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Produktbild: Statistical Inference

Statistical Inference A Short Course

Fr. 183.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.07.2012

Verlag

John Wiley & Sons

Seitenzahl

400

Maße (L/B/H)

23.6/15.7/2.5 cm

Gewicht

680 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-22940-8

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.07.2012

Verlag

John Wiley & Sons

Seitenzahl

400

Maße (L/B/H)

23.6/15.7/2.5 cm

Gewicht

680 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-22940-8

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Statistical Inference
  • Preface xv

    1 The Nature of Statistics 1

    1.1 Statistics Defined 1

    1.2 The Population and the Sample 2

    1.3 Selecting a Sample from a Population 3

    1.4 Measurement Scales 4

    1.5 Let us Add 6

    Exercises 7

    2 Analyzing Quantitative Data 9

    2.1 Imposing Order 9

    2.2 Tabular and Graphical Techniques: Ungrouped Data 9

    2.3 Tabular and Graphical Techniques: Grouped Data 11

    Exercises 16

    Appendix 2.A Histograms with Classes of Different Lengths 18

    3 Descriptive Characteristics of Quantitative Data 22

    3.1 The Search for Summary Characteristics 22

    3.2 The Arithmetic Mean 23

    3.3 The Median 26

    3.4 The Mode 27

    3.5 The Range 27

    3.6 The Standard Deviation 28

    3.7 Relative Variation 33

    3.8 Skewness 34

    3.9 Quantiles 36

    3.10 Kurtosis 38

    3.11 Detection of Outliers 39

    3.12 So What Do We Do with All This Stuff? 41

    Exercises 47

    Appendix 3.A Descriptive Characteristics of Grouped Data 51

    3.A.1 The Arithmetic Mean 52

    3.A.2 The Median 53

    3.A.3 The Mode 55

    3.A.4 The Standard Deviation 57

    3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) 58

    4 Essentials of Probability 61

    4.1 Set Notation 61

    4.2 Events within the Sample Space 63

    4.3 Basic Probability Calculations 64

    4.4 Joint, Marginal, and Conditional Probability 68

    4.5 Sources of Probabilities 73

    Exercises 75

    5 Discrete Probability Distributions and Their Properties 81

    5.1 The Discrete Probability Distribution 81

    5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable 85

    5.3 The Binomial Probability Distribution 89

    5.3.1 Counting Issues 89

    5.3.2 The Bernoulli Probability Distribution 91

    5.3.3 The Binomial Probability Distribution 91

    Exercises 96

    6 The Normal Distribution 101

    6.1 The Continuous Probability Distribution 101

    6.2 The Normal Distribution 102

    6.3 Probability as an Area Under the Normal Curve 104

    6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X 114

    Exercises 116

    Appendix 6.A The Normal Approximation to Binomial Probabilities 120

    7 Simple Random Sampling and the Sampling Distribution of the Mean 122

    7.1 Simple Random Sampling 122

    7.2 The Sampling Distribution of the Mean 123

    7.3 Comments on the Sampling Distribution of the Mean 127

    7.4 A Central Limit Theorem 130

    Exercises 132

    Appendix 7.A Using a Table of Random Numbers 133

    Appendix 7.B Assessing Normality via the Normal Probability Plot 136

    Appendix 7.C Randomness, Risk, and Uncertainty 139

    7.C.1 Introduction to Randomness 139

    7.C.2 Types of Randomness 142

    7.C.2.1 Type I Randomness 142

    7.C.2.2 Type II Randomness 143

    7.C.2.3 Type III Randomness 143

    7.C.3 Pseudo-Random Numbers 144

    7.C.4 Chaotic Behavior 145

    7.C.5 Risk and Uncertainty 146

    8 Confidence Interval Estimation of m 152

    8.1 The Error Bound on X as an Estimator of m 152

    8.2 A Confidence Interval for the Population Mean m (s Known) 154

    8.3 A Sample Size Requirements Formula 159

    8.4 A Confidence Interval for the Population Mean m (s Unknown) 160

    Exercises 165

    Appendix 8.A A Confidence Interval for the Population Median MED 167

    9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation 170

    9.1 The Sampling Distribution of a Proportion 170

    9.2 The Error Bound on ^p as an Estimator for p 173

    9.3 A Confidence Interval for the Population Proportion (of Successes) p 174

    9.4 A Sample Size Requirements Formula 176

    Exercises 177

    Appendix 9.A Ratio Estimation 179

    10 Testing Statistical Hypotheses 184

    10.1 What is a Statistical Hypothesis? 184

    10.2 Errors in Testing 185

    10.3 The Contextual Framework of Hypothesis Testing 186

    10.3.1 Types of Errors in a Legal Context 188

    10.3.2 Types of Errors in a Medical Context 188

    10.3.3 Types of Errors in a Processing or Control Context 189

    10.3.4 Types of Errors in a Sports Context 189

    10.4 Selecting a Test Statistic 190

    10.5 The Classical Approach to Hypothesis Testing 190

    10.6 Types of Hypothesis Tests 191

    10.7 Hypothesis Tests for m (s Known) 194

    10.8 Hypothesis Tests for m (s Unknown and n Small) 195

    10.9 Reporting the Results of Statistical Hypothesis Tests 198

    10.10 Hypothesis Tests for the Population Proportion (of Successes) p 201

    Exercises 204

    Appendix 10.A Assessing the Randomness of a Sample 208

    Appendix 10.B Wilcoxon Signed Rank Test (of a Median) 210

    Appendix 10.C Lilliefors Goodness-of-Fit Test for Normality 213

    11 Comparing Two Population Means and Two Population Proportions 217

    11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations 217

    11.1.1 Sampling from Two Independent Normal Populations with Equal and Known Variances 217

    11.1.2 Sampling from Two Independent Normal Populations with Unequal but Known Variances 218

    11.1.3 Sampling from Two Independent Normal Populations with Equal but Unknown Variances 218

    11.1.4 Sampling from Two Independent Normal Populations with Unequal and Unknown Variances 219

    11.2 Confidence Intervals for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 224

    11.3 Confidence Intervals for the Difference of Proportions when Sampling from Two Independent Binomial Populations 227

    11.4 Statistical Hypothesis Tests for the Difference of Means when Sampling from Two Independent Normal Populations 228

    11.4.1 Population Variances Equal and Known 229

    11.4.2 Population Variances Unequal but Known 229

    11.4.3 Population Variances Equal and Unknown 229

    11.4.4 Population Variances Unequal and Unknown (an Approximate Test) 230

    11.5 Hypothesis Tests for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons 234

    11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations 236

    Exercises 239

    Appendix 11.A Runs Test for Two Independent Samples 243

    Appendix 11.B Mann-Whitney (Rank Sum) Test for Two Independent Populations 245

    Appendix 11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent Populations: Paired Comparisons 249

    12 Bivariate Regression and Correlation 253

    12.1 Introducing an Additional Dimension to our Statistical Analysis 253

    12.2 Linear Relationships 254

    12.2.1 Exact Linear Relationships 254

    12.3 Estimating the Slope and Intercept of the Population Regression Line 257

    12.4 Decomposition of the Sample Variation in Y 262

    12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators ^b0 and ^b1 264

    12.6 Confidence Intervals for b0 and b1 266

    12.7 Testing Hypotheses about b0 and b1 267

    12.8 Predicting the Average Value of Y given X 269

    12.9 The Prediction of a Particular Value of Y given X 270

    12.10 Correlation Analysis 272

    12.10.1 Case A: X and Y Random Variables 272

    12.10.1.1 Estimating the Population Correlation Coefficient r 274

    12.10.1.2 Inferences about the Population Correlation Coefficient r 275

    12.10.2 Case B: X Values Fixed, Y a Random Variable 277

    Exercises 278

    Appendix 12.A Assessing Normality (Appendix 7.B Continued) 280

    Appendix 12.B On Making Causal Inferences 281

    12.B.1 Introduction 281

    12.B.2 Rudiments of Experimental Design 282

    12.B.3 Truth Sets, Propositions, and Logical Implications 283

    12.B.4 Necessary and Sufficient Conditions 285

    12.B.5 Causality Proper 286

    12.B.6 Logical Implications and Causality 287

    12.B.7 Correlation and Causality 288

    12.B.8 Causality from Counterfactuals 289

    12.B.9 Testing Causality 292

    12.B.10 Suggestions for Further Reading 294

    13 An Assortment of Additional Statistical Tests 295

    13.1 Distributional Hypotheses 295

    13.2 The Multinomial Chi-Square Statistic 295

    13.3 The Chi-Square Distribution 298

    13.4 Testing Goodness of Fit 299

    13.5 Testing Independence 304

    13.6 Testing k Proportions 309

    13.7 A Measure of Strength of Association in a Contingency Table 311

    13.8 A Confidence Interval for s2 under Random Sampling from a Normal Population 312

    13.9 The F Distribution 314

    13.10 Applications of the F Statistic to Regression Analysis 316

    13.10.1 Testing the Significance of the Regression Relationship Between X and Y 316

    13.10.2 A Joint Test of the Regression Intercept and Slope 317

    Exercises 318

    Appendix A 323

    Table A.1 Standard Normal Areas [Z is N(0,1)] 323

    Table A.2 Quantiles of the t Distribution (T is tv) 325

    Table A.3 Quantiles of the Chi-Square Distribution (X is w2v) 327

    Table A.4 Quantiles of the F Distribution (F is Fv1;v2 ) 329

    Table A.5 Binomial Probabilities P(X;n,p) 334

    Table A.6 Cumulative Binomial Probabilities 338

    Table A.7 Quantiles of Lilliefors' Test for Normality 342

    Solutions to Exercises 343

    References 369

    Index 373