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1 | (20) |
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1.1 Objectives of Statistics |
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1 | (3) |
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A Definition of Statistics |
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1 | (2) |
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Explained: Descriptive and Inductive Statistics |
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3 | (1) |
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1.2 Statistical Investigation |
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4 | (4) |
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Conducting a Statistical Investigation |
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4 | (1) |
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4 | (2) |
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Explained: Public Sources of Data |
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6 | (1) |
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More Information: Statistical Processes |
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6 | (2) |
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1.3 Statistical Element and Population |
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8 | (2) |
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8 | (1) |
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8 | (1) |
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Explained: Statistical Elements and Population |
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8 | (2) |
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10 | (1) |
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11 | (1) |
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1.6 Qualitative Variables |
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11 | (2) |
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11 | (1) |
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12 | (1) |
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1.7 Quantitative Variables |
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13 | (1) |
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13 | (1) |
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13 | (1) |
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13 | (1) |
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14 | (1) |
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14 | (1) |
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1.8 Grouping Continuous Data |
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14 | (2) |
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Explained: Grouping of Data |
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16 | (1) |
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1.9 Statistical Sequences and Frequencies |
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16 | (5) |
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16 | (1) |
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17 | (1) |
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Explained: Absolute and Relative Frequency |
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18 | (3) |
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2 One-Dimensional Frequency Distributions |
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21 | (48) |
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2.1 One-Dimensional Distribution |
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21 | (5) |
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2.1.1 Frequency Distributions for Discrete Data |
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21 | (1) |
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21 | (1) |
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2.1.2 Graphical Presentation |
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22 | (3) |
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Explained: Job Proportions in Germany |
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25 | (1) |
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Enhanced: Evolution of Household Sizes |
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25 | (1) |
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2.2 Frequency Distribution for Continuous Data |
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26 | (8) |
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27 | (1) |
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27 | (3) |
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Explained: Petrol Consumption of Cars |
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30 | (1) |
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Explained: Net Income of German Nationals |
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31 | (3) |
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2.3 Empirical Distribution Function |
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34 | (6) |
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2.3.1 Empirical Distribution Function for Discrete Data |
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35 | (1) |
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2.3.2 Empirical Distribution Function for Grouped Continuous Data |
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36 | (1) |
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Explained: Petrol Consumption of Cars |
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37 | (1) |
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Explained: Grades in Statistics Examination |
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38 | (2) |
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2.4 Numerical Description of One-Dimensional Frequency Distributions |
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40 | (10) |
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40 | (7) |
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Explained: Average Prices of Cars |
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47 | (2) |
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Interactive: Dotplot with Location Parameters |
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49 | (1) |
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Interactive: Simple Histogram |
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49 | (1) |
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2.5 Location Parameters: Mean Values---Harmonic Mean, Geometric Mean |
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50 | (5) |
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50 | (2) |
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52 | (3) |
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2.6 Measures of Scale or Variation |
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55 | (9) |
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56 | (1) |
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57 | (1) |
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57 | (1) |
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The Variance and the Standard Deviation |
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58 | (2) |
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Explained: Variations of Pizza Prices |
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60 | (1) |
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Enhanced: Parameters of Scale for Cars |
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61 | (1) |
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Interactive: Dotplot with Scale Parameters |
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62 | (2) |
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2.7 Graphical Display of the Location and Scale Parameters |
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64 | (5) |
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Boxplot (Box-Whisker-Plot) |
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64 | (2) |
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Explained: Boxplot of Car Prices |
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66 | (1) |
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Interactive: Visualization of One-Dimensional Distributions |
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67 | (2) |
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69 | (28) |
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3.1 The Sample Space, Events, and Probabilities |
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69 | (1) |
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70 | (1) |
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3.2 Event Relations and Operations |
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70 | (5) |
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70 | (1) |
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71 | (1) |
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71 | (2) |
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Logical Difference of Sets or Events |
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73 | (1) |
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Disjoint Decomposition of the Sample Space |
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74 | (1) |
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75 | (1) |
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75 | (7) |
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76 | (1) |
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76 | (2) |
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Axiomatic Foundation of Probability |
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78 | (1) |
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Addition Rule of Probability |
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78 | (1) |
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More Information: Derivation of the Addition Rule |
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79 | (1) |
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More Information: Implications of the Probability Axioms |
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80 | (1) |
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Explained: A Deck of Cards |
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81 | (1) |
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3.4 Conditional Probability and Independent Events |
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82 | (5) |
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82 | (1) |
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83 | (1) |
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83 | (1) |
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84 | (1) |
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More Information: Derivation of Rules for Independent Events |
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85 | (1) |
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Explained: Two-Way Cross-Tabulation |
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85 | (1) |
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86 | (1) |
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3.5 Theorem of Total Probabilities and Bayes' Rule |
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87 | (10) |
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Theorem of Total Probabilities |
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87 | (1) |
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88 | (1) |
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Explained: The Wine Cellar |
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88 | (2) |
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90 | (1) |
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Interactive: Monty Hall Problem |
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91 | (3) |
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Interactive: Die Rolling Sisters |
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94 | (3) |
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97 | (10) |
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97 | (1) |
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Different Ways of Grouping and Ordering |
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97 | (1) |
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Use of Combinatorial Theory |
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98 | (1) |
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98 | (2) |
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Permutations Without Repetition |
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98 | (1) |
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Permutations with Repetition |
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99 | (1) |
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Permutations with More Groups of Identical Elements |
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99 | (1) |
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Explained: Beauty Competition |
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100 | (1) |
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100 | (2) |
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Variations with Repetition |
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100 | (1) |
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Variations Without Repetition |
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101 | (1) |
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101 | (1) |
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102 | (2) |
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Combinations Without Repetition |
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102 | (1) |
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Combinations with Repetition |
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103 | (1) |
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103 | (1) |
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4.5 Properties of Euler's Numbers (Combination Numbers) |
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104 | (3) |
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104 | (1) |
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104 | (1) |
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Sum of Two Euler's Numbers |
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104 | (1) |
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Euler's Numbers and Binomial Coefficients |
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105 | (2) |
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107 | (42) |
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107 | (2) |
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107 | (1) |
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Explained: The Experiment |
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108 | (1) |
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Enhanced: Household Size I |
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108 | (1) |
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5.2 One-Dimensional Discrete Random Variables |
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109 | (4) |
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109 | (1) |
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Explained: One-Dimensional Discrete Random Variable |
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110 | (1) |
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Enhanced: Household Size II |
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111 | (2) |
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5.3 One-Dimensional Continuous Random Variables |
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113 | (6) |
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113 | (1) |
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113 | (1) |
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More Information: Continuous Random Variable, Density, and Distribution Function |
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114 | (2) |
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Explained: Continuous Random Variable |
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116 | (1) |
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Enhanced: Waiting Times of Supermarket Costumers |
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116 | (3) |
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119 | (5) |
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120 | (1) |
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121 | (1) |
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121 | (1) |
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122 | (1) |
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122 | (1) |
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Explained: Continuous Random Variable |
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123 | (1) |
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Explained: Traffic Accidents |
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124 | (1) |
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5.5 Two-Dimensional Random Variables |
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124 | (7) |
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125 | (1) |
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The Conditional Marginal Distribution Function |
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126 | (1) |
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Explained: Two-Dimensional Random Variable |
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127 | (2) |
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Enhanced: Link Between Circulatory Diseases and Patient Age |
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129 | (2) |
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131 | (8) |
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132 | (1) |
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133 | (1) |
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Explained: Stochastic Independence |
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134 | (2) |
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Enhanced: Economic Conditions in Germany |
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136 | (3) |
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5.7 Parameters of Two-Dimensional Distributions |
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139 | (10) |
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140 | (1) |
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140 | (1) |
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141 | (3) |
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Explained: Parameters of Two-Dimensional Random Variables |
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144 | (2) |
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Enhanced: Investment Funds |
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146 | (3) |
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6 Probability Distributions |
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149 | (60) |
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6.1 Important Distribution Models |
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149 | (1) |
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149 | (5) |
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Discrete Uniform Distribution |
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149 | (1) |
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Continuous Uniform Distribution |
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150 | (1) |
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151 | (1) |
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Explained: Uniform Distribution |
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152 | (2) |
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6.3 Binomial Distribution |
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154 | (9) |
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155 | (2) |
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Explained: Drawing Balls from an Urn |
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157 | (1) |
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Enhanced: Better Chances for Fried Hamburgers |
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158 | (2) |
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160 | (2) |
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Interactive: Binomial Distribution |
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162 | (1) |
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6.4 Hypergeometric Distribution |
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163 | (7) |
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164 | (2) |
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Explained: Choosing Test Questions |
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166 | (1) |
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Enhanced: Selling Life Insurances |
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167 | (1) |
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Enhanced: Insurance Contract Renewal |
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168 | (1) |
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Interactive: Hypergeometric Distribution |
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169 | (1) |
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170 | (6) |
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171 | (1) |
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Explained: Risk of Vaccination Damage |
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172 | (1) |
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Enhanced: Number of Customers in Service Department |
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173 | (2) |
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Interactive: Poisson Distribution |
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175 | (1) |
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6.6 Exponential Distribution |
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176 | (5) |
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177 | (1) |
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Explained: Number of Defects |
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178 | (2) |
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Enhanced: Equipment Failures |
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180 | (1) |
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Interactive: Exponential Distribution |
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181 | (1) |
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181 | (15) |
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Standardized Random Variable |
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183 | (1) |
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Standard Normal Distribution |
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183 | (1) |
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184 | (2) |
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186 | (1) |
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Other Properties of the Normal Distribution |
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187 | (1) |
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Standard Normal Distribution |
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188 | (1) |
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Explained: Normal Distributed Random Variable |
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188 | (7) |
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Interactive: Normal Distribution |
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195 | (1) |
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6.8 Central Limit Theorem |
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196 | (3) |
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197 | (1) |
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197 | (1) |
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Explained: Application to a Uniform Random Variable |
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197 | (2) |
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6.9 Approximation of Distributions |
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199 | (5) |
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Normal Distribution as Limit of Other Distributions |
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199 | (2) |
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Explained: Wrong Tax Returns |
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201 | (2) |
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203 | (1) |
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6.10 Chi-Square Distribution |
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204 | (2) |
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205 | (1) |
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6.11 t-Distribution (Student t-Distribution) |
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206 | (1) |
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207 | (1) |
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207 | (2) |
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208 | (1) |
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209 | (42) |
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209 | (9) |
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209 | (1) |
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210 | (1) |
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211 | (2) |
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213 | (1) |
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Explained: Illustrating the basic Principles of Sampling Theory |
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213 | (5) |
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7.2 Sampling Distribution of the Mean |
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218 | (15) |
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Distribution of the Sample Mean |
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218 | (3) |
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221 | (4) |
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Explained: Sampling Distribution |
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225 | (3) |
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Enhanced: Gross Hourly Earnings of a Worker |
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228 | (5) |
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7.3 Distribution of the Sample Proportion |
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233 | (9) |
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Explained: Distribution of the Sample Proportion |
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237 | (2) |
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Enhanced: Drawing Balls from a Urn |
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239 | (3) |
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7.4 Distribution of the Sample Variance |
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242 | (9) |
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Distribution of the Sample Variance S2 |
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243 | (1) |
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Probability Statements About S2 |
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243 | (1) |
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244 | (3) |
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Explained: Distribution of the Sample Variance |
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247 | (4) |
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251 | (60) |
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251 | (2) |
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251 | (1) |
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The Estimator or Estimating Function |
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251 | (1) |
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Explained: Basic Examples of Estimation Procedures |
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252 | (1) |
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8.2 Properties of Estimators |
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253 | (11) |
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255 | (1) |
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255 | (1) |
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256 | (1) |
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256 | (1) |
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257 | (1) |
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257 | (5) |
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Explained: Properties of Estimators |
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262 | (1) |
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Enhanced: Properties of Estimation Functions |
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263 | (1) |
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8.3 Construction of Estimators |
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264 | (9) |
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264 | (2) |
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266 | (1) |
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266 | (1) |
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266 | (4) |
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Application of Least Squares |
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270 | (1) |
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Explained: ML Estimation of an Exponential Distribution |
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271 | (1) |
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Explained: ML Estimation of a Poisson Distribution |
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272 | (1) |
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273 | (2) |
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8.5 Confidence Interval for the Mean |
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275 | (13) |
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Confidence Interval for the Mean with Known Variance |
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276 | (2) |
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Confidence Interval for the Mean with Unknown Variance |
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278 | (2) |
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Explained: Confidence Intervals for the Average Household Net Income |
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280 | (5) |
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Enhanced: Confidence Intervals for the Lifetime of a Bulb |
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285 | (2) |
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Interactive: Confidence Intervals for the Mean |
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287 | (1) |
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8.6 Confidence Interval for Proportion |
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288 | (4) |
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Properties of Confidence Intervals |
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290 | (1) |
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Explained: Confidence Intervals for the Percentage of Votes |
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291 | (1) |
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Interactive: Confidence Intervals for the Proportion |
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291 | (1) |
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8.7 Confidence Interval for the Variance |
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292 | (3) |
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Properties of the Confidence Interval |
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293 | (1) |
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Explained: Confidence Intervals for the Variance of Household Net Income |
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294 | (1) |
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Interactive: Confidence Intervals for the Variance |
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295 | (1) |
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8.8 Confidence Interval for the Difference of Two Means |
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295 | (10) |
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1 Case: The Variances σ21 and σ22 of the Two Populations Are Known |
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297 | (1) |
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Properties of the Confidence Interval |
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297 | (1) |
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2 Case: The Variances σ21 and σ22 of the Two Populations Are Unknown |
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298 | (1) |
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Properties of Confidence Intervals When Variances Are Unknown |
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299 | (1) |
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Explained: Confidence Interval for the Difference of Car Gas Consumptions |
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300 | (1) |
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Enhanced: Confidence Intervals of the Difference of Two Mean Stock Prices |
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301 | (3) |
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Interactive: Confidence Intervals for the Difference of Two Means |
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304 | (1) |
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8.9 Confidence Interval Length |
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305 | (6) |
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(a) Confidence Interval for μ |
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306 | (1) |
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(b) Confidence Interval for π |
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306 | (1) |
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Explained: Finding a Required Sample Size |
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307 | (1) |
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Enhanced: Finding the Sample Size for an Election Threshold |
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308 | (1) |
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Interactive: Confidence Interval Length for the Mean |
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309 | (2) |
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311 | (108) |
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311 | (19) |
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Formulating the Hypothesis |
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313 | (1) |
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314 | (1) |
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Decision Regions and Significance Level |
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314 | (1) |
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Non-rejection Region of Null Hypothesis |
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315 | (1) |
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Rejection Region of Null Hypothesis |
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315 | (8) |
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323 | (1) |
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324 | (1) |
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A Decision-Theoretical View on Statistical Hypothesis Testing |
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324 | (1) |
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More Information: Examples |
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325 | (2) |
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More Information: Hypothesis Testing Using Statistical Software |
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327 | (3) |
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330 | (30) |
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331 | (1) |
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Test Statistic, Its Distribution, and Derived Decision Regions |
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332 | (4) |
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Calculating the Test Statistic from an Observed Sample |
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336 | (1) |
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Test Decision and Interpretation |
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337 | (1) |
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338 | (4) |
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More Information: Conducting a Statistical Test |
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342 | (6) |
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Explained: Testing the Population Mean |
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348 | (4) |
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Enhanced: Average Life Time of Car Tires |
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352 | (1) |
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353 | (1) |
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354 | (1) |
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355 | (2) |
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357 | (1) |
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Interactive: Testing the Population Mean |
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358 | (1) |
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Interactive: Testing the Population Mean with Type I and II Error |
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359 | (1) |
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9.3 Testing the Proportion in a Binary Population |
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360 | (17) |
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361 | (1) |
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Test Statistic and Its Distribution: Decision Regions |
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361 | (2) |
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Sampling and Computing the Test Statistic |
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363 | (1) |
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Test Decision and Interpretation |
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363 | (1) |
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364 | (1) |
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Explained: Testing a Population Proportion |
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364 | (5) |
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Enhanced: Proportion of Credits with Repayment Problems |
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369 | (7) |
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Interactive: Testing a Proportion in a Binary Population |
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376 | (1) |
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9.4 Testing the Difference of Two Population Means |
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377 | (12) |
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377 | (1) |
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Test Statistic and Its Distribution: Decision Regions |
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378 | (2) |
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Sampling and Computing the Test Statistic |
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380 | (1) |
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Test Decision and Interpretation |
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380 | (1) |
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Explained: Testing the Difference of Two Population Means |
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381 | (2) |
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Enhanced: Average Age Difference of Female and Male Bank Employees |
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383 | (1) |
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384 | (2) |
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386 | (1) |
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387 | (1) |
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Interactive: Testing the Difference of Two Population Means |
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388 | (1) |
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9.5 Chi-Square Goodness-of-Fit Test |
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389 | (15) |
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390 | (1) |
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391 | (1) |
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Test Statistic and Its Distribution: Decision Regions |
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391 | (1) |
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392 | (1) |
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Sampling and Computing the Test Statistic |
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393 | (1) |
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Test Decision and Interpretation |
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394 | (1) |
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394 | (3) |
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Explained: Conducting a Chi-Square Goodness-of-Fit Test |
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397 | (2) |
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Enhanced: Goodness-of-Fit Test for Product Demand |
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399 | (1) |
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400 | (1) |
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401 | (3) |
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9.6 Chi-Square Test of Independence |
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404 | (15) |
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405 | (1) |
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Test Statistic and Its Distribution: Decision Regions |
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406 | (1) |
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Sampling and Computing the Test Statistic |
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407 | (1) |
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Test Decision and Interpretation |
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408 | (1) |
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408 | (3) |
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Explained: The Chi-Square Test of Independence in Action |
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411 | (2) |
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Enhanced: Chi-Square Test of Independence for Economic Situation and Outlook |
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413 | (6) |
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10 Two-Dimensional Frequency Distribution |
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419 | (36) |
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419 | (1) |
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10.2 Two-Dimensional Frequency Tables |
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419 | (4) |
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420 | (1) |
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420 | (1) |
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420 | (1) |
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420 | (1) |
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Explained: Two-Dimensional Frequency Distribution |
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421 | (1) |
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Enhanced: Department Store |
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422 | (1) |
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Interactive: Example for Two-Dimensional Frequency Distribution |
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423 | (1) |
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10.3 Graphical Representation of Multidimensional Data |
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423 | (6) |
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423 | (1) |
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424 | (2) |
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Explained: Graphical Representation of a Two- or Higher Dimensional Frequency Distribution |
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426 | (3) |
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Interactive: Example for the Graphical Representation of a Two- or Higher Dimensional Frequency Distribution |
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429 | (1) |
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10.4 Marginal and Conditional Distributions |
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429 | (6) |
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429 | (1) |
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430 | (2) |
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Explained: Conditional Distributions |
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432 | (1) |
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Enhanced: Smokers and Lung Cancer |
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433 | (1) |
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Enhanced: Educational Level and Age |
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434 | (1) |
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10.5 Characteristics of Two-Dimensional Distributions |
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435 | (3) |
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435 | (2) |
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437 | (1) |
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Explained: How the Covariance Is Calculated |
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437 | (1) |
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10.6 Relation Between Continuous Variables (Correlation, Correlation Coefficients) |
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438 | (7) |
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Properties of the Correlation Coefficient |
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439 | (1) |
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Relation of Correlation and the Scatterplot of X and Y Observations |
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440 | (3) |
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Explained: Relationship of Two Metrically |
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443 | (1) |
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Interactive: Correlation Coefficients |
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444 | (1) |
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10.7 Relation Between Discrete Variables (Rank Correlation) |
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445 | (5) |
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Spearman's Rank Correlation Coefficient |
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445 | (2) |
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Kendall's Rank Correlation Coefficient |
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447 | (1) |
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Explained: Relationship Between Two Ordinally Scaled Variables |
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448 | (2) |
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Interactive: Example for the Relationship Between Two Ordinally Scaled Variables |
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450 | (1) |
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10.8 Relationship Between Nominal Variables (Contingency) |
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450 | (5) |
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Explained: Relationship Between Two Nominally Scaled Variables |
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452 | (2) |
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Interactive: Example for the Relationship Between Two Nominally Scaled Variables |
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454 | (1) |
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455 | (22) |
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455 | (2) |
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The Objectives of Regression Analysis |
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455 | (2) |
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11.2 One-Dimensional Regression Analysis |
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457 | (17) |
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One-Dimensional Linear Regression Function |
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457 | (6) |
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Quality (Fit) of the Regression Line |
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463 | (3) |
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One-Dimensional Nonlinear Regression Function |
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466 | (2) |
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Explained: One-Dimensional Linear Regression |
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468 | (3) |
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Enhanced: Crime Rates in the US |
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471 | (1) |
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Enhanced: Linear Regression for the Car Data |
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472 | (1) |
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Interactive: Simple Linear Regression |
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473 | (1) |
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11.3 Multi-Dimensional Regression Analysis |
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474 | (3) |
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Multi-Dimensional Regression Analysis |
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474 | (3) |
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477 | (18) |
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12.1 Time Series Analysis |
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477 | (2) |
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477 | (1) |
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477 | (1) |
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The Objectives of Time Series Analysis |
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477 | (2) |
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Components of Time Series |
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479 | (1) |
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12.2 Trend of Time Series |
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479 | (8) |
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479 | (2) |
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481 | (2) |
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More Information: Simple Moving Average |
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483 | (2) |
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Explained: Calculation of Moving Averages |
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485 | (1) |
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Interactive: Test of Different Filters for Trend Calculation |
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486 | (1) |
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12.3 Periodic Fluctuations |
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487 | (5) |
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Explained: Decomposition of a Seasonal Series |
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489 | (2) |
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Interactive: Decomposition of Time Series |
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491 | (1) |
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12.4 Quality of the Time Series Model |
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492 | (3) |
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Mean Squared Dispersion (Estimated Standard Deviation) |
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493 | (1) |
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Interactive: Comparison of Time Series Models |
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494 | (1) |
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A Data Sets in the Interactive Examples |
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495 | (12) |
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495 | (4) |
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A.1.1 ALLBUS1992, ALLBUS2002, and ALLBUS2012: Economics |
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495 | (1) |
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A.1.2 ALLBUS1994, ALLBUS2002, and ALLBUS2012: Trust |
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496 | (1) |
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A.1.3 ALLBUS2002, ALLBUS2004, and ALLBUS2012: General |
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497 | (2) |
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499 | (1) |
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499 | (1) |
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500 | (1) |
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501 | (1) |
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A.6 Hair and Eye Color of Statistics Students |
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502 | (1) |
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502 | (1) |
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A.8 Normally Distributed Data |
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503 | (1) |
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503 | (1) |
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504 | (1) |
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504 | (3) |
| Glossary |
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507 | |
Lisainfo e-raamatute kohta