Statistics for the Quality Control Chemistry Laboratory

by Mullins, Eamonn

• ISBN13: 9780854046713
• ISBN10: 0854046712
• Format: Paperback
• Copyright: 2003-10-01
• Publisher: Royal Society of Chemistry

Summary

Statistical methods are essential tools for analysts, particularly those working in Quality Control Laboratories. This book provides a sound introduction to their use in analytical chemistry, without requiring a strong mathematical background. It emphasises simple graphical methods of data analysis, such as control charts, which are a key tool in Internal Laboratory Quality Control and which are also a fundamental requirement in laboratory accreditation. A large part of the book is concerned with the design and analysis of laboratory experiments, including sample size determination. Practical case studies and many real datasets, from both QC laboratories and the research literature, are used to illustrate the ideas in action.The aim of Statistics for the Quality Control Chemistry Laboratory is to give the reader a strong grasp of the concept of statistical variation in laboratory data and of the value of simple statistical ideas and methods in thinking about and manipulating such data. It will be invaluable to analysts working in QC laboratories in industry, hospitals and public health, and will also be welcomed as a textbook for aspiring analysts in colleges and universities.

Author Biography

Eamonn Mullins has taught statistics at Trinity College, Dublin for more than 25 years.

Table of Contents

Variability in Analytical Measurements	1	(34)
Introduction	1	(2)
An Example of Measurement Variability	3	(1)
Describing Measurement Error	4	(4)
A Schematic Inter-laboratory Study	6	(2)
Sources of Analytical Variability	8	(2)
Measuring Precision	10	(12)
The Standard Deviation as a Measure of Precision	13	(2)
Variation of Precision with Concentration	15	(4)
Measures of Repeatability and Reproducibility	19	(3)
Case Study: Estimating Repeatability from Historical Data	22	(4)
Improving Precision by Replication	26	(3)
Conclusion	29	(1)
Review Exercises	29	(4)
References	33	(2)
Control Charts in the Analytical Laboratory	35	(52)
Introduction	35	(1)
Examples of Control Charts	36	(3)
The Theory Underlying the Control Limits	39	(3)
Setting Up Control Charts	42	(8)
Calculating the Limits	42	(3)
Data Scrutiny	45	(2)
Sample Size	47	(3)
Monitoring Precision	50	(5)
Range Charts	50	(1)
The Nature of Replicates	51	(1)
Standard Deviation Charts	52	(3)
Case Study	55	(6)
Control Chart Performance	61	(5)
Average Run Length Analysis	61	(3)
How Many Control Samples?	64	(2)
Learning from Control Charts	66	(10)
Improving Precision by Replication: Revisited	66	(6)
Obtaining Measures of Precision from Control Charts	72	(2)
Using Control Charts	74	(2)
Concluding Remarks	76	(1)
Proficiency Testing	76	(4)
Overview	76	(2)
Technical Issues	78	(1)
Concluding Remarks	79	(1)
Conclusion	80	(1)
Review Exercises	80	(4)
References	84	(3)
Some Important Statistical Ideas	87	(48)
Introduction	87	(1)
Statistical Significance Tests	88	(8)
Example 1: A Method Validation Study	88	(5)
Example 2: Acceptance Sampling	93	(2)
Summary	95	(1)
Determining Sample Size	96	(7)
The Nature of the Problem	96	(2)
Using the Sample Size Table	98	(2)
Discussion	100	(1)
Some Useful Graphs: Power Curves	101	(2)
Confidence Intervals for Means	103	(11)
Example 1: Estimating the Average Potency of a Pharmaceutical Material	104	(4)
Example 2: The Method Validation Study Revisited--Estimating Bias	108	(2)
Example 3: Estimating the Potency of a Pharmaceutical Material: Revisited	110	(2)
Example 4: Error Bounds for Routine Test Results	112	(2)
Sampling	114	(2)
Confidence Intervals for Standard Deviations	116	(5)
Checking Normality	121	(9)
Normal Probability Plots	122	(3)
A Significance Test for Normality	125	(1)
Departures from Normality	126	(2)
Transformations	128	(2)
Concluding Remarks	130	(1)
Review Exercises	131	(1)
References	132	(3)
Simple Comparative Studies	135	(50)
Introduction	135	(1)
A Typical Comparative Study	135	(13)
A Statistical Significance Test for Comparing Method Means	137	(3)
Estimating the Difference in Recovery Rates	140	(3)
Comparing Standard Deviations	143	(2)
Comparing Means when Standard Deviations are Unequal	145	(2)
Validating the Assumption of Normality	147	(1)
Paired Comparisons	148	(11)
A Trouble-shooting Exercise	149	(5)
Case Study	154	(5)
Sample Size for Comparative Studies	159	(9)
Comparing Means of Two Independent Groups	159	(5)
Paired Studies of Relative Bias	164	(2)
Sample sizes for Comparing Standard Deviations	166	(2)
Some Comments on Study Design	168	(11)
Experimental Run Order	169	(2)
Appropriate Measures of Precision	171	(8)
Representativeness	179	(1)
Concluding Remarks	179	(1)
Review Exercises	180	(3)
References	183	(2)
Studying Complex Systems	185	(62)
Introduction	185	(1)
Statistical or Traditional Designs?	186	(3)
The 22 Design	189	(12)
An Example	190	(7)
Model Validation	197	(1)
Organizing the Calculations	198	(3)
The 23 Design	201	(11)
An Example	201	(6)
Data Analysis	207	(3)
Model Validation	210	(2)
Sample Size for Factorial Designs	212	(3)
Experiments with many Factors	215	(4)
Fractional Factorial Designs	219	(11)
A Simple Example	219	(5)
The 25-1 Design	224	(4)
Blocking	228	(2)
Ruggedness Testing	230	(11)
Designing Ruggedness Tests	231	(2)
Example 1	233	(2)
Example 2	235	(6)
Concluding Remarks	241	(1)
Review Exercises	242	(4)
References	246	(1)
Fitting Equations to Data	247	(62)
Introduction	247	(1)
Regression Analysis	248	(16)
Introductory Example	248	(5)
Using the Regression Line	253	(7)
Analysis of Variance	260	(4)
Calibration	264	(11)
Example	265	(2)
Error Bounds for the Estimated Concentration	267	(3)
Zero-intercept Calibration Lines	270	(5)
Detection Limit	275	(3)
Residual Analysis	278	(8)
Weighted Regression	286	(9)
Fitting a Calibration Line by WLS	287	(3)
Is Weighting Worthwhile?	290	(5)
Non-linear Relationships	295	(9)
A Single Predictor Variable	296	(3)
A `Lack-of-fit' Test	299	(2)
Response Surface Modelling	301	(3)
Concluding Remarks	304	(1)
Review Exercises	305	(2)
References	307	(2)
The Design and Analysis of Laboratory Studies Re-visited	309	(56)
Introduction	309	(1)
Comparing Several Means	310	(14)
Example 1: A Laboratory Comparison Study	310	(10)
Multiple Comparisons	320	(1)
Example 2: A Method Development Study	321	(3)
Multi-factor Studies	324	(14)
Example 1: The GC Study Re-visited	324	(6)
Example 2: A 3 x 3 Study	330	(4)
Example 3: A 23 Study	334	(4)
Blocking in Experimental Design	338	(5)
Example 1: The GC Development Study Re-visited, Again!	338	(4)
Example 2: Paired t-Tests Revisited	342	(1)
Estimating Components of Test Result Variability	343	(17)
Example 1: Control Charts	344	(7)
Example 2: Three Variance Components	351	(9)
Conclusion	360	(1)
Review Exercises	361	(3)
References	364	(1)
Assessing Measurement Quality	365	(32)
Introduction	365	(1)
Inter-laboratory Collaborative Trials	366	(11)
Estimating the Reproducibility Standard Deviation	366	(3)
Data Scrutiny	369	(6)
Measuring the Trueness of a Method	375	(2)
Measurement Uncertainty	377	(9)
Example: Preparing a Stock Solution	379	(5)
Discussion	384	(2)
An Integrated Approach to Measurement Uncertainty	386	(2)
Concluding Remarks	388	(5)
Review Exercises	393	(3)
References	396	(1)
Solutions to Exercises	397	(34)
Appendix: Statistical Tables	431	(16)
Subject Index	447