This outline of statistics as an aid in decision making will introduce a reader with limited mathematical background to the most important modern statistical methods. This is a revised and enlarged version, with major extensions and additions, of my "Angewandte Statistik" (5th ed.), which has proved useful for research workers and for consulting statisticians. Applied statistics is at the same time a collection of applicable statistical methods and the application of these methods to measured and/or counted observations. Abstract mathematical concepts and derivations are avoided. Special…mehr
This outline of statistics as an aid in decision making will introduce a reader with limited mathematical background to the most important modern statistical methods. This is a revised and enlarged version, with major extensions and additions, of my "Angewandte Statistik" (5th ed.), which has proved useful for research workers and for consulting statisticians. Applied statistics is at the same time a collection of applicable statistical methods and the application of these methods to measured and/or counted observations. Abstract mathematical concepts and derivations are avoided. Special emphasis is placed on the basic principles of statistical formulation, and on the explanation of the conditions under which a certain formula or a certain test is valid. Preference is given to consideration of the analysis of small sized samples and of distribution-free methods. As a text and reference this book is written for non-mathematicians, in particular for technicians, engineers, executives, students, physicians as well as researchers in other disciplines. It gives any mathematician interested in the practical uses of statistics a general account of the subject. Practical application is the main theme; thus an essential part of the book consists in the 440 fully worked-out numerical examples, some of which are very simple; the 57 exercises with solutions; a number of different compu tational aids; and an extensive bibliography and a very detailed index. In particular, a collection of 232 mathematical and mathematical-statistical tables serves to enable and to simplify the computations.
to Statistics.- 0 Preliminaries.- 0.1 Mathematical Abbreviations.- 0.2 Arithmetical Operations.- 0.3 Computational Aids.- 0.4 Rounding Off.- 0.5 Computations with Inaccurate Numbers.- 1 Statistical Decision Techniques.- 1.1 What Is Statistics? Statistics and the Scientific Method.- 1.2 Elements of Computational Probability.- ?1.2.1 Statistical probability.- ?1.2.2 The addition theorem of probability theory.- ?1.2.3 Conditional probability and statistical independence.- 1.2.4 Bayes's theorem.- ?1.2.5 The random variable.- 1.2.6 The distribution function and the probability function.- 1.3 The Path to the Normal Distribution.- ?1.3.1 The population and the sample.- ?1.3.2 The generation of random samples.- ?1.3.3 A frequency distribution.- ?1.3.4 Bell-shaped curves and the normal distribution.- ?1.3.5 Deviations from the normal distribution.- ?1.3.6 Parameters of unimodal distributions.- ?1.3.7 The probability plot.- 1.3.8 Additional statistics for the characterization of a one dimensional frequency distribution.- 1.3.9 The lognormal distribution.- 1.4 The Road to the Statistical Test.- 1.4.1 The confidence coefficient.- 1.4.2 Null hypotheses and alternative hypotheses.- 1.4.3 Risk I and risk II.- 1.4.4 The significance level and the hypotheses are, if possible, to be specified before collecting the data.- 1.4.5 The statistical test.- 1.4.6 One sided and two sided tests.- 1.4.7 The power of a test.- 1.4.8 Distribution-free procedures.- 1.4.9 Decision principles.- 1.5 Three Important Families of Test Distributions.- 1.5.1 The Student's t-distribution.- 1.5.2 The ?2distribution.- 1.5.3 The F-distribution.- 1.6 Discrete Distributions.- 1.6.1 The binomial coefficient.- ?1.6.2 The binomial distribution.- 1.6.3 The hypergeometric distribution.- 1.6.4 The Poisson distribution.- ?1.6.5 The Thorndike nomogram.- 1.6.6 Comparison of means of Poisson distributions.- 1.6.7 The dispersion index.- 1.6.8 The multinomial coefficient.- 1.6.9 The multinomial distribution.- 2 Statistical Methods in Medicine and Technology.- 2.1 Medical Statistics.- 2.1.1 Critique of the source material.- 2.1.2 The reliability of laboratory methods.- 2.1.3 How to get unbiased information and how to investigate associations.- 2.1.4 Retrospective and prospective comparisons.- 2.1.5 The therapeutic comparison.- 2.1.6 The choice of appropriate sample sizes for the clinical trial.- 2.2 Sequential Test Plans.- 2.3 Evaluation of Biologically Active Substances Based on Dosage-Dichotomous Effect Curves.- 2.4 Statistics in Engineering.- 2.4.1 Quality control in industry.- 2.4.2 Life span and reliability of manufactured products.- 2.5 Operations Research.- 2.5.1 Linear programming.- 2.5.2 Game theory and the war game.- 2.5.3 The Monte Carlo method and computer simulation.- 3 The Comparison of Independent Data Samples.- 3.1 The Confidence Interval of the Mean and of the Median.- ?3.1.1 Confidence interval for the mean.- ?3.1.2 Estimation of sample sizes.- 3.1.3 The mean absolute deviation.- 3.1.4 Confidence interval for the median.- ?3.2 Comparison of an Empirical Mean with the Mean of a Normally Distributed Population.- ?3.3 Comparison of an Empirical Variance with Its Parameter.- 3.4 Confidence Interval for the Variance and for the Coefficient of Variation.- 3.5 Comparison of Two Empirically Determined Variances of Normally Distributed Populations.- 3.5.1 Small to medium sample size.- 3.5.2 Medium to large sample size.- 3.5.3 Large to very large sample size (n1, n2 ? 100).- ?3.6 Comparison of Two Empirical Means of Normally Distributed Populations.- 3.6.1 Unknown but equal variances.- 3.6.2 Unknown, possibly unequal variances.- 3.7 Quick Tests Which Assume Nearly Normally Distributed Data.- 3.7.1 The comparison of the dispersions of two small samples according to Pillai and Buenaventura.- 3.7.2 The comparison of the means of two small samples according to Lord.- 3.7.3 Comparison of the means of several samples of equal size according to Dixon.- 3.8 The Problem of Outliers
to Statistics.- 0 Preliminaries.- 0.1 Mathematical Abbreviations.- 0.2 Arithmetical Operations.- 0.3 Computational Aids.- 0.4 Rounding Off.- 0.5 Computations with Inaccurate Numbers.- 1 Statistical Decision Techniques.- 1.1 What Is Statistics? Statistics and the Scientific Method.- 1.2 Elements of Computational Probability.- ?1.2.1 Statistical probability.- ?1.2.2 The addition theorem of probability theory.- ?1.2.3 Conditional probability and statistical independence.- 1.2.4 Bayes's theorem.- ?1.2.5 The random variable.- 1.2.6 The distribution function and the probability function.- 1.3 The Path to the Normal Distribution.- ?1.3.1 The population and the sample.- ?1.3.2 The generation of random samples.- ?1.3.3 A frequency distribution.- ?1.3.4 Bell-shaped curves and the normal distribution.- ?1.3.5 Deviations from the normal distribution.- ?1.3.6 Parameters of unimodal distributions.- ?1.3.7 The probability plot.- 1.3.8 Additional statistics for the characterization of a one dimensional frequency distribution.- 1.3.9 The lognormal distribution.- 1.4 The Road to the Statistical Test.- 1.4.1 The confidence coefficient.- 1.4.2 Null hypotheses and alternative hypotheses.- 1.4.3 Risk I and risk II.- 1.4.4 The significance level and the hypotheses are, if possible, to be specified before collecting the data.- 1.4.5 The statistical test.- 1.4.6 One sided and two sided tests.- 1.4.7 The power of a test.- 1.4.8 Distribution-free procedures.- 1.4.9 Decision principles.- 1.5 Three Important Families of Test Distributions.- 1.5.1 The Student's t-distribution.- 1.5.2 The ?2distribution.- 1.5.3 The F-distribution.- 1.6 Discrete Distributions.- 1.6.1 The binomial coefficient.- ?1.6.2 The binomial distribution.- 1.6.3 The hypergeometric distribution.- 1.6.4 The Poisson distribution.- ?1.6.5 The Thorndike nomogram.- 1.6.6 Comparison of means of Poisson distributions.- 1.6.7 The dispersion index.- 1.6.8 The multinomial coefficient.- 1.6.9 The multinomial distribution.- 2 Statistical Methods in Medicine and Technology.- 2.1 Medical Statistics.- 2.1.1 Critique of the source material.- 2.1.2 The reliability of laboratory methods.- 2.1.3 How to get unbiased information and how to investigate associations.- 2.1.4 Retrospective and prospective comparisons.- 2.1.5 The therapeutic comparison.- 2.1.6 The choice of appropriate sample sizes for the clinical trial.- 2.2 Sequential Test Plans.- 2.3 Evaluation of Biologically Active Substances Based on Dosage-Dichotomous Effect Curves.- 2.4 Statistics in Engineering.- 2.4.1 Quality control in industry.- 2.4.2 Life span and reliability of manufactured products.- 2.5 Operations Research.- 2.5.1 Linear programming.- 2.5.2 Game theory and the war game.- 2.5.3 The Monte Carlo method and computer simulation.- 3 The Comparison of Independent Data Samples.- 3.1 The Confidence Interval of the Mean and of the Median.- ?3.1.1 Confidence interval for the mean.- ?3.1.2 Estimation of sample sizes.- 3.1.3 The mean absolute deviation.- 3.1.4 Confidence interval for the median.- ?3.2 Comparison of an Empirical Mean with the Mean of a Normally Distributed Population.- ?3.3 Comparison of an Empirical Variance with Its Parameter.- 3.4 Confidence Interval for the Variance and for the Coefficient of Variation.- 3.5 Comparison of Two Empirically Determined Variances of Normally Distributed Populations.- 3.5.1 Small to medium sample size.- 3.5.2 Medium to large sample size.- 3.5.3 Large to very large sample size (n1, n2 ? 100).- ?3.6 Comparison of Two Empirical Means of Normally Distributed Populations.- 3.6.1 Unknown but equal variances.- 3.6.2 Unknown, possibly unequal variances.- 3.7 Quick Tests Which Assume Nearly Normally Distributed Data.- 3.7.1 The comparison of the dispersions of two small samples according to Pillai and Buenaventura.- 3.7.2 The comparison of the means of two small samples according to Lord.- 3.7.3 Comparison of the means of several samples of equal size according to Dixon.- 3.8 The Problem of Outliers
Es gelten unsere Allgemeinen Geschäftsbedingungen: www.buecher.de/agb
Impressum
www.buecher.de ist ein Shop der buecher.de GmbH & Co. KG Bürgermeister-Wegele-Str. 12, 86167 Augsburg Amtsgericht Augsburg HRA 13309