Math 408 - Nonparametric Statistics - Spring 2007

Statistical methods that make almost no assumptions about the probability distribution of data.

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, jackknife and bootstrap methods, Kolmogorov-Smirnov tests, and topics chosen from nonparametric regressions and nonparametric density estimation.
Computer programs in C or a related language will be used to evaluate the accuracy of normal approximations of nonparametric tests, and and to carry out statistical procedures that cannot easily be done by hand (such as bootstrap methods and density estimation). Sample C programs will be posted on the Web site to illustrate the programming techniques that will be used. Math 1201 would be helpful but is not required.

Prerequisites: Mathematics 420 or 493, or permission of the instructor.
Time and Location:   TTh 2:30-4:00pm -- Cupples I  Rm 216
Textbook: Nonparametric Statistical Methods, 2nd edition,
M. Hollander and Douglas A. Wolfe, 1999,   ISBN 0-471-19045-4
Instructor: Prof. Stanley Sawyer -- Cupples I, Room 107
Phone: (314) 935-6703   --   Send an email
Office Hours: MWF 2:00-3:00pm   Office:  Cupples I  Rm 107
(Warn me in advance if you are coming  --  other times are OK by appointment)
Links: TAKE-HOME FINAL
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

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.

Homework Sets, Exams, and Grades:
        There will be around five homework sets, an in-class midterm, and a take-home final. Grades will be based on on the homework sets (around 40%), the midterm (around 20%), and the final (around 40%). Cr means D or better if you elect ``Credit/No Credit.''

Take-Home Final:
        Due on or before Wednesday May 9 at 5:30 PM.

Collaboration:
        Collaboration on homework is allowed and can be helpful (and fun). However, you must (i) write the names of the people that you collaborated with at the top of your homework and (ii) write up your homework in your own words.

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.)
        This is a standard advanced book on nonparametric statistics.

Useful 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/.)

An Extremely Useful Reference Manual:
        1. C: A Reference Manual, 5th edition
        (by S. B. Harbisoon III and G. L. Steele, Prentice Hall, 2002.)
        (A good reference manual for modern C. If a feature or standard library function is not explained clearly in the reference, you cannot assume that it will be in C99 C. A bit condensed for someone who doesn't have experience in computing programming in, for example, BASIC or C or C++, but explains all features of C99 C clearly. Some features and functions may not exist in C 89 versions of C such as Microsoft Visual C, but the very conservation description of C99 C should mean that this may not happen very often. An invaluable companion for Gnu C, which is C 99 and not very well documented.)

Suggested Books for Learning C Programing:
        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 may be too condensed for a new C programmer without 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, appropriately, 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, could be used 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.

Top of this page

Click here for Stanley Sawyer's home page:

Last modified May 25, 2008