Applied Nonparametric Statistical Methods

ISBN-13: 9789401070447 / Angielski / Miękka / 2011 / 260 str.

Peter Sprent

Opis

This book is a practical introduction to statistical techniques called nonpara- metric methods. Using examples, we explain assumptions and demonstrate procedures; theory is kept to a minimum. We show how basic problems are tackled and try to clear up common misapprehensions so as to help both students of statistics meeting the methods for the first time and workers in other fields faced with data needing simple but informative analysis. An analogy between experimenters and car drivers describes our aim. Statistical analyses may be done by following a set of rules without understanding their logical basis, but this has dangers. It is like driving a car with no inkling ofhow the internal combustion engine, the gears, the ignition system, the brakes actually work. Understanding the rudiments helps one get better performance and makesdrivingsafer;appropriate gearchanges become a way to reduce engine stress, prolong engine life, improve fuel economy, minimize wear on brake linings. Knowing how to change the engine oil or replace worn sparking plugs is notessential for adriver, but it will reduce costs. Learning such basics will not make one a fully fledged mechanic, even less an automotive engineer; but it all contributes to more economical and safer driving, alertingone to the dangers ofbald tyres, aleakingexhaust, worn brake linings.

Spis treści

1 Introducing nonparametric methods.- 1.1 Basic statistics.- 1.2 Hypothesis tests.- 1.3 Estimation.- 1.4 Samples and populations.- 1.5 Further reading.- 1.6 Computers and nonparametric methods.- Exercises.- 2 Location estimates for single samples.- 2.1 The sign test.- 2.2 Inferences about medians based on ranks.- 2.3 Other location estimators.- 2.4 Fields of application.- Exercises.- 3 Distribution tests and rank transformations for single samples.- 3.1 Matching samples to distributions.- 3.2 Robustness.- 3.3 Transformations of ranks.- 3.4 Practical implications of efficiency.- 3.5 Modified assumptions.- 3.6 Fields of application.- Exercises.- 4 Methods for paired samples.- 4.1 Comparisons in pairs.- 4.2 A less obvious use of the sign test.- 4.3 Fields of application.- Exercises.- 5 Tests and estimation for two independent samples.- 5.1 Location tests and estimates.- 5.2 Wilcoxon—Mann—Whitney confidence intervals.- 5.3 Tests on functions of ranks.- 5.4 Tests for equality of variance.- 5.5 A test for a common distribution.- 5.6 Fields of application.- Exercises.- 6 Three or more samples.- 6.1 Possible extensions.- 6.2 Location tests for independent samples.- 6.3 Tests for heterogeneity of variance for independent samples.- 6.4 Further tests for several independent samples.- 6.5 Location comparisons for related samples.- 6.6 Fields of application.- Exercises.- 7 Bivariate and multivariate data.- 7.1 Correlation in bivariate data.- 7.2 Nonparametric bivariate linear regression.- 7.3 Monotonie regression.- 7.4 Multivariate data.- 7.5 Fields of application.- Exercises.- 8 Counts and categories.- 8.1 Categorical data.- 8.2 Tests for independence in two-way tables.- 8.3 The log-linear model.- 8.4 Goodness of fit tests for discrete data.- 8.5 Fields of application.- Exercises.- 9 Robustness, jackknives and bootstraps.- 9.1 The computer and robustness.- 9.2 Jackknives and bootstraps.- 9.3 Fields of application.- Exercises.- 10 Looking ahead.- 10.1 Nonparametric methods in a wider context.- 10.2 Developments from basic techniques.- 10.3 More sophisticated developments.- 10.4 The Bayesian approach.- A1 Random variables.- A2 Permutations and combinations.- A6 Least squares regression.- A7 Data sets.- A8 Tables of critical values for nonparametric methods.- References.- Solutions to odd-numbered exercises.