Verfügbarkeit: Introduction to statistics

Introduction to statistics: using interactive MM*Stat Elements

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Bibliographische Detailangaben
Hauptverfasser:	Härdle, Wolfgang 1953- (VerfasserIn), Klinke, Sigbert (VerfasserIn), Rönz, Bernd 1941- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cham Springer [2015]
Schriftenreihe:	Statistics / Business, Economics, and Management
Schlagworte:	Statistik Einführung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	xx, 516 Seiten Illustrationen, Diagramme (überwiegend farbig)
ISBN:	9783319177038

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adam_text	Contents 1 Basics................................................................ 1 1.1 Objectives of Statistics.............................................. 1 A Definition of Statistics.................................... 1 Explained: Descriptive and Inductive Statistics .............. 3 1.2 Statistical Investigation............................................. 4 Conducting a Statistical Investigation........................ 4 Sources of Economic Data...................................... 4 Explained: Public Sources of Data............................. 6 More Information: Statistical Processes ...................... 6 1.3 Statistical Element and Population ................................... 8 Statistical Elements.......................................... 8 Population.................................................... 8 Explained: Statistical Elements and Population................ 8 1.4 Statistical Variable................................................. 10 1.5 Measurement Scales................................................... 11 1.6 Qualitative Variables................................................ 11 Nominal Scale................................................ 11 Ordinal Scale................................................ 12 1.7 Quantitative Variables............................................... 13 Interval Scale............................................... 13 Ratio Scale.................................................. 13 Absolute Scale............................................... 13 Discrete Variable............................................ 14 Continuous Variable.......................................... 14 1.8 Grouping Continuous Data............................................. 14 Explained: Grouping of Data.................................. 16 1.9 Statistical Sequences and Frequencies................................ 16 Statistical Sequence......................................... 16 Frequency.................................................... 17 Explained: Absolute and Relative Frequency................... 18 ix x Contents 2 One-Dimensional Frequency Distributions............................... 21 2.1 One-Dimensional Distribution..................................... 21 2.1.1 Frequency Distributions for Discrete Data................. 21 Frequency Table........................................... 21 2.1.2 Graphical Presentation.................................... 22 Explained: Job Proportions in Germany..................... 25 Enhanced: Evolution of Household Sizes.................... 25 2.2 Frequency Distribution for Continuous Data....................... 26 Frequency Table........................................... 27 Graphical Presentation.................................... 27 Explained: Petrol Consumption of Cars..................... 30 Explained: Net Income of German Nationals................. 31 2.3 Empirical Distribution Function.................................. 34 2.3.1 Empirical Distribution Function for Discrete Data......... 35 2.3.2 Empirical Distribution Function for Grouped Continuous Data........................................... 36 Explained: Petrol Consumption of Cars..................... 37 Explained: Grades in Statistics Examination............... 38 2.4 Numerical Description of One-Dimensional Frequency Distributions.................................................... 40 Measures of Location...................................... 40 Explained: Average Prices of Cars......................... 47 Interactive: Dotplot with Location Parameters ............ 49 Interactive: Simple Histogram............................. 49 2.5 Location Parameters: Mean Values—Harmonic Mean, Geometric Mean................................................... 50 Harmonic Average.......................................... 50 Geometric Average......................................... 52 2.6 Measures of Scale or Variation................................... 55 Range..................................................... 56 Interquartile Range....................................... 57 Mean Absolute Deviation................................. 57 The Variance and the Standard Deviation................... 58 Explained: Variations of Pizza Prices..................... 60 Enhanced: Parameters of Scale for Cars.................... 61 Interactive: Dotplot with Scale Parameters................ 62 2.7 Graphical Display of the Location and Scale Parameters........... 64 Boxplot (Box-Whisker-Plot)................................ 64 Explained: Boxplot of Car Prices ......................... 66 Interactive: Visualization of One-Dimensional Distributions............................................. 67 3 Probability Theory.................................................... 69 3.1 The Sample Space, Events, and Probabilities...................... 69 Venn Diagram.............................................. 70 Contents xi 3.2 Event Relations and Operations................................... 70 Subsets and Complements.................................... 70 Union of Sets.............................................. 71 Intersection of Sets....................................... 71 Logical Difference of Sets or Events....................... 73 Disjoint Decomposition of the Sample Space................. 74 Some Set Theoretic Laws.................................... 75 3.3 Probability Concepts............................................ 75 Classical Probability...................................... 76 Statistical Probability.................................... 76 Axiomatic Foundation of Probability ....................... 78 Addition Rule of Probability .............................. 78 More Information: Derivation of the Addition Rule.......... 79 More Information: Implications of the Probability Axioms.................................. 80 Explained: A Deck of Cards................................. 81 3.4 Conditional Probability and Independent Events.................... 82 Conditional Probability.................................... 82 Multiplication Rule ....................................... 83 Independent Events ........................................ 83 Two-Way Cross-Tabulation................................... 84 More Information: Derivation of Rules for Independent Events .................................... 85 Explained: Two-Way Cross-Tabulation........................ 85 Explained: Screws.......................................... 86 3.5 Theorem of Total Probabilities and Bayes’ Rule.................... 87 Theorem of Total Probabilities............................. 87 Bayes’ Rule................................................ 88 Explained: The Wine Cellar............................. 88 Enhanced: Virus Test....................................... 90 Interactive: Monty Hall Problem............................ 91 Interactive: Die Rolling Sisters........................... 94 4 Combinatorics........................................................... 97 4.1 Introduction....................................... 97 Different Ways of Grouping and Ordering.................... 97 Use of Combinatorial Theory................................ 98 4.2 Permutation....................................................... 98 Permutations Without Repetition............................ 98 Permutations with Repetition............................... 99 Permutations with More Groups of Identical Elements..... 99 Explained: Beauty Competition............................. 100 4.3 Variations ...................................................... 100 Variations with Repetition................................ 100 Variations Without Repetition............................. 101 Explained: Lock Picking................................... 101 Contents xii 4.4 Combinations................................................... 102 Combinations Without Repetition......................... 102 Combinations with Repetition............................ 103 Explained: German Lotto................................. 103 4.5 Properties of Euler’s Numbers (Combination Numbers)............ 104 Symmetry................................................ 104 Specific Cases.......................................... 104 Sum of Two Euler’s Numbers.............................. 104 Euler’s Numbers and Binomial Coefficients............... 105 5 Random Variables.................................................. 107 5.1 The Definition ............................................... 107 More Information ....................................... 107 Explained: The Experiment............................... 108 Enhanced: Household Size 1.............................. 108 5.2 One-Dimensional Discrete Random Variables...................... 109 Discrete Random Variable................................ 109 Explained: One-Dimensional Discrete Random Variable ... 110 Enhanced: Household Size II............................. Ill 5.3 One-Dimensional Continuous Random Variables.................... 113 Density Function........................................ 113 Distribution Function .................................. 113 More Information: Continuous Random Variable, Density, and Distribution Function............ 114 Explained: Continuous Random Variable................. 116 Enhanced: Waiting Times of Supermarket Costumers...... 116 5.4 Parameters .................................................... 119 Expected Value.......................................... 120 Variance............................................— 121 Standard Deviation...................................... 121 Standardization......................................... 122 Chebyshev’s Inequality.................................. 122 Explained: Continuous Random Variable................... 123 Explained: Traffic Accidents ........................... 124 5.5 Two-Dimensional Random Variables............................... 124 Marginal Distribution................................... 125 The Conditional Marginal Distribution Function.......... 126 Explained: Two-Dimensional Random Variable.............. 127 Enhanced: Link Between Circulatory Diseases and Patient Age......................................... 129 5.6 Independence................................................... 131 Conditional Distribution................................ 132 More Information........................................ 133 Explained: Stochastic Independence...................... 134 Enhanced: Economic Conditions in Germany................ 136 Contents xiii 5.7 Parameters of Two-Dimensional Distributions....................... 139 Covariance................................................ 140 Correlation Coefficient................................... 140 More Information.......................................... 141 Explained: Parameters of Two-Dimensional Random Variables.......................................... 144 Enhanced: Investment Funds................................ 146 6 Probability Distributions .......................................... 149 6.1 Important Distribution Models..................................... 149 6.2 Uniform Distribution.............................................. 149 Discrete Uniform Distribution........................... 149 Continuous Uniform Distribution........................... 150 More Information.......................................... 151 Explained: Uniform Distribution........................... 152 6.3 Binomial Distribution ............................................ 154 More Information.......................................... 155 Explained: Drawing Balls from an Urn...................... 157 Enhanced: Better Chances for Fried Hamburgers............. 158 Enhanced: Student Jobs.................................... 160 Interactive: Binomial Distribution........................ 162 6.4 Hypergeometric Distribution....................................... 163 More Information.......................................... 164 Explained: Choosing Test Questions........................ 166 Enhanced: Selling Life Insurances......................... 167 Enhanced: Insurance Contract Renewal...................... 168 Interactive: Hypergeometric Distribution.................. 169 6.5 Poisson Distribution.............................................. 170 More Information........................................ 171 Explained: Risk of Vaccination Damage..................... 172 Enhanced: Number of Customers in Service Department................................................ 173 Interactive: Poisson Distribution ........................ 175 6.6 Exponential Distribution.......................................... 176 More Information.......................................... 177 Explained: Number of Defects ............................. 178 Enhanced: Equipment Failures.............................. 180 Interactive: Exponential Distribution..................... 181 6.7 Normal Distribution............................................... 181 Standardized Random Variable.............................. 183 Standard Normal Distribution.............................. 183 Confidence Interval ...................................... 184 More Information ......................................... 186 Other Properties of the Normal Distribution............... 187 Standard Normal Distribution ............................. 188 XIV Contents Explained: Normal Distributed Random Variable............. 188 Interactive: Normal Distribution.......................... 195 6.8 Central Limit Theorem.......................................... 196 Central Limit Theorem..................................... 197 More Information.......................................... 197 Explained: Application to a Uniform Random Variable — 197 6.9 Approximation of Distributions................................... 199 Normal Distribution as Limit of Other Distributions..... 199 Explained: Wrong Tax Returns.............................. 201 Enhanced: Storm Damage.................................... 203 6.10 Chi-Square Distribution.......................................... 204 More Information.......................................... 205 6.11 t-Distribution (Student t-Distribution).......................... 206 More Information.......................................... 207 6.12 F-Distribution................................................... 207 More Information.......................................... 208 7 Sampling Theory ....................................................... 209 7.1 Basic Ideas...................................................... 209 Population.............................................. 209 Sample.................................................... 210 Statistic ................................................ 211 More Information........................................ 213 Explained: Illustrating the basic Principles of Sampling Theory........................................ 213 7.2 Sampling Distribution of the Mean................................ 218 Distribution of the Sample Mean........................... 218 More Information.......................................... 221 Explained: Sampling Distribution.......................... 225 Enhanced: Gross Hourly Earnings of a Worker............... 228 7.3 Distribution of the Sample Proportion............................ 233 Explained: Distribution of the Sample Proportion.......... 237 Enhanced: Drawing Balls from a Urn........................ 239 7.4 Distribution of the Sample Variance.............................. 242 Distribution of the Sample Variance S2 ................... 243 Probability Statements About S2........................... 243 More Information.......................................... 244 Explained: Distribution of the Sample Variance.......... 247 8 8 Estimation............................................................. 251 8.1 Estimation Theory................................................ 251 Point Estimation.......................................... 251 The Estimator or Estimating Function...................... 251 Explained: Basic Examples of Estimation Procedures...... 252 8.2 Properties of Estimators......................................... 253 Mean Squared Error........................................ 255 XV 255 256 256 257 257 262 263 264 264 266 266 266 270 271 272 273 275 276 278 280 285 287 288 290 291 291 292 293 294 295 295 297 297 298 299 Unbiasedness........................................... Asymptotic Unbiasedness................................ Efficiency............................................. consistency ........................................... More Information....................................... Explained: Properties of Estimators.................... Enhanced: Properties of Estimation Functions........... Construction of Estimators.................................... Maximum Likelihood..................................... Least Squares Estimation............................... More Information.............................................. Applications of ML..................................... Application of Least Squares........................... Explained: ML Estimation of an Exponential Distribution........................................... Explained: ML Estimation of a Poisson Distribution..... Interval Estimation .......................................... Confidence Interval for the Mean.............................. Confidence Interval for the Mean with Known Variance___ Confidence Interval for the Mean with Unknown Variance............................................... Explained: Confidence Intervals for the Average Household Net Income................................... Enhanced: Confidence Intervals for the Lifetime of a Bulb.............................................. Interactive: Confidence Intervals for the Mean......... Confidence Interval for Proportion ........................... Properties of Confidence Intervals .................... Explained: Confidence Intervals for the Percentage of Votes............................ Interactive: Confidence Intervals for the Proportion... Confidence Interval for the Variance ......................... Properties of the Confidence Interval ................. Explained: Confidence Intervals for the Variance of Household Net Income................................ Interactive: Confidence Intervals for the Variance..... Confidence Interval for the Difference of Two Means........... 1. Case: The Variances a and of the Two Populations Are Known.................................. Properties of the Confidence Interval ................. 2. Case: The Variances o and a of the Two Populations Are Unknown................................ Properties of Confidence Intervals When Variances Are Unknown.................................. XVI Contents Explained: Confidence Interval for the Difference of Car Gas Consumptions................ 300 Enhanced: Confidence Intervals of the Difference of Two Mean Stock Prices................ 301 Interactive: Confidence Intervals for the Difference of Two Means........................... 304 8.9 Confidence Interval Length....................................... 305 (a) Confidence Interval for fi............................ 306 (b) Confidence Interval for tz............................ 306 Explained: Finding a Required Sample Size................. 307 Enhanced: Finding the Sample Size for an Election Threshold................................. 308 Interactive: Confidence Interval Length for the Mean.... 309 9 Statistical Tests.................................................... 311 9.1 Key Concepts..................................................... 311 Formulating the Hypothesis................................ 313 Test Statistic............................................ 314 Decision Regions and Significance Level................... 314 Non-rejection Region of Null Hypothesis .................. 315 Rejection Region of Null Hypothesis....................... 315 Power of a Test........................................... 323 OC-Curve.................................................. 324 A Decision-Theoretical View on Statistical Hypothesis Testing........................................ 324 More Information: Examples................................ 325 More Information: Hypothesis Testing Using Statistical Software...................................... 327 9.2 Testing Normal Means............................................. 330 Hypotheses................................................ 331 Test Statistic, Its Distribution, and Derived Decision Regions.......................................... 332 Calculating the Test Statistic from an Observed Sample — 336 Test Decision and Interpretation.......................... 337 Power..................................................... 338 More Information: Conducting a Statistical Test........... 342 Explained: Testing the Population Mean.................... 348 Enhanced: Average Life Time of Car Tires.................. 352 Hypothesis................................................ 353 1st Alternative........................................... 354 2nd Alternative........................................... 355 3rd Alternative........................................... 357 Interactive: Testing the Population Mean.................. 358 Interactive: Testing the Population Mean with Type I and II Error.................................. 359 xvii 360 361 361 363 363 364 364 369 376 377 377 378 380 380 381 383 384 386 387 388 389 390 391 391 392 393 394 394 397 399 400 401 404 405 406 407 408 408 Testing the Proportion in a Binary Population................... Hypotheses............................................... Test Statistic and Its Distribution: Decision Regions.... Sampling and Computing the Test Statistic................ Test Decision and Interpretation......................... Power Curve P(n)......................................... Explained: Testing a Population Proportion............... Enhanced: Proportion of Credits with Repayment Problems.................................. Interactive: Testing a Proportion in a Binary Population_ Testing the Difference of Two Population Means.................. Hypotheses............................................... Test Statistic and Its Distribution: Decision Regions.... Sampling and Computing the Test Statistic................ Test Decision and Interpretation.......................... Explained: Testing the Difference of Two Population Means......................................... Enhanced: Average Age Difference of Female and Male Bank Employees ................................. 1 st Dispute............................................. 2nd Dispute.............................................. 3rd Dispute.............................................. Interactive: Testing the Difference of Two Population Means......................................... Chi-Square Goodness-of-FitTest.................................. Hypothesis............................................... How Is pj Computed?...................................... Test Statistic and Its Distribution: Decision Regions.... Approximation Conditions ................................ Sampling and Computing the Test Statistic................ Test Decision and Interpretation......................... More Information......................................... Explained: Conducting a Chi-Square Goodness-of-Fit Test..................................... Enhanced: Goodness-of-Fit Test for Product Demand........ 1 st Version............................................. 2nd Version.............................................. Chi-Square Test of Independence................................. Hypothesis............................................... Test Statistic and Its Distribution: Decision Regions.... Sampling and Computing the Test Statistic................ Test Decision and Interpretation......................... More Information......................................... xviii Contents Explained: The Chi-Square Test of Independence in Action.............................. 411 Enhanced: Chi-Square Test of Independence for Economic Situation and Outlook........................ 413 10 Two-Dimensional Frequency Distribution................................. 419 10.1 Introduction..................................................... 419 10.2 Two-Dimensional Frequency Tables................................. 419 Realizations m * r........................................ 420 Absolute Frequency........................................ 420 Relative Frequency........................................ 420 Properties................................................ 420 Explained: Two-Dimensional Frequency Distribution...... 421 Enhanced: Department Store................................ 422 Interactive: Example for Two-Dimensional Frequency Distribution............................... — 423 10.3 Graphical Representation of Multidimensional Data................ 423 Frequency Distributions................................... 423 Scatterplots.............................................. 424 Explained: Graphical Representation of a Two- or Higher Dimensional Frequency Distribution.............................................. 426 Interactive: Example for the Graphical Representation of a Two- or Higher Dimensional Frequency Distribution.................................... 429 10.4 Marginal and Conditional Distributions........................... 429 Marginal Distribution..................................... 429 Conditional Distribution.................................. 430 Explained: Conditional Distributions...................... 432 Enhanced: Smokers and Lung Cancer......................... 433 Enhanced: Educational Level and Age....................... 434 10.5 Characteristics of Two-Dimensional Distributions................. 435 Covariance................................................ 435 More Information.......................................... 437 Explained: How the Covariance Is Calculated............... 437 10.6 Relation Between Continuous Variables (Correlation, Correlation Coefficients)......................................... 438 Properties of the Correlation Coefficient................. 439 Relation of Correlation and the Scatterplot of X and Y Observations........................................ 440 Explained: Relationship of Two Metrically Scaled Variables.......................................... 443 Interactive: Correlation Coefficients .................... 444 10.7 Relation Between Discrete Variables (Rank Correlation)........... 445 Spearman’s Rank Correlation Coefficient................... 445 Contents xix Kendall’s Rank Correlation Coefficient................. 447 Explained: Relationship Between Two Ordinally Scaled Variables......................................... 448 Interactive: Example for the Relationship Between Two Ordinally Scaled Variables................. 450 10.8 Relationship Between Nominal Variables (Contingency)......... 450 Explained: Relationship Between Two Nominally Scaled Variables............................... 452 Interactive: Example for the Relationship Between Two Nominally Scaled Variables................... 454 11 Regression........................................................... 455 11.1 Regression Analysis............................................ 455 The Objectives of Regression Analysis.................... 455 11.2 One-Dimensional Regression Analysis........................... 457 One-Dimensional Linear Regression Function............... 457 Quality (Fit) of the Regression Line................... 463 One-Dimensional Nonlinear Regression Function............ 466 Explained: One-Dimensional Linear Regression............. 468 Enhanced: Crime Rates in the US.......................... 471 Enhanced: Linear Regression for the Car Data........... 472 Interactive: Simple Linear Regression ................... 473 11.3 Multi-Dimensional Regression Analysis.......................... 474 Multi-Dimensional Regression Analysis.................... 474 12 Time Series Analysis............................................... 477 12.1 Time Series Analysis........................................... 477 Definition............................................... 477 Graphical Representation................................. 477 The Objectives of Time Series Analysis................... 477 Components of Time Series ............................... 479 12.2 Trend of Time Series........................................... 479 Method of Moving Average................................ 479 Least-Squares Method..................................... 481 More Information: Simple Moving Average.................. 483 Explained: Calculation of Moving Averages ............... 485 Interactive: Test of Different Filters for Trend Calculation ............................................. 486 12.3 Periodic Fluctuations........................................ 487 Explained: Decomposition of a Seasonal Series.......... 489 Interactive: Decomposition of Time Series................ 491 12.4 Quality of the Time Series Model .............................. 492 Mean Squared Dispersion (Estimated Standard Deviation) .............................................. 493 Interactive: Comparison of Time Series Models............ 494 XX Contents A Data Sets in the Interactive Examples......................... 495 A.l ALLBUS Data............................................. 495 АЛЛ ALLBUS 1992, ALLBUS2002, and ALLBUS2012: Economics............................. 495 АЛ.2 ALLBUS 1994, ALLBUS2002, and ALLBUS2012: Trust............................... 496 АЛ.З ALLBUS2002, ALLBUS2004, and ALLBUS2012: General............................... 497 A.2 Boston Housing Data..................................... 499 A.3 Car Data................................................ 499 A.4 Credit Data............................................. 500 A.5 Decathlon Data........................................ 501 A.6 Hair and Eye Color of Statistics Students............... 502 A.l Index of Basic Rent..................................... 502 A.8 Normally Distributed Data............................... 503 A.9 Telephone Data.......................................... 503 АЛ0 Titanic Data............................................ 504 АЛ1 US Crime Data........................................... 504 Glossary....................................................... 507
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spellingShingle	Härdle, Wolfgang 1953- Klinke, Sigbert Rönz, Bernd 1941- Introduction to statistics using interactive MM*Stat Elements Statistik (DE-588)4056995-0 gnd
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title	Introduction to statistics using interactive MM*Stat Elements
title_auth	Introduction to statistics using interactive MM*Stat Elements
title_exact_search	Introduction to statistics using interactive MM*Stat Elements
title_full	Introduction to statistics using interactive MM*Stat Elements Wolfgang Karl Härdle, Sigbert Klinke, Bernd Rönz
title_fullStr	Introduction to statistics using interactive MM*Stat Elements Wolfgang Karl Härdle, Sigbert Klinke, Bernd Rönz
title_full_unstemmed	Introduction to statistics using interactive MM*Stat Elements Wolfgang Karl Härdle, Sigbert Klinke, Bernd Rönz
title_short	Introduction to statistics
title_sort	introduction to statistics using interactive mm stat elements
title_sub	using interactive MM*Stat Elements
topic	Statistik (DE-588)4056995-0 gnd
topic_facet	Statistik Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028759149&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT hardlewolfgang introductiontostatisticsusinginteractivemmstatelements AT klinkesigbert introductiontostatisticsusinginteractivemmstatelements AT ronzbernd introductiontostatisticsusinginteractivemmstatelements

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