john a rice mathematical statistics and data analysis, second edition 1994

[...]... informal data analytic methods I have organized this book around various kinds of problems that entail the use of statistical methods and have included many real examples to motivate and introduce the theory Among the advantages of such an approach are that XIV Preface theoretical constructs are presented in meaningful contexts, that they are gradually supplemented and reinforced, and that they are integrated... wildlife population Suppose that 10 animals are captured, tagged, and released On a later occasion, 20 animals are captured, and it is found that 4 of them are tagged How large is the population? We assume that there are n animals in the population, of which 10 are tagged If the 20 animals captured later are taken in such a way that all ( 2n0) possible groups are equally likely (this is a big assumption),... list could go on and on This book develops the basic ideas of probability and statistics The first part explores the theory of probability as a mathematical model for chance phenomena The second part of the book is about statistics, which is essentially concerned with procedures for analyzing data, especially data that in some vague sense have a 2 Chapter 1: Probability random character In order to... Massachusetts, Amherst; Robert Schaefer, Miami University; and Ruth Williams, University of California, San Diego Richard Royall and W G Cumberland kindly provided the data sets used in chapter 7 on survey sampling Several other data sets were brought to my attention by statisticians at the National Bureau of Standards, where I was fortunate to spend a year while on sabbatical I deeply appreciate the patience,... typically taught in an introductory one-quarter course In particular, I have not developed a geometric analysis of the general linear model or made any attempt to unify Preface XVII regression and analysis of variance Throughout this chapter, theoretical results are balanced by more qualitative data analytic procedures based on analysis of residuals Chapter 15 is an introduction to decision theory and. .. statistical concepts have developed, and it can be used as a vehicle for introducing concepts and techniques that are developed further in later chapters, for example: • • • • • The idea of an estimate as a random variable with an associated sampling distribution The concepts of bias, standard error, and mean squared error Confidence intervals and the application of the central limit theorem An exposure... and the Bayesian approach I believe that students are most likely to appreciate this material after having been exposed to the classical material developed in earlier chapters Computer Use and Problem Solving A VAX and a SUN were used in working the examples in the text and are used by my students on most problems involving real data My students and I have used both S and Minitab; other packages could... data analysis, seems to me artificial Furthermore, many students take only one course in statistics and do not have time for two or more Analysis of Data and the Practice of Statistics In order to draw the above themes together, I have endeavored to write a book closely tied to the prktice of statistics It is in the analysis of real data that one sees the roles played by both formal theory and informal... that she continues through all three lights, C = (ccc), then A and C have no outcomes in common, and we can write Anc=0 In such cases, A and C are said to be disjoint Venn diagrams, such as those in Figure 1.1, are often a useful tool for visualizing set operations The following are some laws of set theory Commutative Laws: AUB=BUA AnB=BnA Associative Laws: (AUB)UC=AU (B U C) (A nB)nc=An(Bno 4 Chapter... statistics and data analysis with special attention to graphical displays, aspects of experimental design, and realistic applications of some complexity It should also reflect the quickly growing use of computers in statistics These themes, properly interwoven, can give students a view of the nature of modern statistics The alternative of teaching two separate courses, one on theory and one on data . Cataloging-in-Publication Data Rice, John A. , Mathematical statistics and data analysis / John A. Rice. —2nd ed. p.  cm. Includes bibliographical references and indexes. ISBN 0-534-20934-3 (acid-free).