Notes on Statistics and Data Quality for Analytical Chemists

by Thompson, Michael; Lowthian, Philip J.

• ISBN13: 9781848166172
• ISBN10: 1848166176
• Format: Paperback
• Copyright: 2011-02-16
• Publisher: World Scientific Pub Co Inc

Summary

The book is intended to help analytical chemists feel comfortable with the commonly used statistical operations and help them make effective use of the results. The emphasis is on 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 book is divided into quite short sections, each dealing with a single topic. The sections are as far as possible self-contained, 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.

Table of Contents

Preface	p. v
Statistics	p. 1
Preliminaries	p. 3
Measurement Variation	p. 3
Conditions of Measurement and the Dispersion (Spread) of Results	p. 4
Variation in Objects	p. 5
Data Displays	p. 6
Statistics	p. 6
Levels of Probability	p. 7
An Example - Ethanol in Blood - a One-Tailed Test	p. 8
What Exactly Does the Probability Mean?	p. 9
Another Example - Accuracy of a Nitrogen Analyser - a Two-Tailed Test	p. 10
Null Hypotheses and Alternative Hypotheses	p. 12
Statements about Statistical Inferences	p. 12
Thinking about Probabilities and Distributions	p. 15
The Properties of the Normal Curve	p. 15
Probabilities Relating to Means of n Results	p. 17
Probabilities from Data	p. 19
Probability and Statistical Inference	p. 20
Pre-computer Statistics	p. 21
Confidence Intervals	p. 22
Simple Tests of Significance	p. 25
One-Sample Test - Example 1: Mercury in Fish	p. 25
One-Sample Test - Example 2: Alumina (Al2 O3) in Cement	p. 27
Comparing Two Independent Datasets - Method	p. 28
Comparing Means of Two Datasets with Equal Variances	p. 30
The Variance Ratio Test or F-Test	p. 31
Two-Sample Two-Tailed Test - An Example	p. 32
Two-Sample One-Tailed Test - An Example	p. 34
Paired Data	p. 36
Paired Data - One-Tailed Test	p. 38
Potential Problems with Paired Data	p. 40
Analysis of Variance (ANOVA) and Its Applications	p. 43
Introduction - The Comparison of Several Means	p. 43
The Calculations of One-Way ANOVA	p. 45
Example Calculations with One-Way ANOVA	p. 47
Applications of ANOVA: Example 1 - Catalysts for the Kjeldahl Method	p. 49
Applications of ANOVA: Example 2 - Homogeneity Testing	p. 51
ANOVA Application 3 - The Collaborative Trial	p. 54
ANOVA Application 4 - Sampling and Analytical Variance	p. 57
More Elaborate ANOVA - Nested Designs	p. 60
Two-Way ANOVA - Crossed Designs	p. 63
Cochran Test	p. 65
Ruggedness Tests	p. 66
Regression and Calibration	p. 71
Regression	p. 71
How Regression Works	p. 73
Calibration: Example 1	p. 76
The Use of Residuals	p. 78
Suspect Patterns in Residuals	p. 80
Effect of Outliers and Leverage Points on Regression	p. 82
Variances of the Regression Coefficients: Testing the Intercept and Slope for Significance	p. 83
Regression and ANOVA	p. 85
Correlation	p. 87
A Statistically-Sound Test for Lack of Fit	p. 90
Example Data/Calibration for Manganese	p. 91
A Regression Approach to Bias Between Methods	p. 94
Comparison of Analytical Methods: Example	p. 97
Regression - More Complex Aspects	p. 101
Evaluation Limits - How Precise is an Estimated x-value?	p. 101
Reducing the Confidence Interval Around an Estimated Value of Concentration	p. 104
Polynomial Regression	p. 105
Polynomial Calibration - Example	p. 108
Multiple Regression	p. 109
Multiple Regression - An Environmental Example	p. 111
Weighted Regression	p. 116
Example of Weighted Regression - Calibration for 239Pu by ICP-MS	p. 119
Non-linear Regression	p. 122
Example of Regression with Transformed Variables	p. 124
Additional Statistical Topics	p. 127
Control Charts	p. 127
Suspect Results and Outliers	p. 130
Dixon's Test for Outliers	p. 132
The Grubbs Test	p. 133
Robust Statistics - MAD Method	p. 135
Robust Statistics - Huber's H15 Method	p. 137
Lognormal Distributions	p. 139
Rounding	p. 141
Non-parametric Statistics	p. 142
Testing for Specific Distributions - the Kolmogorov-Smirnov One-Sample Test	p. 144
Statistical Power and the Planning of Experiments	p. 146
Data Quality in Analytical Measurement	p. 151
Quality in Chemical Measurement	p. 153
Quality - An Overview	p. 153
Uncertainty	p. 154
Why Uncertainty is Important	p. 156
Estimating Uncertainty by Modelling the Analytical System	p. 158
The Propagation of Uncertainty	p. 160
Estimating Uncertainty by Replication	p. 162
Traceability	p. 163
Fitness for Purpose	p. 165
Statistical Methods Involved in Validation	p. 167
Precision of Analytical Methods	p. 167
Experimental Conditions for Observing Precision	p. 169
External Calibration	p. 171
Example - A Complete Regression Analysis of a Calibration	p. 172
Calibration by Standard Additions	p. 175
Detection Limits	p. 177
Collaborative Trials - Overview	p. 180
The Collaborative Trial - Outlier Removal	p. 182
Collaborative Trials - Summarising the Results as a Function of Concentration	p. 184
Comparing two Analytical Methods by Using Paired Results	p. 186
Internal Quality Control	p. 189
Repeatability Precision and the Analytical Run	p. 189
Examples of Within-Run Quality Control	p. 192
Internal Quality Control (IQC) and Run-to-Run Precision	p. 195
Setting Up a Control Chart	p. 197
Internal Quality Control - Example	p. 198
Multivariate Internal Quality Control	p. 201
Proficiency Testing	p. 205
Proficiency Tests - Purpose and Organisation	p. 205
Scoring in Proficiency Tests	p. 207
Setting the Value of the Assigned Value xA in Proficiency Tests	p. 208
Calculating a Participant Consensus	p. 210
Setting the Value of the 'Target Value' ¿p in Proficiency Tests	p. 215
Using Information from Proficiency Test Scores	p. 216
Occasional Use of Certified Reference Materials in Quality Assurance	p. 219
Sampling in Chemical Measurement	p. 221
Traditional and Modern Approaches to Sampling Uncertainty	p. 221
Sampling Uncertainty in Context	p. 223
Random and Systematic Sampling	p. 226
Random Replication of Sampling	p. 227
Sampling Bias	p. 229
Sampling Precision	p. 231
Precision of the Estimated Value of ¿s	p. 234
Quality Control of Sampling	p. 236
Index	p. 239
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