Course Description
Techniques and applications of nonparametric statistical methods, estimates, confidence intervals, one sample tests, two sample tests, several sample tests, tests of fit, nonparametric analysis of variance, correlation tests, chi-square test of independence and homogeneity, sample size determination for some nonparametric tests.
Additional Requirements for Graduate Students:
Additional and/or alternative problems of a more challenging
nature will be required for graduate students on homework and
exams.
Athena Title
Nonparametric Methods
Undergraduate Prerequisite
(MATH 3300 or MATH 3300E or MATH 3000) and STAT 4510/6510 and (STAT 4360/6360 or STAT 4360E/6360E or STAT 4365/6365)
Graduate Prerequisite
STAT 6220 or STAT 6315 or permission of department
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
This course aims to give students a broad understanding of nonparametric statistical methods; that is, what types of statistical analysis can be carried out either when the samples are small, or when standard normality assumptions do not hold. Students will first learn about tests based on the binomial distribution, as these are likely to be most familiar from previous statistics classes. From this starting point, students will expand their knowledge base to include a number of relevant practical situations, such as the analysis of categorical data arranged in arrays. We will explore the trade-offs between nonparametric and parametric approaches in terms of statistical power, ease of computation, and other criteria. Students will also be exposed to "modern nonparametric" methods, such as the bootstrap. Students will learn how to use specific statistical methods and general modes of statistical thinking to make inferences from data, and to support (or refute) an argument or point of view with quantitative information. Students will learn the mathematical and probabilistic underpinnings of statistical methods, they will develop an understanding of the underlying rationale for specific statistical methods, and they will learn how to assess the relative merits and applicability of competing statistical techniques. Students will analyze data using the methods learned in lecture, with appropriate statistical software. Some amount of independent programming will be necessary as not all nonparametric procedures covered over the course of the semester are "built in" to existing software packages.
Topical Outline
Tests based on the binomial distribution. Contingency table analysis. Methods based on ranks. Goodness of fit statistics (Kolmogorov-Smirnov and related tests). Tests based on runs. Modern nonparametric statistics (smoothing, bootstrap).
Syllabus