Burr / Schmidt Applied Statistical Methods

1. Auflage 2014
ISBN: 978-1-4832-7786-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 500 Seiten, Web PDF

Applied Statistical Methods covers the fundamental understanding of statistical methods necessary to deal with a wide variety of practical problems. This 14-chapter text presents the topics covered in a manner that stresses clarity of understanding, interpretation, and method of application. The introductory chapter illustrates the importance of statistical analysis. The next chapters introduce the methods of data summarization, including frequency distributions, cumulative frequency distributions, and measures of central tendency and variability. These topics are followed by discussions of the fundamental principles of probability, the concepts of sample spaces, outcomes, events, probability, independence of events, and the characterization of discrete and continuous random variables. Other chapters explore the distribution of several important statistics; statistical tests of hypotheses; point and interval estimation; and simple linear regression. The concluding chapters review the elements of single- and two-factor analysis of variance and the design of analysis of variance experiments. This book is intended primarily for advanced undergraduate and graduate students in the mathematical, physical, and engineering sciences, as well as in economics, business, and related areas. Researchers and line personnel in industry and government will find this book useful in self-study.

Autoren/Hrsg.

Burr, Irving W.

Schmidt, J. William

Inhaltsverzeichnis

1;Front Cover;1
2;Applied Statistical Methods;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;18
6;Acknowledgments;20
7;Chapter 1. Introduction;22
7.1;1.1 Why Statistical Methods?;22
7.2;1.2 Advice to the Student;23
8;Chapter 2. The Frequency Distribution — A Tool and a Concept;25
8.1;2.1 Introduction;25
8.2;2.2 An Example of a Frequency Distribution;25
8.3;2.3 Frequency Class Nomenclature and Tabulation;27
8.4;2.4 Discrete versus Continuous Data;29
8.5;2.5 Graphical Representation of a Frequency Distribution;29
8.6;2.6 The Cumulative Frequency Graph;31
8.7;2.7 What a Frequency Distribution Shows;33
8.8;2.8 Some Examples of Use of Frequency Tables and Graphs;34
8.9;2.9 Sample versus Population;37
8.10;2.10 Summary;40
8.11;Problems;40
9;Chapter 3. Summarization of Data by Objective Measures;54
9.1;3.1 Introduction;54
9.2;3.2 Some Averages;54
9.3;3.3 Some Measures of Variability;56
9.4;3.4 Efficient Calculation of Averages and Standard Deviations;59
9.5;3.5 Further Descriptive Measures of Frequency Distributions, Third and Fourth Moments;63
9.6;3.6 Summary;66
9.7;Problems;67
10;Chapter 4. Some Elementary Probability;69
10.1;4.1 Introduction;69
10.2;4.2 Sample Spaces of Outcomes;70
10.3;4.3 Events;71
10.4;4.4 Probabilities of Events;76
10.5;4.5 Probabilities on Discrete Sample Spaces;78
10.6;4.6 Independent and Dependent Events;80
10.7;4.7 Discrete Probabilities;87
10.8;4.8 Probabilities on Continuous Spaces;98
10.9;4.9 Applied Bayes' Probabilities—Posterior Probabilities;101
10.10;4.10 Interpretation of a Probability;103
10.11;4.11 Random Variables;104
10.12;4.12 Summary;104
10.13;Problems;105
11;Chapter 5. Some Discrete Probability Distributions;111
11.1;5.1 Theoretical Populations;111
11.2;5.2 Discrete Probability Distributions in General;112
11.3;5.3 The Binomial Distribution;116
11.4;5.4 The Poisson Distribution;124
11.5;5.5 The Hypergeometric Distribution;132
11.6;5.6 The Uniform Distribution;140
11.7;5.7 The Geometric Distribution;141
11.8;5.8 The Negative Binomial Distribution;143
11.9;5.9 Generating Samples from Discrete Distributions;145
11.10;5.10 Summary;146
11.11;References;146
11.12;Problems;147
12;Chapter 6. Some Continuous Probability Distributions;152
12.1;6.1 Continuous Probability Distributions;152
12.2;6.2 Some General Properties of Continuous Distributions;152
12.3;6.3 The Normal Curve;156
12.4;6.4 The Rectangular Distribution;162
12.5;6.5 The Exponential Distribution;163
12.6;6.6 The Gamma Distribution;165
12.7;6.7 The Beta Distribution;169
12.8;6.8 The Weibull Distribution;171
12.9;6.9 The Pearson System of Distributions;172
12.10;6.10 An Easily Fitted General System of Frequency Curves;173
12.11;6.11 Sums and Averages and a Central Limit Theorem;173
12.12;6.12 Tchebycheff's Theorem;176
12.13;6.13 Summary;177
12.14;6.14 Proofs of Some Relations in Section 6.11;178
12.15;References;181
12.16;Problems;182
13;Chapter 7. Some Sampling Distributions;187
13.1;7.1 Distribution of Sample Statistics from Populations;187
13.2;7.2 Choice of Sample;188
13.3;7.3 Sampling Distributions of a Sample Statistic;190
13.4;7.4 Distribution of Sample Means;191
13.5;7.5 Distribution of Sample Variances;195
13.6;7.6 Joint Distribution of y and s from a Normal Population;198
13.7;7.7 Two Normal Populations, Independent Samples;198
13.8;7.8 Sampling Aspects of the Binomial and Poisson Distributions;202
13.9;7.9 Sum of Two Independent Chi-Square Variables;203
13.10;7.10 Noncentral Distributions;203
13.11;7.11 Summary;204
13.12;References;204
13.13;Problems;205
14;Chapter 8. Statistical Tests of Hypotheses—General and One Sample;208
14.1;8.1 Introduction;208
14.2;8.2 An Example;209
14.3;8.3 Summary of the Elements in Tests of Hypotheses on One Parameter;215
14.4;8.4 Summary of Significance Testing for One Mean with s Unknown;217
14.5;8.5 Interpretation of Decisions in Hypothesis Testing;218
14.6;8.6 Nonnormal Populations of y's;219
14.7;8.7 Significance Testing for Mean µ, with s Unknown;219
14.8;8.8 Significance Tests for Variability;223
14.9;8.9 Significance Testing for Attributes;228
14.10;8.10 Relation of Significance Testing to Decision Theory;233
14.11;8.11 Summary;235
14.12;References;238
14.13;Problems;239
15;Chapter 9. Significance Tests– Two Samples;244
15.1;9.1 The General Problem;244
15.2;9.2 Tests on Two Variances–The F Test;246
15.3;9.3 Differences between Means;249
15.4;9.4 Significance of Differences–Binomial Data;255
15.5;9.5 Significance of Differences–Poisson Data;257
15.6;9.6 Matched Pair Data. Importance of Experimental Design;260
15.7;9.7 Sample Sizes Needed for Tests of Two Means;263
15.8;9.8 Summary;267
15.9;References;267
15.10;Problems;268
16;Chapter 10. Estimation of Population Characteristics;274
16.1;10.1 Point Estimates–General Idea;274
16.2;10.2 Which Estimator to Use–Characteristics of Estimation;275
16.3;10.3 How to Find a Desirable Estimator;277
16.4;10.4 Point Estimates–Common Cases;277
16.5;10.5 Interval Estimation in General;278
16.6;10.6 Confidence Intervals for µ;280
16.7;10.7 Confidence Intervals for s;282
16.8;10.8 How to Have Narrower Confidence Intervals;284
16.9;10.9 Confidence Intervals for Functions of Two Parameters Two– Samples;284
16.10;10.10 Confidence Limits for Attribute Data;288
16.11;10.11 Relation between Interval Estimation and Significance Testing;294
16.12;10.12 Summary;298
16.13;References;298
16.14;Problems;299
17;Chapter 11. Simple Regression;306
17.1;11.1 Regression, A Study of Relationship;306
17.2;11.2 The Scatter Diagram;307
17.3;11.3 Line of Best Fit to "Linear" Data;308
17.4;11.4 Sampling Distributions for Estimates;314
17.5;11.5 Significance Tests and Confidence Intervals for Parameters in Linear Regression;316
17.6;11.6 Correlational Aspects;319
17.7;11.7 Grouped Bivariate Data;321
17.8;11.8 Special Case µY.X = ß1X;325
17.9;11.9 Significance of Differences between Two Slopes;326
17.10;11.10 Nonlinearity Test;326
17.11;11.11 Use of Least Squares Fitting for Other Trends;327
17.12;11.12 Applications to Industry and the Laboratory;331
17.13;11.13 Summary;333
17.14;References;333
17.15;Problems;334
18;Chapter 12. Simple Analysis of Variance ;343
18.1;12.1 General Concept of Analysis of Variance;343
18.2;12.2 One-Factor Analysis of Variance;344
18.3;12.3 Orthogonal Polynomials and Tests;355
18.4;12.4 A Method of Multiple Contrasts;362
18.5;12.5 Testing Homogeneity of Variances;366
18.6;12.6 Types of Factors;369
18.7;12.7 Analysis of Variance for Two Factors;370
18.8;12.8 Other Models;383
18.9;12.9 Summary;384
18.10;References;384
18.11;Problems;386
19;Chapter 13. Multiple Regression;393
19.1;13.1 Introduction;393
19.2;13.2 First Approach;395
19.3;13.3 Second Approach;409
19.4;13.4 Summary of Approach;418
19.5;13.5 Adequacy of Regression Model;419
19.6;13.6 Comments and Precautions;420
19.7;References;421
19.8;Problems;422
20;Chapter 14. Goodness of Fit Tests, Contingency Tables;428
20.1;14.1 Introduction;428
20.2;14.2 The Chi-square Test for Cell Frequencies, Observed versus Theoretical;429
20.3;14.3 Testing Goodness of Fit of Theoretical Distributions;430
20.4;14.4 Other Goodness of Fit Tests;437
20.5;14.5 Contingency Tables;438
20.6;14.6 The Sign Test;443
20.7;14.7 Summary;444
20.8;References;444
20.9;Problems;445
21;Appendix;450
22;Answers to Odd-Numbered Problems;482
23;Index;490