Pesticide concentrations in soil samples, for example, are rarely believed to follow a Gaussian distribution Zacharias, Heatwole, Mostaghimi, and Dillaha Another example is comparing home prices for two residential areas. Home prices tend to come from a right-skewed distribution with some very large values pulling the mean upward, so the median home price for a particular area is usually reported instead of the mean. One would be more interested in a difference between the medians than in a difference between the means.
Data sets with outliers are appropriate because nonparametric procedures tend to be inherently robust. A data set with one or more outliers can be used to illustrate differences between the sign and signed rank tests. These are only a few of many such examples. Indeed, Micceri claimed that Gaussian or symmetric light-tailed distributions occur very rarely in social and behavioral science research thanks to a referee for pointing out this reference. Many times the two approaches will lead to the same conclusion, but the assumptions may only be valid for one of the procedures.
When the classical and nonparametric procedures yield different results, it is usually the nonparametric method that is considered more appropriate. It must be stressed that a comparison of the results of the two approaches is suggested here for pedagogical purposes only and not in order to determine which test is appropriate for the problem at hand.
The correct procedure parametric or nonparametric should be chosen on the basis of the experimental design, the parameter s of interest, the hypotheses being tested, and the strength of the assumptions that can be made. Finally, it is important to recognize that there may not be a clear answer as to which procedure is most appropriate in a given problem American Statistical Association In addition to the usual merits of writing expounded by these and other authors, the inclusion of some writing has several unique benefits in a nonparametric statistics course:.
Students might be asked to compare and contrast the computation or efficiencies of parametric and nonparametric procedures. Writing assignments can also be used to ensure that students understand the various meanings of the terms 'nonparametric' and 'distribution-free. Another possibility is to ask for a short, purely verbal description of how a particular nonparametric test works. For example, the Wilcoxon signed rank test adds the ranks of the absolute values of the positive observations rather than the ranks of the positive observations, as is sometimes incorrectly stated.
In the two-sample location problem, the Hodges-Lehmann estimator of the difference in population medians based on Mood's median statistic is the difference in the sample medians, while the Hodges-Lehmann estimator based on the Mann-Whitney-Wilcoxon statistic is the median of the pairwise differences.
Forcing students to put concepts such as these into words will strengthen their understanding of those concepts. In this section we discuss some issues related to the use of projects in nonparametric statistics courses in particular. By a project we mean, at the very least, a complete statistical analysis of a problem, including an introduction, discussion of statistical methods used, critique of assumptions, analysis of data, and conclusions. Projects may be done individually or in groups.
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Some of the facets of projects can also be incorporated in other aspects of a course, such as homework assignments. In this way students will learn that experimental design is not simply another topic from classical statistics, but that it is also important in nonparametric statistics. This does not mean that a course in experimental design must be a prerequisite to the nonparametric statistics course. The basic designs used in most nonparametrics courses one and two-sample location models, one and two-way layouts and regression are usually simple enough to be understood by students without extensive training in design.
It can be very helpful for undergraduates especially those majoring in statistics or mathematics to see real applications of statistics in other fields of study. Often such applications yield legitimate questions about the validity of the assumptions of classical statistical procedures. This reinforces the importance of nonparametric methods to sound statistical practice. Advanced students can read journal articles and prepare statistical reports on them. In a graduate service course, the students often use data from their own research for class projects.
The effectiveness of this approach is enhanced by requiring that a particular model, for example the one-way layout or two-way layout, be used. Students are thereby forced to think about how to design a study or an experiment so that the appropriate statistical procedures can be used. The idea of having students collect their own data has been very successful in the author's experience, with a number of students commenting favorably on this aspect of a recent course in their end-of-semester evaluations.
In other words, should students analyze their data in the way they believe to be the most appropriate statistically or should the project always include the nonparametric procedures being covered in class? There are obvious advantages and disadvantages to each approach and of course some compromise between these two approaches is possible.
Applied Nonparametric Statistical Methods, 3rd Edition - Semantic Scholar
This list also emphasizes the point that having students collect their own data permits them to combine their personal interests with statistics, thus increasing student excitement in the course. Because it can make for a rather dry lecture to go through hand calculations in class, a good way to demonstrate the calculations is through a handout given to students to study between classes.
Questions on it can be received at the beginning of the next class meeting. Hand calculations can also be included on homework assignments or examinations, provided that the students are aware that this is expected of them. In nonparametric statistics the hand calculations have a nature all their own. Evidences of this include the prevalence of integer arithmetic, counting techniques, and indicator functions. An excellent example of the type of hand calculations that should be well understood by students of nonparametric statistics except perhaps those in service courses is the derivation of the exact distribution, mean, and variance of the Wilcoxon signed rank statistic.
They have been referred to as 'rough and ready,' 'quick and dirty,' and 'back-of-the-envelope' methods. The author has often reminded his students that many nonparametric procedures can be carried out by researchers while they are collecting data in the laboratory or in the field where a computer is not readily available. The choice of computing package is a difficult one and no specific recommendations are made here.
These programs permit students to carry out many of the nonparametric procedures that are taught in the course but are not readily available in the major statistical computing packages. Examples include the Kolmogorov-Smirnov one and two-sample tests, the Moses and jackknife two-sample dispersion tests Moses , Miller , Kendall's tau Kendall , and kernel regression Nadaraya , Watson A complete list of these macros and a summary of the commands for them are given in Appendix B.
Each main macro file. MAC is accompanied by a help file. HLP containing detailed information about how the program should be used. The macros can be downloaded electronically from the Journal of Statistics Education. This name was chosen before the author was aware that the journal Teaching Statistics has had a Computing Corner in most issues published since the Spring issue.
The Computing Corner could just as easily be held at the end of class or in the middle of class in the form of a well-timed 'commercial break' which is especially appreciated by students in classes longer than one hour.
This provides a time for discussion of issues related to computer commands, programs, and output. The book has a clear style with well-organized material. The book works well as a reference book for users of nonparametric methods in different research areas. It is also a good textbook for undergraduate courses in statistics as well as courses for students majoring in other disciplines. Applied Nonparametric Statistical Methods provides a very clear exposition of modern nonparametric methods.
Many students and practitioners will find it an excellent resource and reference for nonparametric statistics. This well-written book is highly recommended for those readers who want to get a feeling for the nonparametric methods which they apply when analysing their data. Betrokkenen Auteur Prof.
Smeeton Co-auteur Nigel C. Smeeton Uitgever Springer. Reviews Schrijf een review. Kies je bindwijze. Verkoop door bol. In winkelwagen Op verlanglijstje. Gratis verzending 30 dagen bedenktijd en gratis retourneren Ophalen bij een bol. Anderen bekeken ook.
Takezawa Introduction to Nonparametric Regression , Rupert G. Miller Survival Analysis , Jenny A. Larry Wasserman All of Nonparametric Statistics , Stat Papers — DOI One is to provide a textbook for undergraduates for a first contact with nonparametric methods. The second is to provide a kind of manual for people with basic knowledge in statistics who wish to get acquainted with nonparametric methods.
The assumed background is an introductory course in statistics of some h duration. This book consists of 15 chapters. Chapter 1 gives an introduction in some basic concepts in statistics, i. The basics of nonparametric methods permutation test, binomial test, order statistics and ranks are described in Chap.
Chapter 3 38 pp introduces location inference for single samples, followed by Chapter 4 dealing with other single-sample inferences 42 pp, Kolmogorov Test, Lilliefors Test, Runs Test. Chapter 7 overviews basic tests for three or more sam- ples 31 pp. The following two chapters are new in comparison with the third edition: Chap. The subject of Chapter 10 is correla- tion and concordance, followed by bivariate linear regression in Chap. Categorical data are the topics of Chaps. Chapter 14 deals with robust estimation and gives a short overview about tests for outliers, bootstrapping, jackknifing and robust estimators 32 pp.
Chapter 15 is the last chapter and is addi- tional compared to the third edition 33 pp.