 and 3:30 generally being
the best time to meet --- send me e-mail if you want to schedule a time to meet
- put STAT 657 in the subject line when you send me e-mail
- please do not leave long messages on my voice-mail,
and since I often do not get around to returning calls until the
evening, you should
leave both your day and evening phone numbers, speaking slowly
(even though you may have given them to me previously); I much prefer to
communicate in person or via e-mail than over the phone (phone tag gets
frustrating, and I've experienced problems with the reliability of the
GMU voice-mail system --- but I will try to return your calls if you're unable to
communicate via e-mail when you're off campus)
- please abide by the university policy that cell phone ringers be
turned off while class is in session
- please do not make a lot of noise eating during class --- if you
feel that you must eat during class, please choose a soft candy bar
rather than a bag of potato chips (since both the chips and the bag they
come in tend to make too much noise when eaten and handled)
- you are expected to familiarize yourself with the
George Mason University honor code and abide by it; although it is
perfectly okay to have limited discussion with others on most of the
homework problems, you shouldn't look at another student's work or use his/hers StatXact results while writing up your solutions, and you
will be considered to be a violation of the honor code if you give or
receive unauthorized aid on certain specified homework problems or the final exam
- you are expected to take the final exam during the
designated time slot; Incompletes will
not be granted except under very unusual circumstances
- any class meetings canceled by the university due to
snow, sleet, power outage, bombing,
etc. will be made up if possible;
with regard to bad weather, I plan to teach class if
the university is open and not teach it if the university is closed, so
instead of calling me if it snows, simply check to determine if the
university is open or closed
- if you are a student with a disability and desire academic accommodations, please see me during the first two week of classes and
contact the
Office of Disability Services (ODS); all academic accommodations must be arranged through the ODS
- caveat: the schedule and procedures described
here for this course are subject to change; it is the responsibility of
students to attend all class meetings, and to check this web site
regularly, in order to keep themselves informed of
any changes