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Notes on Statistics and Data Quality for Analytical Chemists - Michael Thompson

Notes on Statistics and Data Quality for Analytical Chemists


Published: 11th April 2011
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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.

Prefacep. v
Statisticsp. 1
Preliminariesp. 3
Measurement Variationp. 3
Conditions of Measurement and the Dispersion (Spread) of Resultsp. 4
Variation in Objectsp. 5
Data Displaysp. 6
Statisticsp. 6
Levels of Probabilityp. 7
An Example - Ethanol in Blood - a One-Tailed Testp. 8
What Exactly Does the Probability Mean?p. 9
Another Example - Accuracy of a Nitrogen Analyser - a Two-Tailed Testp. 10
Null Hypotheses and Alternative Hypothesesp. 12
Statements about Statistical Inferencesp. 12
Thinking about Probabilities and Distributionsp. 15
The Properties of the Normal Curvep. 15
Probabilities Relating to Means of n Resultsp. 17
Probabilities from Datap. 19
Probability and Statistical Inferencep. 20
Pre-computer Statisticsp. 21
Confidence Intervalsp. 22
Simple Tests of Significancep. 25
One-Sample Test - Example 1: Mercury in Fishp. 25
One-Sample Test - Example 2: Alumina (Al2 O3) in Cementp. 27
Comparing Two Independent Datasets - Methodp. 28
Comparing Means of Two Datasets with Equal Variancesp. 30
The Variance Ratio Test or F-Testp. 31
Two-Sample Two-Tailed Test - An Examplep. 32
Two-Sample One-Tailed Test - An Examplep. 34
Paired Datap. 36
Paired Data - One-Tailed Testp. 38
Potential Problems with Paired Datap. 40
Analysis of Variance (ANOVA) and Its Applicationsp. 43
Introduction - The Comparison of Several Meansp. 43
The Calculations of One-Way ANOVAp. 45
Example Calculations with One-Way ANOVAp. 47
Applications of ANOVA: Example 1 - Catalysts for the Kjeldahl Methodp. 49
Applications of ANOVA: Example 2 - Homogeneity Testingp. 51
ANOVA Application 3 - The Collaborative Trialp. 54
ANOVA Application 4 - Sampling and Analytical Variancep. 57
More Elaborate ANOVA - Nested Designsp. 60
Two-Way ANOVA - Crossed Designsp. 63
Cochran Testp. 65
Ruggedness Testsp. 66
Regression and Calibrationp. 71
Regressionp. 71
How Regression Worksp. 73
Calibration: Example 1p. 76
The Use of Residualsp. 78
Suspect Patterns in Residualsp. 80
Effect of Outliers and Leverage Points on Regressionp. 82
Variances of the Regression Coefficients: Testing the Intercept and Slope for Significancep. 83
Regression and ANOVAp. 85
Correlationp. 87
A Statistically-Sound Test for Lack of Fitp. 90
Example Data/Calibration for Manganesep. 91
A Regression Approach to Bias Between Methodsp. 94
Comparison of Analytical Methods: Examplep. 97
Regression - More Complex Aspectsp. 101
Evaluation Limits - How Precise is an Estimated x-value?p. 101
Reducing the Confidence Interval Around an Estimated Value of Concentrationp. 104
Polynomial Regressionp. 105
Polynomial Calibration - Examplep. 108
Multiple Regressionp. 109
Multiple Regression - An Environmental Examplep. 111
Weighted Regressionp. 116
Example of Weighted Regression - Calibration for 239Pu by ICP-MSp. 119
Non-linear Regressionp. 122
Example of Regression with Transformed Variablesp. 124
Additional Statistical Topicsp. 127
Control Chartsp. 127
Suspect Results and Outliersp. 130
Dixon's Test for Outliersp. 132
The Grubbs Testp. 133
Robust Statistics - MAD Methodp. 135
Robust Statistics - Huber's H15 Methodp. 137
Lognormal Distributionsp. 139
Roundingp. 141
Non-parametric Statisticsp. 142
Testing for Specific Distributions - the Kolmogorov-Smirnov One-Sample Testp. 144
Statistical Power and the Planning of Experimentsp. 146
Data Quality in Analytical Measurementp. 151
Quality in Chemical Measurementp. 153
Quality - An Overviewp. 153
Uncertaintyp. 154
Why Uncertainty is Importantp. 156
Estimating Uncertainty by Modelling the Analytical Systemp. 158
The Propagation of Uncertaintyp. 160
Estimating Uncertainty by Replicationp. 162
Traceabilityp. 163
Fitness for Purposep. 165
Statistical Methods Involved in Validationp. 167
Precision of Analytical Methodsp. 167
Experimental Conditions for Observing Precisionp. 169
External Calibrationp. 171
Example - A Complete Regression Analysis of a Calibrationp. 172
Calibration by Standard Additionsp. 175
Detection Limitsp. 177
Collaborative Trials - Overviewp. 180
The Collaborative Trial - Outlier Removalp. 182
Collaborative Trials - Summarising the Results as a Function of Concentrationp. 184
Comparing two Analytical Methods by Using Paired Resultsp. 186
Internal Quality Controlp. 189
Repeatability Precision and the Analytical Runp. 189
Examples of Within-Run Quality Controlp. 192
Internal Quality Control (IQC) and Run-to-Run Precisionp. 195
Setting Up a Control Chartp. 197
Internal Quality Control - Examplep. 198
Multivariate Internal Quality Controlp. 201
Proficiency Testingp. 205
Proficiency Tests - Purpose and Organisationp. 205
Scoring in Proficiency Testsp. 207
Setting the Value of the Assigned Value xA in Proficiency Testsp. 208
Calculating a Participant Consensusp. 210
Setting the Value of the 'Target Value' ¿p in Proficiency Testsp. 215
Using Information from Proficiency Test Scoresp. 216
Occasional Use of Certified Reference Materials in Quality Assurancep. 219
Sampling in Chemical Measurementp. 221
Traditional and Modern Approaches to Sampling Uncertaintyp. 221
Sampling Uncertainty in Contextp. 223
Random and Systematic Samplingp. 226
Random Replication of Samplingp. 227
Sampling Biasp. 229
Sampling Precisionp. 231
Precision of the Estimated Value of ¿sp. 234
Quality Control of Samplingp. 236
Indexp. 239
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781848166172
ISBN-10: 1848166176
Audience: General
Format: Paperback
Language: English
Number Of Pages: 245
Published: 11th April 2011
Publisher: Imperial College Press
Country of Publication: GB
Dimensions (cm): 22.35 x 14.99  x 1.52
Weight (kg): 0.39