**Milan Meloun: Chemometrics in Instrumental Laboratory in J. Churáček (Ed.): Advanced Instrumental Methods of Chemical Analysis, Ellis Horwood, Chichester 1993, ISBN 0-13-913195-7, Academia Praha 1993, ISBN 80-200-0424-6.**

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### INTRODUCTION

Chemistry deals with many quantities. Some are purely physical (time, mass, volume, temperature, electrical quantities), others are physico-chemical (pH, potential, viscosity) and finally, some are connected with the chemical composition of the system. A description of the chemical composition requires the determination of a number of quantitative characteristics, the concentrations of the components. This is the purpose of analytical chemistry. This subject became a separate field about 180 years ago, and has now far exceeded its original boundaries. The use of physical, mathematical, biological and other methods has transformed it into an interdisciplinary field that is closely connected with industry. Every branch of research needs to use analytical chemistry to obtain data on chemical compositions. This use of analytical chemistry may be considered to be a subsystem that can be subdivided into the following blocks:

(a) Sample preparation and treatment, including operations that are mostly carried out outside the laboratory, to ensure that the sample is representative.

(b) Sample preparation for the measurement (sample decomposition, separation operations, procedures defining the chemical substance) includes those operations preceding the actual measurement. In instrumental methods, there may be an attempt to combine the actual measuring operation with the operations necessary for forming a measurable species.

(c) The actual measurement of the analytical signal.

(d) Evaluation of the analytical signal to obtain the analytical description of the chemical composition.

The analytical signal is usually a physical quantity and is measured instrumentally. It has a quantitative aspect, its magnitude (e.g. radiation intensity at a given wavelength) and a qualitative aspect, its position (e.g. wavelength).

The magnitude of the signal, S, is generally a function of the concentration of the test component, the analyte, e.g. cA, cM, cL, cH, and also of procedural variables xi which can be reagent volumes, wavelength, etc.; S = f(cA, cM, cL, cH; xi). The analytical method is characterized by its sensitivity, which is defined as the derivative of the signal with respect to the concentration of the test component (dS/dcA)cM,cl,cH,xi, where cM, cL and cH and xi are maintained constant, so that the analytical signal can be considered a function of a single variable cA, S = f(cA), which is then termed the calibration function.

In practice, the variability of the conditions and parameters leads to variations of the signal, i.e. noise. A set of replicate results can be considered to consist of a range of random numbers with a given distribution and characteristic parameters. The measured signal is treated according to the following rules:

(1) There is always a limit to the precision of measurements. Even results obtained with best instrumental precision and experimental care are not the "true" values (except by chance) but approximations to them.

(2) Only certain physical quantities can be monitored directly, i.e. length, mass, and time. Most other quantities are measured indirectly. The relationship between the analytical signal and the analyte concentration is derived from mathematical relationships, The measured results are approximate values, so the calculated analyte content must also be an approximate value.

(3) The arithmetic mean of repeated measurements corresponds to the most probable approximation to the true value of the measured quantity; however, the true value remains unknown.

(4) The measured results are often plotted as a graph. If the relationship between the test quantities is periodie in character, harmonic analysis is used to decompose the periodic function into sinusoidal components.

(5) Finding empirical model functions constitutes the first step in finding more basic relationships. In addition to the test quantities, the model also contains unknown parameters that are estimated from the experimental data by regression methods.

Discussions of chemometrics and computer-assisted data treatment in the chemical laboratory may be found in chapter.

### Content

**16 Chemometrics in the Instrumental Laboratory** ,**Doc. RNDr. Milan Meloun, DrSc., Institute of Chemical Technology, Pardubice**

16.1 Measurement Errors and the Law of Error Propagation 407

16.2 Measures of Position and Spread. 410

16.2.1 Point Estimates of the Position Parameters. 411

16.2.2 Point Estimates of Variability 412

16.2.3 Point Estimates of Skewness and Kurtosis 414

16.2.4 Interval Estimates of Position and Variability 414

16.3 Statistical Hypothesis Testing 417

16.4 ANOVA, Analysis of Variance 421

16.4.1 One-Way ANOVA 421

16.4.2 Two-Way ANOVA 422

16.5 Regression Analysis of Calibration Graphs 426

16.5.1 Linear Calibration Models 427

16.5.2 Non-linear Calibration Models 429

16.5.3 Goodness-of-Fit Test of the Calibration Graph 430

16.6 Regression Analysis of Non-linear Models 432

16.6.1 Estimation of the Parameters of the Non-linear Model 433

16.6.2 Classification of Minimization Methods 434

16.6.3 Error Analysis 439

16.6.4 Reliability of Model Building and Testing 439

16.7 Factor Analysis 442

16.8 Interpolation 445

16.8.1 Linear Interpolation 445

16.8.2 Lagrange Interpolation 446

16.8.3 Newton Interpolation 446

16.8.4 Gaussian Interpolation 446

16.9 Differentiation and Integration 447

16.9.1 Differentiation 447

16.9.2 Integration 449

16.10 Chemical Model Building by Regression Analysis of Instrumental Data. 450

References 464

Index 478