Non Constant Coefficient of Variance

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 168

Figure B.56: Simulation 14: Constant Coefficient of Variance, Three Outliers, High Outlier Term, Clustered Outliers -The LORELIA Residual Test

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 169

Figure B.58: Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers -Outlier Test for the Normalized Relative Differences

Figure B.59: Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers -Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 170

Figure B.60: Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers -The LORELIA Residual Test

Figure B.61: Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier, Medium Outlier Term - Outlier Test for the Absolute Differences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 171

Figure B.62: Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier, Medium Outlier Term - Outlier Test for the Normalized Relative Differences

Figure B.63: Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier, Medium Outlier Term - Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 172

Figure B.64: Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier, Medium Outlier Term -The LORELIA Residual Test

Figure B.65: Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier, High Outlier Term - Outlier Test for the Absolute Differences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 173

Figure B.66: Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier, High Outlier Term - Outlier Test for the Normalized Relative Differences

Figure B.67: Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier, High Outlier Term - Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 174

Figure B.68: Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier, High Outlier Term -The LORELIA Residual Test

Figure B.69: Simulation 18: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differ-ences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 175

Figure B.70: Simulation 18: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Normalized Rel-ative Differences

Figure B.71: Simulation 18: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Resid-uals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 176

Figure B.72: Simulation 18: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Uniformly Distributed Outliers -The LORELIA Residual Test

Figure B.73: Simulation 19: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Clustered Outliers - Outlier Test for the Absolute Differences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 177

Figure B.74: Simulation 19: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Clustered Outliers - Outlier Test for the Normalized Relative Differ-ences

Figure B.75: Simulation 19: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Clustered Outliers - Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 178

Figure B.76: Simulation 19: Non Constant Coefficient of Residual Variance, Three Outliers, Medium Outlier Term, Clustered Outliers -The LORELIA Residual Test

Figure B.77: Simulation 20: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 179

Figure B.78: Simulation 20: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Normalized Relative Differences

Figure B.79: Simulation 20: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 180

Figure B.80: Simulation 20: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Uniformly Distributed Outliers -The LORELIA Residual Test

Figure B.81: Simulation 21: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Clustered Outliers - Outlier Test for the Absolute Differences

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 181

Figure B.82: Simulation 21: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Clustered Outliers - Outlier Test for the Normalized Relative Differences

Figure B.83: Simulation 21: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Clustered Outliers - Outlier Test for the Orthogonal Residuals

APPENDIX B. TEST RESULTS OF SECTION 7.1.3 182

Figure B.84: Simulation 21: Non Constant Coefficient of Residual Variance, Three Outliers, High Outlier Term, Clustered Outliers -The LORELIA Residual Test

Symbols

N Natural Numbers

R Real Numbers

R⁺0 Positive Real Numbers Including0

U(a, b) Continuous Uniform Distribution on[a, b]⊂R

N(μ, σ²) Normal Distribution with Expected Valueμand Varianceσ² logN(μ, σ²) Log Normal Distribution with Parametersμandσ²

χ²_DF χ² Distribution withDF Degrees of Freedom

Φ() Distribution Function of the Standard Normal Distribution z_(1−α) (1−α)Quantile of the Standard Normal Distribution

t_DF,(1−α) (1− α) Quantile of the Students t Distribution with DF Degrees of Freedom

X₁, ..., X_n ^iid∼ X X₁, ..., X_nare independent and identically distributed asX x₁, ..., x_n Realizations of the Random VariablesX₁, ..., X_n

x₍₁₎, ..., x_(n) Ordered Sequence ofx₁, ..., x_n

E(X) Expected Value of the Random VariableX V ar(X) Variance of the Random VariableX x Mean Value ofx₁, ..., x_ngiven by_n¹ _n

i=1x_i S_xx² Empirical Variance ofX given by_n−¹_1n

i=1(x_i−x)² S_xy² Empirical Covariance ofX andY given by _n−¹_1n

i=1(x_i−x)(y_i−y) med(x) Median ofx₁, ..., x_n

mad68(x) 68%Median Absolute Deviation min_{1≤i≤n}{x_i} Minimum ofx₁, ..., x_n

max_{1≤i≤n}{x_i} Maximum ofx₁, ..., x_n inf_{1≤i≤n}{x_i} Infimum ofx₁, ..., x_n sup_{1≤i≤n}{x_i} Supremum ofx₁, ..., x_n

sign() Signum Function

mod() Modulus Function

∂f

∂t Partial Derivative of the Functionf tot

183

SYMBOLS 184 H₀ Null Hypothesis of a Statistical Test

H₁ Alternative Hypothesis of a Statistical Test

α Level of Significance

α_loc Local Level of Significance for a Multiple Test Situation α_glob Global Level of Significance for a Multiple Test Situation P_int Population of Interest

P_cont Contaminating Population

M_x, M_y Methods which are to be compared

X, Y Random Variables for the True Measurement Values of Methods M_x andM_y

E_x, E_y Random Variables for the Measurement Errors in MethodsM_xandM_y c₁, ..., c_n True Concentrations for Measurement Values(x₁, y₁), ...,(x_n, y_n) R₁, ..., R_n Random Variables for the Orthogonal Residuals

out_x, out_y Outlier Term for MethodsM_x andM_y

D_i^abs Random Variable for the Absolute Difference betweenxandy D_i^rel Random Variable for the Relative Difference betweenxandy

D_i^normrel Random Variable for the Normalized Relative Difference betweenxand y

α_PCA,β_PCA Parameter Estimators for Principal Component Analysis

α_SPCA,β_SPCA Parameter Estimators for Standardized Principal Component Analysis

α_PB,β_PB Parameter Estimators for Passing-Bablok Regression R² Squared Correlation Coefficient for Linear Regression C_α (1−α)%Approximative Confidence Intervall

(x^p_i, y_i^p) Orthogonal Projection of the Measurement Tuple(x_i, y_i)to the Regres-sion Line

w^Shep Shepard’s Weights (Inverse Distance Weights) w^Kon Weights proposed by [Konnert, 2005]

w_ik LORELIA Weights

δ_ik Squared Absolute Distance between(x^p_i, y^p_i)and(x^p_k, y_k^p) Δ_ik LORELIA Distance Weight, Transformation ofδ_ik

γ_k,n Reliability Measure

Γ_k,n LORELIA Reliability Weight, Transformation ofγ_k,n

List of Figures

2.1 Outliers in Different Data Situations - Bar Diagram . . . 6

2.2 Outliers in Different Data Situations - Linear Model . . . 7

2.3 Outliers in Different Data Situations - Normal Distribution . . . 7

2.4 Mixed Distribution: 0.9·N(3,1) + 0.1·logN(7,1) . . . 9

2.5 Mixed Distribution: 0.9·N(5,1) + 0.1·logN(5,2) . . . 10

2.6 Population Affiliations . . . 11

2.7 Extreme Observation for the U-Distribution . . . 12

2.8 Error in the Model Assumption . . . 13

2.9 Corrected Model Assumption . . . 13

2.10 Outlier Candidate from a Two-Dimensional Linear Regression Model . . . . 14

2.11 Outlier Candidates in Location and in Variance . . . 15

2.12 Ambiguity of Extreme Values . . . 15

2.13 Linear Fits for Excluded Upper or Lower Extreme Value . . . 16

2.14 Linear Fits with both Extreme Values Excluded . . . 17

2.15 Classification of Outlier Candidates . . . 19

3.1 The Masking Effect . . . 26

3.2 The Swamping Effect . . . 26

3.3 Linear Regression with the First Leverage Point Included . . . 28

3.4 Linear Regression with the Second Leverage Point Included . . . 28

3.5 Linear Regression without the Leverage Points . . . 29

4.1 Method Comparison based on the Absolute Differences . . . 32

4.2 Proportional Bias Between Methods . . . 33

4.3 Method Comparison based on the Normalized Relative Differences . . . 34

4.4 Method Comparison based on the Relative Differences . . . 36

4.5 The Concept of Deming Regression . . . 38

4.6 Residuals for PCA and SPCA . . . 40

185

LIST OF FIGURES 186

5.1 Outlier Identification Based on the Normalized Relative Differences . . . 45

5.2 Confidence Bounds for the Residuals . . . 46

5.3 Examples for Heteroscedastic Residual Variance Models . . . 47

6.1 The Orthogonal Residuals . . . 50

6.2 Distance between the Orthogonal Residuals . . . 52

6.3 The Method of A. Konnert for a Dataset With No Obvious Outlier . . . 54

6.4 The Method of A. Konnert for the Dataset with One Outlier . . . 54

6.5 The Method of A. Konnert for the Dataset with Two Neighbored Outliers . . 55

6.6 Local Outlier Limits for Scaled Measuring Ranges . . . 56

6.7 Influence of the Neighbored Residuals . . . 57

6.8 The Local Reliability . . . 58

6.9 Different Areas of Information Density . . . 59

6.10 Increasing Distanceδ_(i−1)i . . . 62

6.11 The Values of the Distance MeasureΔ_ikfor Different Sample Sizes . . . 64

6.12 The Local Reliability MeasureΓ_k,nfor Different Sample Sizes andc= 10 . . 66

7.1 Example 1 - No Suspicious Values for Inhomogeneously Distributed Data . . 72

7.2 Example 1 - Outlier Test for the Absolute Differences . . . 73

7.3 Example 1 - Outlier Test for the Residuals . . . 73

7.4 Example 1 - Outlier Test for the Normalized Relative Differences . . . 74

7.5 Example 1 - The LORELIA Residual Test . . . 74

7.6 Example 1 - Reliability Plot with Identified Outliers . . . 75

7.7 Example 2 - One Outlier Candidate for Inhomogeneously Distributed Data . . 76

7.8 Example 2 - Outlier Test for the Absolute Differences . . . 76

7.9 Example 2 - Outlier Test for the Residuals . . . 77

7.10 Example 2 - Outlier Test for the Normalized Relative Differences . . . 77

7.11 Example 2 - Identified Outliers in the Regression and the Residual Plot . . . . 78

7.12 Example 2 - Reliability Plot with Identified Outlier . . . 78

7.13 Example 3 - Uncertain Outlier Situation . . . 79

7.14 Example 3 - Outlier Test for the Absolute Differences . . . 79

7.15 Example 3 - Outlier Test for the Residuals . . . 80

7.16 Example 3 - Outlier Test for the Normalized Relative Differences . . . 80

7.17 Example 3 - The LORELIA Residual Test . . . 81

7.18 Example 3 - Reliability Plot . . . 81

7.19 Example 4 - Decreasing Residual Variance . . . 82

7.20 Example 4 - Outlier Test for the Absolute Differences . . . 82

LIST OF FIGURES 187

7.21 Example 4 - Outlier Test for the Residuals . . . 83

7.22 Example 4 - Outlier Test for the Normalized Relative Differences . . . 83

7.23 Example 4 - The LORELIA Residual Test . . . 84

7.24 Example 4 - Reliability Plot with Identified Outliers . . . 84

7.25 Example 5 - Very Inhomogeneous Data Dispersion . . . 85

7.26 Example 5 - Outlier Test for the Absolute Differences . . . 85

7.27 Example 5 - Outlier Test for the Residuals . . . 86

7.28 Example 5 - Outlier Test for the Normalized Relative Differences . . . 86

7.29 Example 5 - The LORELIA Residual Test . . . 87

7.30 Example 5 - Reliability Plot with Identified Outliers . . . 87

7.31 Exemplary Dataset from the Model ClassM . . . 94

7.32 Evaluation of the Exemplary Dataset with the Global Outlier Tests Based on the Absolute Differences, on the Orthogonal Residuals and on the Normalized Relative Differences . . . 95

7.33 Evaluation of the Exemplary Dataset with the LORELIA Residual Test . . . . 95

7.34 Percentages of True Positive Test Results, Constant Residual Variance . . . . 101

7.35 Percentages of False Positive Test Results, Constant Residual Variance . . . . 102

7.36 Percentages of True Positive Test Results for a Constant Coefficient of Variance103 7.37 Percentages of False Positive Test Results for a Constant Coefficient of Variance104 7.38 Percentages of True Positive Test Results, Non Constant Coefficient of Variance106 7.39 Means of True Positive and False Positive Test Results - Homogeneous Data Distribution, Non Constant Coefficient of Variance . . . 106

7.40 Homogeneous Data Distribution, Constant Coefficient of Variance, Three Out-liers, Medium Outlier Term, Uniformly Distributed Outliers . . . 108

7.41 Homogeneous Data Distribution, Constant Residual Variance, Three Outliers, Medium Outlier Term, Clustered Outliers . . . 109

7.42 The Outlier Residual . . . 114

7.43 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Homogeneous Data Distribution, Constant Residual Variance, Medium Outlier Term . . . 115

7.44 Polynomial Fit for Percentages of True Positive Test Results - Homogeneous Data Distribution, Constant Residual Variance, Medium Outlier Term . . . . 116

7.45 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Homogeneous Data Distribution, Constant Residual Variance, High Outlier Term . . . 117

7.46 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Homogeneous Data Distribution, Constant Coefficient of Variance, Medium Outlier Term . . . 119

LIST OF FIGURES 188 7.47 Relation between Outlier Position and Percentages of True Positive Test

Re-sults - Homogeneous Data Distribution, Constant Coefficient of Variance,

High Outlier Term . . . 119

7.48 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Residual Variance, Medium Outlier Term . . . 121

7.49 Relation between Outlier Location and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Residual Variance, Medium Outlier Term . . . 122

7.50 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Residual Variance, High Outlier Term . . . 122

7.51 Relation between Outlier Location and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Residual Variance, High Outlier Term . . . 123

7.52 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Coefficient of Variance, Medium Outlier Term . . . 124

7.53 Relation between Outlier Location and Percentages of True Positive Test Re-sults - Histogram, Inhomogeneous Data Distribution, Constant Coefficient of Variance, Medium Outlier Term . . . 125

7.54 Relation between Outlier Position and Percentages of True Positive Test Re-sults - Inhomogeneous Data Distribution, Constant Coefficient of Variance, High Outlier Term . . . 125

7.55 Relation between Outlier Location and Percentages of True Positive Test Re-sults - Histogram, Inhomogeneous Data Distribution, Constant Coefficient of Variance, High Outlier Term . . . 126

7.56 Exemplary Dataset - Bad Performance of the LORELIA Residual Test . . . . 127

7.57 Exemplary Dataset - Reliability Plot . . . 127

7.58 Exemplary Dataset, Low Part - Improved Performance . . . 128

7.59 Exemplary Dataset, Low Part - Reliability Plot . . . 128

7.60 Exemplary Dataset, Upper Part - Improved Performance . . . 129

7.61 Exemplary Dataset, High Part - Reliability Plot . . . 129

A.1 Documented SAS^®Program Files with Brief Descriptions . . . 139

B.1 Simulation 1: Constant Residual Variance, No Outliers - Outlier Test for the Absolute Differences . . . 140

B.2 Simulation 1: Constant Residual Variance, No Outliers - Outlier Test for the Normalized Relative Differences . . . 141

LIST OF FIGURES 189 B.3 Simulation 1: Constant Residual Variance, No Outliers - Outlier Test for the

Orthogonal Residuals . . . 141 B.4 Simulation 1: Constant Residual Variance, No Outliers -The LORELIA

Resid-ual Test . . . 142 B.5 Simulation 2: Constant Residual Variance, One Outlier, Medium Outlier Term

- Outlier Test for the Absolute Differences . . . 142 B.6 Simulation 2: Constant Residual Variance, One Outlier, Medium Outlier Term

- Outlier Test for the Normalized Relative Differences . . . 143 B.7 Simulation 2: Constant Residual Variance, One Outlier, Medium Outlier Term

- Outlier Test for the Orthogonal Residuals . . . 143 B.8 Simulation 2: Constant Residual Variance, One Outlier, Medium Outlier Term

-The LORELIA Residual Test . . . 144 B.9 Simulation 3: Constant Residual Variance, One Outlier, High Outlier Term

-Outlier Test for the Absolute Differences . . . 144 B.10 Simulation 3: Constant Residual Variance, One Outlier, High Outlier Term

-Outlier Test for the Normalized Relative Differences . . . 145 B.11 Simulation 3: Constant Residual Variance, One Outlier, High Outlier Term

-Outlier Test for the Orthogonal Residuals . . . 145 B.12 Simulation 3: Constant Residual Variance, One Outlier, High Outlier Term

-The LORELIA Residual Test . . . 146 B.13 Simulation 4: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differences146 B.14 Simulation 4: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Uniformly Distributed Outliers - Outlier Test for the Normalized Rela-tive Differences . . . 147 B.15 Simulation 4: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals147 B.16 Simulation 4: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Uniformly Distributed Outliers -The LORELIA Residual Test . . . 148 B.17 Simulation 5: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Clustered Outliers - Outlier Test for the Absolute Differences . . . 148 B.18 Simulation 5: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Clustered Outliers - Outlier Test for the Normalized Relative Differences 149 B.19 Simulation 5: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Clustered Outliers - Outlier Test for the Orthogonal Residuals . . . 149 B.20 Simulation 5: Constant Residual Variance, Three Outliers, Medium Outlier

Term, Clustered Outliers -The LORELIA Residual Test . . . 150 B.21 Simulation 6: Constant Residual Variance, Three Outliers, High Outlier Term,

Uniformly Distributed Outliers - Outlier Test for the Absolute Differences . . 150

LIST OF FIGURES 190 B.22 Simulation 6: Constant Residual Variance, Three Outliers, High Outlier Term,

Uniformly Distributed Outliers - Outlier Test for the Normalized Relative Dif-ferences . . . 151 B.23 Simulation 6: Constant Residual Variance, Three Outliers, High Outlier Term,

Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals . . 151 B.24 Simulation 6: Constant Residual Variance, Three Outliers, High Outlier Term,

Uniformly Distributed Outliers -The LORELIA Residual Test . . . 152 B.25 Simulation 7: Constant Residual Variance, Three Outliers, High Outlier Term,

Clustered Outliers - Outlier Test for the Absolute Differences . . . 152 B.26 Simulation 7: Constant Residual Variance, Three Outliers, High Outlier Term,

Clustered Outliers - Outlier Test for the Normalized Relative Differences . . . 153 B.27 Simulation 7: Constant Residual Variance, Three Outliers, High Outlier Term,

Clustered Outliers - Outlier Test for the Orthogonal Residuals . . . 153 B.28 Simulation 7: Constant Residual Variance, Three Outliers, High Outlier Term,

Clustered Outliers -The LORELIA Residual Test . . . 154 B.29 Simulation 8: Constant Coefficient of Variance, No Outliers - Outlier Test for

the Absolute Differences . . . 154 B.30 Simulation 8: Constant Coefficient of Variance, No Outliers - Outlier Test for

the Normalized Relative Differences . . . 155 B.31 Simulation 8: Constant Coefficient of Variance, No Outliers - Outlier Test for

the Orthogonal Residuals . . . 155 B.32 Simulation 8: Constant Coefficient of Variance, No Outliers -The LORELIA

Residual Test . . . 156 B.33 Simulation 9: Constant Coefficient of Variance, One Outlier, Medium Outlier

Term - Outlier Test for the Absolute Differences . . . 156 B.34 Simulation 9: Constant Coefficient of Variance, One Outlier, Medium Outlier

Term - Outlier Test for the Normalized Relative Differences . . . 157 B.35 Simulation 9: Constant Coefficient of Variance, One Outlier, Medium Outlier

Term - Outlier Test for the Orthogonal Residuals . . . 157 B.36 Simulation 9: Constant Coefficient of Variance, One Outlier, Medium Outlier

Term -The LORELIA Residual Test . . . 158 B.37 Simulation 10: Constant Coefficient of Variance, One Outlier, High Outlier

Term - Outlier Test for the Absolute Differences . . . 158 B.38 Simulation 10: Constant Coefficient of Variance, One Outlier, High Outlier

Term - Outlier Test for the Normalized Relative Differences . . . 159 B.39 Simulation 10: Constant Coefficient of Variance, One Outlier, High Outlier

Term - Outlier Test for the Orthogonal Residuals . . . 159 B.40 Simulation 10: Constant Coefficient of Variance, One Outlier, High Outlier

Term -The LORELIA Residual Test . . . 160

LIST OF FIGURES 191 B.41 Simulation 11: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differences . . . 160 B.42 Simulation 11: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Normal-ized Relative Differences . . . 161 B.43 Simulation 11: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals . . . 161 B.44 Simulation 11: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Uniformly Distributed Outliers -The LORELIA Residual Test . 162 B.45 Simulation 12: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Clustered Outliers - Outlier Test for the Absolute Differences . 162 B.46 Simulation 12: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Clustered Outliers - Outlier Test for the Normalized Relative Differences . . . 163 B.47 Simulation 12: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Clustered Outliers - Outlier Test for the Orthogonal Residuals . 163 B.48 Simulation 12: Constant Coefficient of Variance, Three Outliers, Medium

Outlier Term, Clustered Outliers -The LORELIA Residual Test . . . 164 B.49 Simulation 13: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differences164 B.50 Simulation 13: Constant Coefficient of Variance, Three Outliers, High

Out-lier Term, Uniformly Distributed OutOut-liers - OutOut-lier Test for the Normalized Relative Differences . . . 165 B.51 Simulation 13: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals165 B.52 Simulation 13: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Uniformly Distributed Outliers -The LORELIA Residual Test . . . 166 B.53 Simulation 14: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Clustered Outliers - Outlier Test for the Absolute Differences . . . 166 B.54 Simulation 14: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Clustered Outliers - Outlier Test for the Normalized Relative Differences 167 B.55 Simulation 14: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Clustered Outliers - Outlier Test for the Orthogonal Residuals . . . 167 B.56 Simulation 14: Constant Coefficient of Variance, Three Outliers, High Outlier

Term, Clustered Outliers -The LORELIA Residual Test . . . 168 B.57 Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers

-Outlier Test for the Absolute Differences . . . 168

LIST OF FIGURES 192 B.58 Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers

-Outlier Test for the Normalized Relative Differences . . . 169 B.59 Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers

-Outlier Test for the Orthogonal Residuals . . . 169 B.60 Simulation 15: Non Constant Coefficient of Residual Variance, No Outliers

-The LORELIA Residual Test . . . 170 B.61 Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier,

Medium Outlier Term - Outlier Test for the Absolute Differences . . . 170 B.62 Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier,

Medium Outlier Term - Outlier Test for the Normalized Relative Differences . 171 B.63 Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier,

Medium Outlier Term - Outlier Test for the Orthogonal Residuals . . . 171 B.64 Simulation 16: Non Constant Coefficient of Residual Variance, One Outlier,

Medium Outlier Term -The LORELIA Residual Test . . . 172 B.65 Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier,

High Outlier Term - Outlier Test for the Absolute Differences . . . 172 B.66 Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier,

High Outlier Term - Outlier Test for the Normalized Relative Differences . . 173 B.67 Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier,

High Outlier Term - Outlier Test for the Orthogonal Residuals . . . 173 B.68 Simulation 17: Non Constant Coefficient of Residual Variance, One Outlier,

High Outlier Term -The LORELIA Residual Test . . . 174 B.69 Simulation 18: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Absolute Differences . . . 174 B.70 Simulation 18: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Normalized Relative Differences . . . 175 B.71 Simulation 18: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Uniformly Distributed Outliers - Outlier Test for the Orthogonal Residuals . . . 175 B.72 Simulation 18: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Uniformly Distributed Outliers -The LORELIA Residual Test . . . 176 B.73 Simulation 19: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Clustered Outliers - Outlier Test for the Absolute Differences . . . 176 B.74 Simulation 19: Non Constant Coefficient of Residual Variance, Three

Out-liers, Medium Outlier Term, Clustered Outliers - Outlier Test for the Normal-ized Relative Differences . . . 177

Im Dokument The LORELIA Residual Test - A New Outlier Identification Test for Method Comparison Studies (Seite 174-200)