Handbook of Chemometrics and Qualimetrics

Introduction. The aims of chemometrics. An overview of chemometrics. Some historical considerations. Chemometrics in industry and academia. References. Statistical Description of the Quality of Processes and Measurements. Introductory concepts about chemical data. Measurement of quality. Quality of processes and statistical process control. Quality of measurements in relation to quality of processes. Precision and bias of measurements. Some other types of error. Propagation of errors. Rounding and rounding errors. References. The Normal Distribution. Population parameters and their estimators. Moments of a distribution: mean, variance, skewness. The normal distribution: description and notation. Tables for the standardized normal distribution. Standard errors. Confidence intervals for the mean. Small samples and the t-distribution. Normality tests: a graphical procedure. How to convert a non-normal distribution into a normal one. References. An Introduction to Hypothesis Testing. Comparison of the mean with a given value. Null and alternative hypotheses. Using confidence intervals. Comparing a test value with a critical value. Presentation of results of a hypothesis test. Level of significance and type I error. Power and type II errors. Sample size. One- and two-sided tests. An alternative approach: interval hypotheses. References. Some Important Hypothesis Tests. Comparison of two means. Multiple comparisons. &bgr; error and sample size. Comparison of variances. Outliers. Distribution tests. References. Analysis of Variance. One-way analysis of variance. Assumptions. Fixed effect models: testing differences between means of columns. Random effect models: variance components. Two-way and multi-way ANOVA. Interaction. Incorporation of interaction in the residual. Experimental design and modelling. Blocking. Repeated testing by ANOVA. Nested ANOVA. References. Control Charts. Quality control. Mean and range charts. Charts for attributes. Moving average and related charts. Further developments. References. Straight Line Regression and Calibration. Introduction. Straight line regression. Correlation. References. Vectors and Matrices. The data table as data matrix. Vectors. Matrices. References. Multiple and Polynomial Regression. Introduction. Estimation of the regression parameters. Validation of the model. Confidence intervals. Multicollinearity. Ridge regression. Multicomponent analysis by multiple linear regression. Polynomial regression. Outliers. References. Non-linear Regression. Introduction. Mechanistic modelling. Empirical modelling. References. Robust Statistics. Methods based on the median. Biweight and winsorized mean. Iteratively reweighted least squares. Randomization tests. Monte Carlo methods. References. Internal Method Validation. Definition and types of method validation. The golden rules of method validation. Types of internal method validation. Precision. Accuracy and bias. Linearity of calibration lines. Detection limit and related quantities. Sensitivity. Selectivity and interferences. References. Method Validation by Interlaboratory Studies. Types of interlaboratory studies. Method-performance studies. Laboratory-performance studies. References. Other Distributions. Introduction—probabilities. The binomial distribution. The hypergeometric distribution. The Poisson distribution. The negative exponential distribution and the Weibull distribution. Extreme value distributions. References. The 2×2 Contingency Table. Statistical descriptors. Tests of hypothesis. References. Principal Components. Latent variables. Score plots. Loading plots. Biplots. Applications in method validation. The singular value decompostion. The resolution of mixtures by evolving factor analysis and the HELP method. Principal component regression and multivariate calibration. Other latent variable methods. References. Information Theory. Uncertainty and information. An application to thin layer chromatography. The information content of combined procedures. Inductive expert systems. Information theory in data analysis. References. Fuzzy Methods. Conventional set theory and fuzzy set theory. Definitions and operations with fuzzy sets. Applications. References. Process Modelling and Sampling. Introduction. Measurability and controllability. Estimators of system states. Models for process fluctuations. Measurability and measuring system. Choice of an optimal measuring system: cost considerations. Multivariate statistical process control. Sampling for spatial description. Sampling for global description. Sampling for prediction. Acceptance sampling. References. An Introduction to Experimental Design. Definition and terminology. Aims of experimental design. The experimental factors. Selection of responses. Optimization strategies. Response functions: the model. An overview of simultanous (factorial) designs. References. Two-level Factorial Designs. Terminology: a pharmaceutical technology example. Direct estimation of effects. Yates' method of estimating effects. An example from analytical chemistry. Significance of the estimated effects: visual interpretation. Significance of the estimated effects: by using the standard deviation of the effects. Significance of the estimated effects: by ANOVA. Least squares modelling. Artefacts. References. Fractional Factorial Designs. Need for fractional designs. Confounding: example of a half-fraction factorial design. Defining contrasts and generators. Resolution. Embedded full factorials. Selection of additional experiments. Screening designs. References. Multi-level Designs. Linear and quadratic response surfaces. Quality criteria. Classical symmetrical designs. Non-symmetrical designs. Response surface methodology. Non-linear models. Latin square designs. References. Mixture Designs. The sum constraint. The ternary diagram. Introduction to the Simplex design. Simplex lattice and -centroid designs. Upper or lower bounds. Upper and lower bounds. Combining mixture and process variables. References. Other Optimization Methods. Introduction. Sequential optimization methods. Steepest ascent methods. Multicriteria decision making. Taguchi methods. References. Genetic Algorithms and Other Global Search Strategies. Introduction. Application scope. Principle of genetic algorithms. Configuration of genetic algorithms. Search behaviour of genetic algorithms. Hybridization of genetic algorithms. Example. Applications. Simulated annealing. Tabu search. References. Index.