Statistics and chemometrics for analytical chemistry

목차 (Table of Contents)

• CONTENTS
• Preface to the seventh edition = ix
• Preface to the first edition = xi
• Publisher's acknowledgements = xiii
• Glossary of symbols = xvii
• 1 Introduction = 1
• 1.1 Analytical problems = 1
• 1.2 Errors in quantitative analysis = 2
• 1.3 Types of error = 3
• 1.4 Random and systematic errors in titrimetric analysis = 6
• 1.5 Handling systematic errors = 8
• 1.6 Planning and design of experiments = 11
• 1.7 Statistical calculations = 12
• Bibliography and resources = 14
• Exercises = 15
• 2 Statistics of repeated measurements = 16
• 2.1 Mean and standard deviation = 16
• 2.2 The distribution of repeated measurements = 18
• 2.3 Log-normal distribution = 23
• 2.4 Definition of a 'sample' = 24
• 2.5 The sampling distribution of the mean = 25
• 2.6 Confidence limits of the mean for large samples = 26
• 2.7 Confidence limits of the mean for small samples = 27
• 2.8 Presentation of results = 29
• 2.9 Other uses of confidence limits = 30
• 2.10 Confidence limits of the geometric mean for a log-normal distribution = 30
• 2.11 Propagation of random errors = 31
• 2.12 Propagation of systematic errors = 34
• Bibliography = 35
• Exercises = 35
• 3 Significance tests = 37
• 3.1 Introduction = 37
• 3.2 Comparison of an experimental mean with a known value = 38
• 3.3 Comparison of two experimental means = 39
• 3.4 Paired t-test = 43
• 3.5 One-sided and two-sided tests = 45
• 3.6 F-test for the comparison of standard deviations = 47
• 3.7 Outliers = 49
• 3.8 Analysis of variance = 52
• 3.9 Comparison of several means = 53
• 3.10 The arithmetic of ANOVA calculations = 56
• 3.11 The chi-squared test = 59
• 3.12 Testing for normality of distribution = 61
• 3.13 Conclusions from significance tests = 65
• 3.14 Bayesian statistics = 67
• Bibliography = 70
• Exercises = 71
• 4 The quality of analytical measurements = 75
• 4.1 Introduction = 75
• 4.2 Sampling = 76
• 4.3 Separation and estimation of variances using ANOVA = 77
• 4.4 Sampling strategy = 78
• 4.5 Introduction to quality control methods = 79
• 4.6 Shewhart charts for mean values = 80
• 4.7 Shewhart charts for ranges = 82
• 4.8 Establishing the process capability = 84
• 4.9 Average run length: CUSUM charts = 87
• 4.10 Zone control charts (J-charts) = 91
• 4.11 Proficiency testing schemes = 93
• 4.12 Method performance studies (collaborative trials) = 96
• 4.13 Uncertainty = 100
• 4.14 Acceptance sampling = 109
• 4.15 Method validation = 112
• Bibliography = 116
• Exercises = 117
• 5 Calibration methods in instrumental analysis: Regression and correlation = 120
• 5.1 Introduction : instrumental analysis = 120
• 5.2 Calibration graphs in instrumental analysis = 122
• 5.3 The product-moment correlation coefficient = 124
• 5.4 The line of regression of y on x = 128
• 5.5 Errors in the slope and intercept of the regression line = 129
• 5.6 Calculation of a concentration and its random error = 131
• 5.7 Limits of detection = 134
• 5.8 The method of standard additions = 138
• 5.9 Use of regression lines for comparing analytical methods = 140
• 5.10 Weighted regression lines = 145
• 5.11 Intersection of two straight lines = 150
• 5.12 ANOVA and regression calculations = 152
• 5.13 Introduction to curvilinear regression methods = 153
• 5.14 Curve fitting = 156
• 5.15 Outliers in regression =160
• Bibliography = 162
• Exercises = 162
• 6 Non-parametric and robust methods = 165
• 6.1 Introduction = 165
• 6.2 The median: initial data analysis = 166
• 6.3 The sign test = 171
• 6.4 The Wald-Wolfowitz runs test = 173
• 6.5 The Wilcoxon signed rank test = 174
• 6.6 Simple tests for two independent samples = 177
• 6.7 Non-parametric tests for more than two samples = 180
• 6.8 Rank correlation = 182
• 6.9 Non-parametric regression methods = 183
• 6.10 Introduction to robust methods = 186
• 6.11 Simple robust methods : trimming and winsorisation = 187
• 6.12 Further robust estimates of location and spread = 188
• 6.13 Robust ANOVA = 190
• 6.14 Robust regression methods = 191
• 6.15 Re-sampling statistics = 193
• 6.16 Conclusion = 194
• Bibliography and resources = 195
• Exercises = 196
• 7 Experimental design and optimisation = 198
• 7.1 Introduction = 198
• 7.2 Randomisation and blocking = 200
• 7.3 Two-way ANOVA = 201
• 7.4 Latin squares and other designs = 204
• 7.5 Interactions = 205
• 7.6 Identifying the important factors : factorial designs = 211
• 7.7 Fractional factorial designs = 216
• 7.8 Optimal experimental designs = 219
• 7.9 Optimisation : basic principles and univariate methods = 220
• 7.10 Optimisation using the alternating variable search method = 223
• 7.11 The method of steepest ascent = 225
• 7.12 Simplex optimisation = 227
• 7.13 Simulated annealing = 231
• Bibliography and resources = 232
• Exercises = 232
• 8 Multivariate analysis = 235
• 8.1 Introduction = 235
• 8.2 Initial analysis = 237
• 8.3 Principal component analysis = 238
• 8.4 Cluster analysis = 242
• 8.5 Discriminant analysis = 246
• 8.6 K-nearest neighbour (KNN) method = 250
• 8.7 Disjoint class modelling = 251
• 8.8 Regression methods = 251
• 8.9 Multiple linear regression (MLR) = 253
• 8.10 Principal components regression (PCR) = 255
• 8.11 Partial least-squares (PLS) regression = 257
• 8.12 Natural computation methods : artificial neural networks = 260
• 8.13 Conclusion = 261
• Bibliography and resources = 262
• Exercises = 262
• Solutions to exercises = 265
• Appendix 1 : Commonly used statistical significance tests = 275
• Appendix 2 : Statistical tables = 278
• Index = 287