Notes On Statistics And Data Quality For Analytical Chemists

by Michael Thompson, Philip James Lowthian

Overview

This book is intended to help analytical chemists feel comfortable with more commonly used statistical operations and help them make effective use of the results. Emphasis is put upon computer-based methods that are applied in relation to measurement and the quality of the resulting data. The book is intended for analytical chemists working in industry but is also appropriate for students taking first degrees or an MSc in analytical chemistry.The authors have divided this book into quite short sections, each dealing with a single topic. The sections are as far as possible selfcontained, but are extensively cross-referenced. The book can therefore be used either systematically by reading the sections sequentially, or as a quick reference by going directly to the topic of interest. Every statistical method and application covered has at least one example where the results are analysed in detail. This enables readers to emulate this analysis on their own examples. All of the datasets used in examples are available for download, so that readers can compare their own output with that of the book and thus verify that they are entering data correctly into the statistical package that they happen to use.

Product Details

ISBN-13:	9781848166172
Publisher:	Imperial College Press
Publication date:	02/17/2011
Pages:	260
Product dimensions:	5.90(w) x 8.80(h) x 0.60(d)

Table of Contents

Preface v

Part 1 Statistics 1

1 Preliminaries 3

1.1 Measurement Variation 3

1.2 Conditions of Measurement and the Dispersion (Spread) of Results 4

1.3 Variation in Objects 5

1.4 Data Displays 6

1.5 Statistics 6

1.6 Levels of Probability 7

1.7 An Example - Ethanol in Blood - a One-Tailed Test 8

1.8 What Exactly Does the Probability Mean? 9

1.9 Another Example - Accuracy of a Nitrogen Analyser - a Two-Tailed Test 10

1.10 Null Hypotheses and Alternative Hypotheses 12

1.11 Statements about Statistical Inferences 12

2 Thinking about Probabilities and Distributions 15

2.1 The Properties of the Normal Curve 15

2.2 Probabilities Relating to Means of n Results 17

2.3 Probabilities from Data 19

2.4 Probability and Statistical Inference 20

2.5 Pre-computer Statistics 21

2.6 Confidence Intervals 22

3 Simple Tests of Significance 25

3.1 One-Sample Test - Example 1: Mercury in Fish 25

3.2 One-Sample Test - Example 2: Alumina (Al₂ O₃) in Cement 27

3.3 Comparing Two Independent Datasets - Method 28

3.4 Comparing Means of Two Datasets with Equal Variances 30

3.5 The Variance Ratio Test or F-Test 31

3.6 Two-Sample Two-Tailed Test - An Example 32

3.7 Two-Sample One-Tailed Test - An Example 34

3.8 Paired Data 36

3.9 Paired Data - One-Tailed Test 38

3.10 Potential Problems with Paired Data 40

4 Analysis of Variance (ANOVA) and Its Applications 43

4.1 Introduction - The Comparison of Several Means 43

4.2 The Calculations of One-Way ANOVA 45

4.3 Example Calculations with One-Way ANOVA 47

4.4 Applications of ANOVA: Example 1 - Catalysts for the Kjeldahl Method 49

4.5 Applications of ANOVA: Example 2 - Homogeneity Testing 51

4.6 ANOVA Application 3 - The Collaborative Trial 54

4.7 ANOVA Application 4 - Sampling and Analytical Variance 57

4.8 More Elaborate ANOVA - Nested Designs 60

4.9 Two-Way ANOVA - Crossed Designs 63

4.10 Cochran Test 65

4.11 Ruggedness Tests 66

5 Regression and Calibration 71

5.1 Regression 71

5.2 How Regression Works 73

5.3 Calibration: Example 1 76

5.4 The Use of Residuals 78

5.5 Suspect Patterns in Residuals 80

5.6 Effect of Outliers and Leverage Points on Regression 82

5.7 Variances of the Regression Coefficients: Testing the Intercept and Slope for Significance 83

5.8 Regression and ANOVA 85

5.9 Correlation 87

5.10 A Statistically-Sound Test for Lack of Fit 90

5.11 Example Data/Calibration for Manganese 91

5.12 A Regression Approach to Bias Between Methods 94

5.13 Comparison of Analytical Methods: Example 97

6 Regression - More Complex Aspects 101

6.1 Evaluation Limits - How Precise is an Estimated x-value? 101

6.2 Reducing the Confidence Interval Around an Estimated Value of Concentration 104

6.3 Polynomial Regression 105

6.4 Polynomial Calibration - Example 108

6.5 Multiple Regression 109

6.6 Multiple Regression - An Environmental Example 111

6.7 Weighted Regression 116

6.8 Example of Weighted Regression - Calibration for ²³⁹Pu by ICP-MS 119

6.9 Non-linear Regression 122

6.10 Example of Regression with Transformed Variables 124

7 Additional Statistical Topics 127

7.1 Control Charts 127

7.2 Suspect Results and Outliers 130

7.3 Dixon's Test for Outliers 132

7.4 The Grubbs Test 133

7.5 Robust Statistics - MAD Method 135

7.6 Robust Statistics - Huber's H15 Method 137

7.7 Lognormal Distributions 139

7.8 Rounding 141

7.9 Non-parametric Statistics 142

7.10 Testing for Specific Distributions - the Kolmogorov-Smirnov One-Sample Test 144

7.11 Statistical Power and the Planning of Experiments 146

Part 2 Data Quality in Analytical Measurement 151

8 Quality in Chemical Measurement 153

8.1 Quality - An Overview 153

8.2 Uncertainty 154

8.3 Why Uncertainty is Important 156

8.4 Estimating Uncertainty by Modelling the Analytical System 158

8.5 The Propagation of Uncertainty 160

8.6 Estimating Uncertainty by Replication 162

8.7 Traceability 163

8.8 Fitness for Purpose 165

9 Statistical Methods Involved in Validation 167

9.1 Precision of Analytical Methods 167

9.2 Experimental Conditions for Observing Precision 169

9.3 External Calibration 171

9.4 Example - A Complete Regression Analysis of a Calibration 172

9.5 Calibration by Standard Additions 175

9.6 Detection Limits 177

9.7 Collaborative Trials - Overview 180

9.8 The Collaborative Trial - Outlier Removal 182

9.9 Collaborative Trials - Summarising the Results as a Function of Concentration 184

9.10 Comparing two Analytical Methods by Using Paired Results 186

10 Internal Quality Control 189

10.1 Repeatability Precision and the Analytical Run 189

10.2 Examples of Within-Run Quality Control 192

10.3 Internal Quality Control (IQC) and Run-to-Run Precision 195

10.4 Setting Up a Control Chart 197

10.5 Internal Quality Control - Example 198

10.6 Multivariate Internal Quality Control 201

11 Proficiency Testing 205

11.1 Proficiency Tests - Purpose and Organisation 205

11.2 Scoring in Proficiency Tests 207

11.3 Setting the Value of the Assigned Value x_A in Proficiency Tests 208

11.4 Calculating a Participant Consensus 210

11.5 Setting the Value of the 'Target Value' σ_p in Proficiency Tests 215

11.6 Using Information from Proficiency Test Scores 216

11.7 Occasional Use of Certified Reference Materials in Quality Assurance 219

12 Sampling in Chemical Measurement 221

12.1 Traditional and Modern Approaches to Sampling Uncertainty 221

12.2 Sampling Uncertainty in Context 223

12.3 Random and Systematic Sampling 226

12.4 Random Replication of Sampling 227

12.5 Sampling Bias 229

12.6 Sampling Precision 231

12.7 Precision of the Estimated Value of σ_s 234

12.8 Quality Control of Sampling 236

Index 239