ISBN:
9789400959583
Sprache:
Englisch
Seiten:
Online-Ressource
,
online resource
Ausgabe:
Third Edition
Ausgabe:
Springer eBook Collection. Humanities, Social Sciences and Law
Paralleltitel:
Erscheint auch als
Paralleltitel:
Erscheint auch als
Schlagwort(e):
Science (General)
;
Social sciences.
;
Humanities.
Kurzfassung:
1 Introduction -- 1.1 Examples of random variation -- 1.2 One-dimensional frequency distributions -- 1.3 Summarizing quantities -- 1.4 Frequency distributions in two or more dimensions -- 1.5 Some illustrative examples -- 1.6 Populations, samples and probability -- 2 Probability and Probability Distributions -- 2.1 Probability -- 2.2 Addition law of probability -- 2.3 Conditional probability and statistical independence -- 2.4 Examples -- 2.5 Discrete random variables -- 2.6 Continuous random variables -- 2.7 Several random variables -- 3 Expectation and its Applications -- 3.1 Expectation -- 3.2 Variance -- 3.3 Higher moments -- 3.4 Dependence and covariance -- 3.5 Normal models -- 4 Sampling Distributions and Statistical Inference -- 4.1 Statistical inference -- 4.2 Pseudo random deviates -- 4.3 A sampling experiment -- 4.4 Estimation -- 4.5 Significance tests -- 5 Single Sample Problems -- 5.1 Introduction -- 5.2 Point estimates of µ and ?2 -- 5.3 Interval estimates for µ (?2 unknown) -- 5.4 Interval estimates for ?2 -- 5.5 Significance test for a mean -- 5.6 Significance test for a variance -- 5.7 Departures from assumptions -- 6 Two Sample Problems -- 6.1 Introduction -- 6.2 The comparison of two independent sample means -- 6.3 The comparison of two independent sample variances -- 6.4 Analysis of paired samples -- 6.5 An example -- 6.6 Departures from assumptions -- 7 Non-parametric Tests -- 7.1 Introduction -- 7.2 Normal approximation to the binomial distribution -- 7.3 The sign test -- 7.4 The signed rank (Wilcoxon one sample) test -- 7.5 Two sample rank (Wilcoxon) test -- 7.6 Discussion -- 8 The Analysis of Discrete Data -- 8.1 Introduction -- 8.2 Distributions and approximations -- 8.3 Inference about a single Poisson mean -- 8.4 Inference about a single binomial probability -- 8.5 The comparison of two Poisson variates -- 8.6 The comparison of two binomial variates -- 8.7 Comparison of proportions in matched pairs -- 8.8 Examination of Poisson frequency table -- 8.9 Examination of binomial frequency tables -- 8.10 Comparison of observed and expected frequencies -- 8.11 Contingency tables -- 8.12 A tasting experiment -- 9 Statistical Models and Least Squares -- 9.1 General points -- 9.2 An example -- 9.3 Least squares -- 10 Linear Regression -- 10.1 Introduction -- 10.2 Least squares estimates -- 10.3 Properties of ? and ? -- 10.4 Predictions from regressions -- 10.5 Comparison of two regression lines -- 10.6 Equally spaced x-values -- 10.7 Use of residuals -- 10.8 Discussion of models -- 11 Multiple Regression -- 11.1 Introduction -- 11.2 Theory for two explanatory variables only -- 11.3 Analysis of Example 11.2 -- 11.4 Discussion -- 12 Analysis of Variance -- 12.1 The problem -- 12.2 Theory of one-way analysis of variance -- 12.3 Procedure for analysis -- 12.4 Two-way analysis of variance -- 12.5 Linear contrasts -- 12.6 Randomized blocks -- 12.7 Components of variance -- 12.8 Departures from assumptions -- Miscellaneous Exercises -- Appendix One Notes on calculation and computing 307 -- Appendix Two Statistical tables -- Appendix Three Hints to the solution of selected exercises -- References -- Author Index.
Kurzfassung:
This book is mainly based on lectures given by Professor D. R. Cox and myself at Birkbeck College over a period of eight to nine years. It began as a. joint venture, but pressure of other work made it necessary for Professor Cox to withdraw early on. I have throughout received much valuable advice and encouragement from Professor Cox, but of course, I am solely responsible for the text, and any errors remaining in it. The book is intended as a first course on statistical methods, and there is a liberal supply of exercises. Although the mathematical level of the book is low, I have tried to explain carefully the logical reasoning behind the use of the methods discussed. Some of the exercises which require more difficult mathematics are marked with an asterisk, and these may be omitted. In this way, I hope that the book will satisfy the needs for a course on statistical methods at a range of mathematical levels. It is essential for the reader to work through the numerical exercises, for only in this way can he grasp the full meaning and usefulness of the statistical techniques, and gain practice in the interpretation of the results. Chapters 7 and 8 discuss methods appropriate for use on ranked or discrete data, and Chapters 9-12 do not depend on these chapters. Chapters 7 and 8 may therefore be omitted, if desired.
Beschreibung / Inhaltsverzeichnis:
1 Introduction1.1 Examples of random variation -- 1.2 One-dimensional frequency distributions -- 1.3 Summarizing quantities -- 1.4 Frequency distributions in two or more dimensions -- 1.5 Some illustrative examples -- 1.6 Populations, samples and probability -- 2 Probability and Probability Distributions -- 2.1 Probability -- 2.2 Addition law of probability -- 2.3 Conditional probability and statistical independence -- 2.4 Examples -- 2.5 Discrete random variables -- 2.6 Continuous random variables -- 2.7 Several random variables -- 3 Expectation and its Applications -- 3.1 Expectation -- 3.2 Variance -- 3.3 Higher moments -- 3.4 Dependence and covariance -- 3.5 Normal models -- 4 Sampling Distributions and Statistical Inference -- 4.1 Statistical inference -- 4.2 Pseudo random deviates -- 4.3 A sampling experiment -- 4.4 Estimation -- 4.5 Significance tests -- 5 Single Sample Problems -- 5.1 Introduction -- 5.2 Point estimates of µ and ?2 -- 5.3 Interval estimates for µ (?2 unknown) -- 5.4 Interval estimates for ?2 -- 5.5 Significance test for a mean -- 5.6 Significance test for a variance -- 5.7 Departures from assumptions -- 6 Two Sample Problems -- 6.1 Introduction -- 6.2 The comparison of two independent sample means -- 6.3 The comparison of two independent sample variances -- 6.4 Analysis of paired samples -- 6.5 An example -- 6.6 Departures from assumptions -- 7 Non-parametric Tests -- 7.1 Introduction -- 7.2 Normal approximation to the binomial distribution -- 7.3 The sign test -- 7.4 The signed rank (Wilcoxon one sample) test -- 7.5 Two sample rank (Wilcoxon) test -- 7.6 Discussion -- 8 The Analysis of Discrete Data -- 8.1 Introduction -- 8.2 Distributions and approximations -- 8.3 Inference about a single Poisson mean -- 8.4 Inference about a single binomial probability -- 8.5 The comparison of two Poisson variates -- 8.6 The comparison of two binomial variates -- 8.7 Comparison of proportions in matched pairs -- 8.8 Examination of Poisson frequency table -- 8.9 Examination of binomial frequency tables -- 8.10 Comparison of observed and expected frequencies -- 8.11 Contingency tables -- 8.12 A tasting experiment -- 9 Statistical Models and Least Squares -- 9.1 General points -- 9.2 An example -- 9.3 Least squares -- 10 Linear Regression -- 10.1 Introduction -- 10.2 Least squares estimates -- 10.3 Properties of ? and ? -- 10.4 Predictions from regressions -- 10.5 Comparison of two regression lines -- 10.6 Equally spaced x-values -- 10.7 Use of residuals -- 10.8 Discussion of models -- 11 Multiple Regression -- 11.1 Introduction -- 11.2 Theory for two explanatory variables only -- 11.3 Analysis of Example 11.2 -- 11.4 Discussion -- 12 Analysis of Variance -- 12.1 The problem -- 12.2 Theory of one-way analysis of variance -- 12.3 Procedure for analysis -- 12.4 Two-way analysis of variance -- 12.5 Linear contrasts -- 12.6 Randomized blocks -- 12.7 Components of variance -- 12.8 Departures from assumptions -- Miscellaneous Exercises -- Appendix One Notes on calculation and computing 307 -- Appendix Two Statistical tables -- Appendix Three Hints to the solution of selected exercises -- References -- Author Index.
DOI:
10.1007/978-94-009-5958-3
URL:
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