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E-raamat: Handbook of Chemometrics and Qualimetrics: Part A

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Provides coverage of the various fields of chemometrics, starting with classical statistics for hypothesis testing to advanced methods such as neural networks, genetic algorithms and latent variable based methods.

Arvustused

"There seems to be little doubt that this book will become a bible for all chemometricians... ...the order of chapters chosen by the authors turns out to be excellent, and the clarity of presentations, the uniformity of style between chapters presumably contributed by different authors, the plentiful cross-referencing between sections, and the good index, all provide testimony to the great care with which the volume has been written: clearly a labour of love! Moreover it is hard to point to a single area of any significance which has been omitted or which has received inadequate treatment and the use of simple and relevant example data sets throughout ensures a stimulating read and brings these potentially rather dry topics to life. In short, this is a magnificent book, written by world-class innovators and users of chemometrics, and it deserves to be on the shelves of all teachers and researchers in the analytical sciences." --Journal of Pharmaceutical Analysis

"...there is evidence of considerable thought having been given to the problems that the material could present to a novice reader. In each chapter the discussion progresses smoothly from an elementary introductory section to the development of the target subject. With the type of material that this book covers, newcomers often experience difficulty in understanding the utility of abstract concepts. The authors have dealt effectively with this problem by a generous use of examples that are couched in terms that are meaningful to chemists. This book is a welcome addition to the field of chemometrics." --Applied Spectroscopy

Preface v
Introduction
1(20)
The aims of chemometrics
1(2)
Chemometrics and the `Arch of Knowledge'
1(1)
Chemometrics and quality
2(1)
An overview of chemometrics
3(9)
Experiments and experimental design
3(1)
Extraction of information from data
3(1)
Displaying data
3(2)
Hypothesis testing
5(1)
Modelling
6(2)
Classification
8(2)
Chemical knowledge and (artificial) intelligence
10(1)
Chemical domains and quality aspects
10(1)
Mathematical and statistical tools
11(1)
Organisation of the book
11(1)
Some historical considerations
12(3)
Chemometrics in industry and academia
15(6)
References
18(3)
Statistical Description of the Quality of Processes and Measurements
21(26)
Introductory concepts about chemical data
21(11)
Populations and samples
21(1)
Variables and attributes
22(1)
Histograms and distributions
23(3)
Descriptive statistics
26(1)
Population parameters and their estimators
26(1)
Mean and other parameters for central location
27(1)
Standard deviation and variance
27(1)
Pooled standard deviation and standard deviation from paired data
28(2)
Range and its relation to the standard deviation
30(2)
Measurement of quality
32(1)
Quality and errors
32(1)
Systematic versus random errors
33(1)
Quality of processes and statistical process control
33(6)
Process capability indexes for dispersion
34(1)
Process capability index for setting
35(1)
Process capability indexes for dispersion and setting
36(1)
Some other statistical process control tools and concepts
37(2)
Quality of measurements in relation to quality of processes
39(1)
Precision and bias of measurements
40(1)
Some other types of error
41(1)
Propagation of errors
42(2)
Rounding and rounding errors
44(3)
References
45(2)
The Normal Distribution
47(26)
Population parameters and their estimators
47(2)
Moments of a distribution: mean, variance, skewness
49(1)
The normal distribution: description and notation
50(2)
Tables for the standardized normal distribution
52(4)
Standard errors
56(2)
Confidence intervals for the mean
58(2)
Small samples and the t-distribution
60(3)
Normality tests: a graphical procedure
63(7)
How to convert a non-normal distribution into a normal one
70(3)
References
72(1)
An Introduction To Hypothesis Testing
73(20)
Comparison of the mean with a given value
73(1)
Null and alternative hypotheses
74(1)
Using confidence intervals
75(1)
Comparing a test value with a critical value
76(2)
Presentation of results of a hypothesis test
78(1)
Level of significance and type I error
79(1)
Power and type II errors
79(3)
Sample size
82(3)
One- and two-sided tests
85(3)
An alternative approach: interval hypotheses
88(5)
References
91(2)
Some Important Hypothesis Tests
93(28)
Comparison of two means
93(7)
Comparison of the means of two independent samples
93(1)
Large samples
93(2)
Small samples
95(2)
Comparison of the means of two paired samples
97(2)
Large samples
99(1)
Small samples
99(1)
Multiple comparisons
100(2)
β error and sample size
102(2)
Comparison of variances
104(5)
Comparison of two variances
104(3)
Comparison of a variance with a known value
107(2)
Outliers
109(5)
Dixon's test
109(3)
Grubbs' test
112(2)
Distribution tests
114(7)
Chi-square test
116(1)
Kolmogorov-Smirnov test
117(3)
References
120(1)
Analysis of Variance
121(30)
One-way analysis of variance
121(10)
Terminology --- examples
121(3)
Estimating sources of variance and their significance
124(2)
Breaking up total variance in its components
126(2)
Random and fixed effect models
128(2)
The ANOVA table
130(1)
Assumptions
131(4)
Fixed effect models: testing differences between means of columns
135(2)
Random effect models: variance components
137(1)
Two-way and multi-way ANOVA
138(4)
Interaction
142(2)
Incorporation of interaction in the residual
144(1)
Experimental design and modelling
145(1)
Blocking
145(1)
Repeated testing by ANOVA
146(1)
Nested ANOVA
147(4)
References
150(1)
Control Charts
151(20)
Quality control
151(1)
Mean and range charts
151(10)
Mean charts
151(1)
Setting up a mean chart
151(4)
Application of the mean chart
155(3)
Range charts
158(2)
Other charts for central location and spread
160(1)
Charts for the analytical laboratory
160(1)
Charts for attributes
161(1)
Moving average and related charts
161(8)
Moving average and range charts
161(2)
The cumulative sum (CUSUM) chart
163(3)
Exponentially weighted moving average charts
166(3)
Further developments
169(2)
References
169(2)
Straight Line Regression and Calibration
171(60)
Introduction
171(1)
Straight line regression
172(47)
Estimation of the regression parameters
172(7)
Validation of the model
179(1)
Analysis of the residuals
179(1)
Analysis of variance
180(6)
Heteroscedasticity
186(1)
Transformation
187(1)
Weighted least squares
187(2)
Confidence intervals and hypothesis tests
189(1)
Confidence interval for the intercept and the slope
189(4)
Joint confidence region for slope and intercept
193(2)
Confidence interval for the true response at a given value of x
195(1)
Predictions made on the basis of the fitted line
196(1)
Prediction of new responses
196(1)
Prediction of x from y
197(5)
Outliers
202(5)
Inverse regression
207(1)
Standard addition method
207(1)
Comparison of the slopes of two regression lines
208(2)
The intersection of two regression lines
210(3)
Regression when both the predictor and the response variable are subject to error
213(3)
Straight line regression through a fixed point
216(1)
Linearization of a curved line
217(2)
Correlation
219(12)
The correlation coefficient
221(2)
Hypothesis tests and confidence limits
223(5)
Correlation and regression
228(1)
References
229(2)
Vectors and Matrices
231(32)
The data table as data matrix
231(1)
Vectors
232(17)
Definitions
232(2)
Operations on vectors
234(1)
Addition of vectors
234(1)
Multiplication by a scalar
235(1)
Vector multiplication
236(1)
Length and distance
236(3)
Normed vectors
239(1)
Angle between vectors
239(1)
Orthogonal projection
240(1)
Orthogonalization
241(4)
Linear combinations, linear dependence and collinearity
245(2)
Dimensionality
247(2)
Matrices
249(14)
Definitions
249(1)
Matrix operations
250(1)
Addition and substraction
250(1)
Multiplication by a scalar
251(1)
Matrix multiplication
251(2)
Examples of matrix multiplication
253(3)
Inverse of a square matrix
256(1)
Regression modelling and projection
257(2)
Determinant of a square matrix
259(2)
Rank of a square matrix
261(1)
References
261(2)
Multiple and Polynomial Regression
263(42)
Introduction
263(1)
Estimation of the regression parameters
264(6)
Validation of the model
270(14)
Examination of the overall regression equation
270(1)
Analysis of variance
270(3)
The coefficient of multiple determination
273(1)
Analysis of the residuals
274(1)
Importance of the predictor variables
275(3)
Selection of predictor variables
278(4)
Validation of the prediction accuracy of the model
282(2)
Confidence intervals
284(2)
Multicollinearity
286(3)
Ridge regression
289(3)
Multicomponent analysis by multiple linear regression
292(4)
Polynomial regression
296(4)
Outliers
300(5)
References
302(3)
Non-linear Regression
305(34)
Introduction
305(1)
Mechanistic modelling
306(16)
Linearization
308(1)
Least-squares parameter estimation
309(1)
Gauss-Newton linearization
310(4)
Steepest descent and Marquardt procedure
314(1)
An example
315(6)
Advanced topics
321(1)
Empirical modelling
322(17)
Polynomial regression
322(1)
Splines
323(1)
Regression splines
323(4)
Smoothing splines
327(2)
Other techniques
329(1)
ACE
329(3)
MARS
332(4)
Recent developments
336(1)
References
336(3)
Robust Statistics
339(40)
Methods based on the median
339(22)
Introduction
339(1)
The median and the interquartile range
339(2)
Box plots
341(3)
Hypothesis tests based on ranking
344(1)
The sign test for two related samples
344(1)
The Wilcoxon signed rank test or the Wilcoxon T-test for two paired samples
345(2)
Mann-Witney U-test for two independent samples
347(2)
Kruskal-Wallis one-way analysis of variance by ranks
349(1)
The Spearman rank correlation coefficient
350(1)
Detection of trends by the runs test
351(3)
Median-based robust regression
354(1)
Single median method
355(1)
Repeated median method
356(2)
The least median of squares (LMS) method
358(3)
Comparison of least squares and different median based robust regression procedures
361(1)
Biweight and winsorized mean
361(4)
Iteratively reweighted least squares
365(2)
Randomization tests
367(2)
Monte Carlo Methods
369(10)
Probabilistic MC for statistical methods
370(2)
Probabilistic MC for physical systems
372(2)
Deterministic MC
374(2)
References
376(3)
Internal Method Validation
379(62)
Definition and types of method validation
379(2)
The golden rules of method validation
381(1)
Types of internal method validation
381(2)
Precision
383(10)
Terminology
383(1)
Repeatability
384(4)
An intermediate precision measure: within-laboratory reproducibility
388(1)
Requirements for precision measurements
389(1)
Ruggedness
390(3)
Accuracy and bias
393(24)
Definitions
393(4)
Restricted concentration range --- reconstitution of sample possible
397(1)
Restricted concentration range --- reference material available
398(1)
Large concentration range --- blank material available
399(5)
Large concentration range --- blank material not available
404(4)
Comparison of two methods or two laboratories
408(6)
An alternative approach to hypothesis testing in method validation
414(1)
Comparison of more than two methods or laboratories
414(3)
Linearity of calibration lines
417(5)
The correlation coefficient
418(1)
The quality coefficient
418(3)
The F-test for lack of fit
421(1)
Test of the significance of b2
421(1)
Use of robust regression or non-parametric methods
422(1)
Detection limit and related quantities
422(13)
Decision limit
423(2)
Detection limit
425(1)
Quantification limit
426(1)
Measuring the blank
427(2)
Concentration limits
429(1)
Example
430(1)
Alternatives
431(1)
Determination of the concentration limits from the calibration line
432(3)
Sensitivity
435(1)
Sensitivity in quantitative analysis
435(1)
Sensitivity and specificity in qualitative analysis
436(1)
Selectivity and interferences
436(5)
References
438(3)
Method Validation by Interlaboratory Studies
441(20)
Types of interlaboratory studies
441(1)
Method-performance studies
441(10)
Definition of reproducibility and repeatability
441(2)
Method-performance precision experiments
443(1)
Repeatability and reproducibility in a method-performance experiment
444(1)
Statistical analysis of the data obtained in a method-performance experiment
444(5)
What precision to expect
449(2)
Method-performance bias experiments
451(1)
Laboratory-performance studies
451(10)
Visual display methods
451(1)
Box plots
452(1)
Youden plots
452(2)
Mandel's h and k consistency statistics
454(3)
Ranking method
457(1)
The z-score method
457(3)
References
460(1)
Other Distributions
461(14)
Introduction --- probabilities
461(2)
The binomial distribution
463(4)
An example: the counter-current distribution
463(2)
The distribution
465(1)
Applications in quality control: the np and p charts
466(1)
The hypergeometric distribution
467(1)
The Poisson distribution
468(3)
Rare events and the Poisson distribution
468(2)
Application in quality control: the c and u-charts
470(1)
Interrelationships between the binomial, Poisson and normal distributions
471(1)
The negative exponential distribution and the Weibull distribution
471(1)
Extreme value distributions
472(3)
References
473(2)
The 2x2 Contingency Table
475(44)
Statistical descriptors
475(14)
Variables, categories, frequencies and marginal totals
475(1)
Probability and conditional probability
476(2)
Sensitivity and specificity
478(3)
Predictive values
481(1)
Posterior and prior probabilities, Bayes' theorem and likelihood ratio
482(1)
Posterior and prior odds
483(2)
Decision limit
485(2)
Receiver operating characteristic
487(2)
Tests of hypothesis
489(30)
Test of hypotheses for 2 x 2 contingency tables
489(2)
Fisher's exact test for two independent samples
491(2)
Pearson's X2 test for two independent samples
493(3)
Graphical X2 test for two independent samples
496(2)
Large-scale X2 test statistic for two independent samples
498(1)
McNemar's X2 test statistic for two related samples
498(2)
Tetrachoric correlation
500(1)
Mantel-Haenszel X2 test statistic for multiple 2 x 2 contingency tables
501(3)
Odds ratio
504(1)
Log odds ratio
505(4)
Multiple 2 x 2 contingency tables, meta-analysis
509(2)
Logistic regression, confounding, interaction
511(2)
Venn diagram
513(2)
General contingency table
515(2)
References
517(2)
Principal Components
519(38)
Latent variables
519(8)
Score plots
527(3)
Loading plots
530(6)
Biplots
536(2)
Applications in method validation
538(3)
Comparison of two methods
538(1)
Intercomparison studies
539(2)
The singular value decomposition
541(5)
Eigenvalues
541(2)
Score and loading matrices
543(3)
The resolution of mixtures by evolving factor analysis and the HELP method
546(6)
Principal component regression and multivariate calibration
552(1)
Other latent variable methods
553(4)
References
556(1)
Information Theory
557(16)
Uncertainty and information
557(4)
An application to thin layer chromatography
561(3)
The information content of combined procedures
564(3)
Inductive expert systems
567(2)
Information theory in data analysis
569(4)
References
570(3)
Fuzzy Methods
573(14)
Conventional set theory and fuzzy set theory
573(3)
Definitions and operations with fuzzy sets
576(3)
Applications
579(8)
Identification of patterns
579(4)
Regression
583(3)
Other applications
586(1)
References
586(1)
Process Modelling and Sampling
587(56)
Introduction
587(1)
Measurability and controllability
588(3)
Estimators of system states
591(2)
Models for process fluctuations
593(11)
Time series
593(1)
Autoregressive models
594(1)
Autocorrelation function and time constant
594(7)
The autoregressive moving average model (ARMA)
601(3)
Measurability and measuring system
604(3)
Choice of an optimal measuring system: cost considerations
607(4)
Multivariate statistical process control
611(7)
Sampling for spatial description
618(1)
Sampling for global description
619(4)
Probability sampling
619(1)
Non-probability sampling
620(1)
Bulk sampling
621(2)
Sampling for prediction
623(13)
h-scatter plots, autocorrelogram, covariogram and variogram
624(5)
Interpolation methods
629(1)
Interpolation methods using only location information
630(1)
Kriging
631(2)
Modelling the variogram
633(1)
Assessing the uncertainty of the prediction
634(2)
Acceptance sampling
636(7)
Operating characteristic curve
637(1)
Sequential sampling plans
638(2)
References
640(3)
An Introduction to Experimental Design
643(16)
Definition and terminology
643(1)
Aims of experimental design
644(3)
The experimental factors
647(2)
Selection of responses
649(2)
Optimization strategies
651(3)
Response functions: the model
654(2)
An overview of simultaneous (factorial) designs
656(3)
References
658(1)
Two-level Factorial Designs
659(24)
Terminology: a pharmaceutical technology example
659(3)
Direct estimation of effects
662(3)
Yates' method of estimating effects
665(2)
An example from analytical chemistry
667(1)
Significance of the estimated effects: visual interpretation
668(4)
Factor plots
668(2)
Normal probability plots
670(2)
Significance of the estimated effects: by using the standard deviation of the effects
672(3)
Determination of the standard deviation of the effects by using duplicated experiments
672(1)
Determination of the standard deviation of the effects by neglecting higher interactions
673(1)
Determination of the standard deviation of the effects by using the centre point
674(1)
Significance of the estimated effects: by ANOVA
675(2)
Least squares modelling
677(2)
Artefacts
679(4)
Effect of aberrant values
679(1)
Blocking and randomization
680(1)
Curvature
681(1)
References
682(1)
Fractional Factorial Designs
683(18)
Need for fractional designs
683(1)
Confounding: example of a half-fraction factorial design
684(4)
Defining contrasts and generators
688(3)
Resolution
691(2)
Embedded full factorials
693(1)
Selection of additional experiments
693(1)
Screening designs
694(7)
Saturated fractional factorial designs
694(3)
Plackett-Burman designs
697(2)
References
699(2)
Multi-level Designs
701(38)
Linear and quadratic response surfaces
701(3)
Quality criteria
704(4)
D-, M- and A-optimality
704(3)
Rotatability, uniformity and variance-related criteria
707(1)
Classical symmetrical designs
708(14)
Three-level factorial designs
709(2)
Central composite designs
711(5)
Box-Behnken designs
716(2)
Doehlert uniform shell design
718(4)
Non-symmetrical designs
722(7)
D-optimal designs
722(4)
Uniform mapping algorithms
726(3)
Response surface methodology
729(5)
Non-linear models
734(1)
Latin square designs
735(4)
References
737(2)
Mixture Designs
739(32)
The sum constraint
739(2)
The ternary diagram
741(2)
Introduction to the Simplex design
743(3)
Simplex lattice and -centroid designs
746(11)
The (3,2) Simplex lattice design
746(2)
(k,m) Simplex lattice designs
748(4)
Simplex centroid design
752(1)
Validation of the models
753(1)
Designs based on inner points
754(2)
Regression modelling of mixture designs
756(1)
Upper or lower bounds
757(4)
Upper and lower bounds
761(5)
Combining mixture and process variables
766(5)
References
768(3)
Other Optimization Methods
771(34)
Introduction
771(1)
Sequential optimization methods
771(9)
Fibonacci numbers
771(3)
The Simplex method
774(4)
The modified Simplex method
778(1)
Advantages and disadvantages of Simplex methods
779(1)
Steepest ascent methods
780(3)
Multicriteria decision making
783(16)
Window programming
783(2)
Threshold approaches
785(3)
Utility functions
788(1)
Derringer functions
788(2)
Pareto optimality methods
790(2)
Electre outranking relationships
792(4)
Promethee
796(3)
Taguchi methods
799(6)
Signal-to-noise ratios
799(1)
Inner and outer arrays
799(4)
References
803(2)
Genetic Algorithms and Other Global Search Strategies
805(44)
Introduction
805(1)
Application scope
806(1)
Principle of genetic algorithms
807(14)
Candidate solutions: representation
807(4)
Flowchart of genetic algorithms
811(1)
Initiation
811(1)
Evaluation and termination
812(1)
Selection phase
813(3)
Recombination and mutation
816(5)
Replace and continue
821(1)
Performance measure of a generation
821(1)
Configuration of genetic algorithms
821(2)
Search behaviour of genetic algorithms
823(1)
Search accuracy and precision
823(1)
Behaviour of genetic algorithms in the presence of multiple optima
824(1)
Hybridization of genetic algorithms
824(2)
Example
826(14)
Applications
840(1)
Simulated annealing
841(3)
Principle of simulated annealing
841(2)
Configuration parameters for the simulated annealing algorithm
843(1)
Applications
844(1)
Tabu search
844(5)
References
845(4)
Index 849