Notes on Statistics and Data Quality for Analytical Chemists

Contents......Page 10
Preface......Page 6
Part 1: Statistics......Page 16
1.1 Measurement Variation......Page 18
1.2 Conditions of Measurement and the Dispersion (Spread) of Results......Page 19
1.3 Variation in Objects......Page 20
1.5 Statistics......Page 21
1.6 Levels of Probability......Page 22
1.7 An Example — Ethanol in Blood — a One-Tailed Test......Page 23
1.8 What Exactly Does the Probability Mean?......Page 24
1.9 Another Example — Accuracy of a Nitrogen Analyser — a Two-Tailed Test......Page 25
1.11 Statements about Statistical Inferences......Page 27
2.1 The Properties of the Normal Curve......Page 30
2.2 Probabilities Relating to Means of n Results......Page 32
2.3 Probabilities from Data......Page 34
2.4 Probability and Statistical Inference......Page 35
2.5 Pre-computer Statistics......Page 36
2.6 Confidence Intervals......Page 37
3.1 One-Sample Test — Example 1: Mercury in Fish......Page 40
3.2 One-Sample Test — Example 2: Alumina (Al2O3) in Cement......Page 42
3.3 Comparing Two Independent Datasets — Method......Page 43
3.4 Comparing Means of Two Datasets with Equal Variances......Page 45
3.5 The Variance Ratio Test or F-Test......Page 46
3.6 Two-Sample Two-Tailed Test — An Example......Page 47
3.7 Two-Sample One-Tailed Test — An Example......Page 49
3.8 Paired Data......Page 51
3.9 Paired Data — One-Tailed Test......Page 53
3.10 Potential Problems with Paired Data......Page 55
4.1 Introduction — The Comparison of Several Means......Page 58
4.2 The Calculations of One-Way ANOVA......Page 60
4.3 Example Calculations with One-Way ANOVA......Page 62
4.4 Applications of ANOVA: Example 1 — Catalysts for the Kjeldahl Method......Page 64
4.5 Applications of ANOVA: Example 2 — Homogeneity Testing......Page 66
4.6 ANOVA Application 3 — The Collaborative Trial......Page 69
4.7 ANOVA Application 4 — Sampling and Analytical Variance......Page 72
4.8 More Elaborate ANOVA — Nested Designs......Page 75
4.9 Two-Way ANOVA — Crossed Designs......Page 78
4.10 Cochran Test......Page 80
4.11 Ruggedness Tests......Page 81
5.1 Regression......Page 86
5.2 How Regression Works......Page 88
5.3 Calibration: Example 1......Page 91
5.4 The Use of Residuals......Page 93
5.5 Suspect Patterns in Residuals......Page 95
5.6 Effect of Outliers and Leverage Points on Regression......Page 97
5.7 Variances of the Regression Coefficients: Testing the Intercept and Slope for Significance......Page 98
5.8 Regression and ANOVA......Page 100
5.9 Correlation......Page 102
5.10 A Statistically-Sound Test for Lack of Fit......Page 105
5.11 Example Data/Calibration for Manganese......Page 106
5.12 A Regression Approach to Bias Between Methods......Page 109
5.13 Comparison of Analytical Methods: Example......Page 112
6.1 Evaluation Limits — How Precise is an Estimated x-value?......Page 116
6.2 Reducing the Confidence Interval Around an Estimated Value of Concentration......Page 119
6.3 Polynomial Regression......Page 120
6.4 Polynomial Calibration — Example......Page 123
6.5 Multiple Regression......Page 124
6.6 Multiple Regression — An Environmental Example......Page 126
6.7 Weighted Regression......Page 131
6.8 Example of Weighted Regression — Calibration for 239Pu by ICP–MS......Page 134
6.9 Non-linear Regression......Page 137
6.10 Example of Regression with Transformed Variables......Page 139
7.1 Control Charts......Page 142
7.2 Suspect Results and Outliers......Page 145
7.3 Dixon’s Test for Outliers......Page 147
7.4 The Grubbs Test......Page 148
7.5 Robust Statistics — MAD Method......Page 150
7.6 Robust Statistics — Huber’s H15 Method......Page 152
7.7 Lognormal Distributions......Page 154
7.8 Rounding......Page 156
7.9 Non-parametric Statistics......Page 157
7.10 Testing for Specific Distributions — the Kolmogorov–Smirnov One-Sample Test......Page 159
7.11 Statistical Power and the Planning of Experiments......Page 161
Part 2: Data Quality in Analytical Measurement......Page 166
8.1 Quality — An Overview......Page 168
8.2 Uncertainty......Page 169
8.3 Why Uncertainty is Important......Page 171
8.4 Estimating Uncertainty by Modelling the Analytical System......Page 173
8.5 The Propagation of Uncertainty......Page 175
8.6 Estimating Uncertainty by Replication......Page 177
8.7 Traceability......Page 178
8.8 Fitness for Purpose......Page 180
9.1 Precision of Analytical Methods......Page 182
9.2 Experimental Conditions for Observing Precision......Page 184
9.3 External Calibration......Page 186
9.4 Example — A Complete Regression Analysis of a Calibration......Page 187
9.5 Calibration by Standard Additions......Page 190
9.6 Detection Limits......Page 192
9.7 Collaborative Trials — Overview......Page 195
9.8 The Collaborative Trial — Outlier Removal......Page 197
9.9 Collaborative Trials — Summarising the Results as a Function of Concentration......Page 199
9.10 Comparing two Analytical Methods by Using Paired Results......Page 201
10.1 Repeatability Precision and the Analytical Run......Page 204
10.2 Examples of Within-Run Quality Control......Page 207
10.3 Internal Quality Control (IQC) and Run-to-Run Precision......Page 210
10.4 Setting Up a Control Chart......Page 212
10.5 Internal Quality Control — Example......Page 213
10.6 Multivariate Internal Quality Control......Page 216
11.1 Proficiency Tests — Purpose and Organisation......Page 220
11.2 Scoring in Proficiency Tests......Page 222
11.3 Setting the Value of the Assigned Value xA in Proficiency Tests......Page 223
11.4 Calculating a Participant Consensus......Page 225
11.5 Setting the Value of the ‘Target Value’ σp in Proficiency Tests......Page 230
11.6 Using Information from Proficiency Test Scores......Page 231
11.7 Occasional Use of Certified Reference Materials in Quality Assurance......Page 234
12.1 Traditional and Modern Approaches to Sampling Uncertainty......Page 236
12.2 Sampling Uncertainty in Context......Page 238
12.3 Random and Systematic Sampling......Page 241
12.4 Random Replication of Sampling......Page 242
12.5 Sampling Bias......Page 244
12.6 Sampling Precision......Page 246
12.7 Precision of the Estimated Value of σs......Page 249
12.8 Quality Control of Sampling......Page 251
Index......Page 254