Math 408 - Nonparametric Statistics - Spring 2005

Statistical methods that make minimal assumptions about probability distributions.

Topics covered:

Sign test, Wilcoxon signed rank and rank sum tests, nonparametric confidence intervals, Kruskal-Wallis and Jonckheere-Terpstra tests (like a one-way ANOVA), Friedman and Lehmann aligned-rank tests (like a two-way ANOVA), Spearman and Kendall correlation coefficients, Kolmogorov-Smirnov tests, nonparametric regressions, and related topics.
Other nonparametric methods: Jackknifes, Bootstrap estimation and testing, bootstrap confidence intervals, parametric and nonparametric bootstraps.
Computer programs in C or a related language will be used to study the properties of tests and estimators and to carry out statistical procedures that cannot be done by hand. Sample C programs will be posted on the Web site to illustrate the relevant programming techniques. Math 1201 would be helpful but is not required.

Course Hours and Room:

TTh 2:30-4:00pm -- Cupples I  Rm 115
Office Hours:
MWF 2:30-3:30pm -- Rm 107 Cupples I

Instructor:

Prof. Stanley Sawyer -- Cupples I, Room 107
Phone: (314) 935-6703
Email: sawyer@math.wustl.edu

Prerequisites:

Mathematics 420 or 493, or permission of the instructor.

Textbook:

Nonparametric Statistical Methods, 2nd edition,
M. Hollander and Douglas A. Wolfe, John Wiley and Sons, 1999, ISBN 0-471-19045-4
AN IMPORTANT NOTE ABOUT PROGRAMMING:
You should also have a book that explains C program syntex for reference and more examples (unless you want to use a programming language other than C, in which case you should have a good reference for that language).
For most programming exercises in this course, you will be able to make small modifications to a posted example C program on the Math408 Web site, but to get maximum benefit from the course you should also have a book that explains enough of C syntax so that you understand what the program statements mean in detail and how they could be modified to get different results.
See below for some suggestions for books about C.

Take-Home Final:

Due by 5:30 PM on Wednesday May 11 .

Links:

Homework Assignments
Sample C Programs
Notes about C Compilers and compiling C programs
Notes about C Compilers in the ArtSci Computer Lab
What to do when your program doesn't run
Jackknife handout (PDF)     Bootstrap handout (PDF)
Stanley Sawyer's home page
Mathematics Department Home Page
Washington University Home Page

Exams, Homework Sets, and Grades:

There will be around five or six homework sets, an inclass midterm, and a final. Grades will be based on on the homework sets (around 45%), the midterm (around 15%), and the final (around 40%). Cr means D or better if you elect ``Credit/No Credit.''

Collaboration:

Collaboration on homework is allowed and can be helpful (and fun). However, you must do all written work yourself, and write and run all computer programs yourself.

Warning:

Make a copy of each homework before you hand it in!!
It may not be returned before you need to refer to it for the next homework (or for the next test).

NOTE:   If you use a computer to do a homework problem, then hand in (in the following order):

(i) your answers to the homework problems, with references to page numbers in part (iii) if your answer depends on your computer output and the output has more than one or two pages,
(ii) the source code for all the computer program or programs that you used in part (i), and
(iii) the computer output on which you based your answers in part (i), with hand-written (or other) page numbers that you can use in part (i).

Additional Reading for Statistics:
Nonparametrics: statistical methods based on ranks

(E. L. Lehmann (1975), Holden-Day/McGraw-Hill, Oakland, California.)

References for Scientific Programming:
1. Numerical recipes in C: the art of scientific computing, 2nd edition.

(W. Press, S. Teukolsky, W. Vetterling, and B. Flannery (1992), Cambridge University Press.)
2. The GNU Scientific Library (GSL).  (See the Web site http://www.gnu.org/software/gsl/.)

Suggested Books for C Programming:
1. The C Programming Language, 2nd edition

(by B. Kernighan and D. Ritchie, Prentice Hall, 1988.)
(The standard and the most precise book for standard ANSI/ISO C89 C, which was written by the people who invented C.  Has lots of examples, but is probably too condensed for a new C programmer without good experience with other programming languages. Make sure that you get the 2nd edition of this book: The 1st edition was the bible of an earlier, now obsolete dialect of C that was called K&R C.)
2. SAMS Teach Yourself C in 21 days, 6th 3rd edition.
(by Bradley Jones and Peter Aitken, SAMS publishing, 2003.)
(Very leisurely presentation but easy to skim sections, very well written, lots of detail, good for self study, introductory chapters on Java, C++, and C#, but very out-of-date description of current C compilers.)
3. Teach Yourself C, 3rd edition.
(by Herbert Schild, McGraw-Hill, 1997.)
(Leisurely presentation, more condensed than 2., well written, good for a stand-alone course on C.)

This is by no means a complete list: You can browse through other introductory C books at the WashU bookstore and at the Borders near the Galleria. Pick one that you like, but make sure that the primary emphasis is on C and not C++, Java, or C#. The latter languages are more complex and tend to lead to programs in which you have to write much more code for overhead. The programs that you will write for this course will be relatively short as computer programs go. A more complex language than C is not necessary, although Java or C++ (or even BASIC) will work fine if you don't mind doing the extra work.

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Last modified May 2, 2005