Statistics and Quality Control in Analytical Chemistry   (353H2)

Academic year:

2024/2025.

Attendance requirements:

There are no requirements.

ECTS:

9

Study level:

Study programs:

Teacher:

Filip Lj. Andrić, Ph.D.
associate professor, Faculty of Chemistry, Studentski trg 12-16, Beograd

Assistants:

—

Hours of instruction:

Weekly: four hours of lectures + two hours of exercises + three hours of labwork (4+2+3)

Goals:

The course aims to acquaint the students with the practical application of statistics in analytical chemistry and prepare them for the future work in accredited analytical laboratories and laboratories for quality control.

Considering immense importance of statistical techniques in fulfilling requirements of accreditation and certification of analytical laboratories, starting from the sampling strategies, analytical measurements, method comparisons, validation and verification, internal and external quality control and quality assurance, as well as good laboratory practice, the aim of the course is to present elements of statistics in a simple, clear and intuitive way to students, with emphasis on practical perspectives in different stages of the analytical process.

Outcome:

After completing the course, a student should understand, identify and correctly use selected statistical techniques and procedures in the various phases of chemical analysis, and use modern software packages for statistical processing of data and be familiar with contemporary quality control and quality assurance practice in analytical laboratories.

Teaching methods:

Lectures, theoretical exercises, labwork, colloquia, seminar papers.

Extracurricular activities:

—

Coursebooks:

• James N. Miller, Jane C. Miller: Statistics and Chemometrics for Analytical Chemistry, Pearson Education, Harlow, 2000.

Additional material:

—

Lectures:

10 points (4 hours a week)

Syllabus:

1. INTRODUCTION
Analytical chemistry, identification and quantitative determination of analytes. Statistics and its place in analytical chemistry.

2. ABOUT THE PROBABILITY THEORY
Concept of elementary and complex random events, probability, probability distribution, types of variables in analytical chemistry - discrete and continuous random variable, basic probability distributions in analytical chemistry (binomial, Gaussian, Student's t-distribution, Fisher's F-distribution, Hi-square distribution).

3. STATISTICS OF REPEATED MEASUREMENTS
Population and statistical sample. Elements of descriptive statistics, their calculation and graphical representation (measures of central tendency and dispersion. Central limit theorem.

4. ERRORS AND UNCERTAINTY OF ANALYTICAL MEASUREMENTS
The notion of accuracy, precision and trueness. Errors (gross, random and systematic). Uncertainty of measurements. Uncertainty of the derived results. Rules of number rounding and proper result display.

5. HYPOTHESIS TESTING - PARAMETRIC METHODS - PART I
The notion of statistical testing, null and alternative hypotheses. Confidence and statistical significance. Power, conservativeness, and sensitivity of statistical tests. Detection of outliers in chemical analysis. Comparison of accuracy and precision of analytical methods.

6. HYPOTHESIS TESTING - PARAMETRIC METHODS - PART II (ANALYSIS OF VARIANCE)
One-factor and two-factor analysis of variance (ANOVA). A priori and post hoc significance tests (Fisher's LSD, Tukey's HSD, Chief's test). Selection of significant factors and their interactions for the outcome of analytical process. Testing sample homogeneity using analysis of variance calculations and constructing an optimal sample strategy.

7. HYPOTHESIS TESTING - NON-PARAMETRIC METHODS 
Characteristics of nonparametric tests, sign test, signed-rank test, testing for trends in analytical measurements (Val-Wolfowitz test), Wilcoxon rank sum test, Mann-Whitney U-test, Kruskal-Wallis and Friedman analysis of variance, Kolmogorov-Smirnov test for normality of distribution.

8. CALIBRATION - PART I (CORRELATION AND LINEAR REGRESSION) 
Concept of correlation. Linear regression and least squares method. Statistical parameters of regression quality. Determination of limits of detection and quantification. Calculation of unknown concentration and its uncertainty. Method of standard addition. Comparison of two analytical methods by linear regression.

9. CALIBRATION - PART II (NON-LINEAR REGRESSION)
Nonlinear regression, quality parameters of the regression model, coefficient of determination.

10. QUALITY CONTROL AND GOOD LABORATORY PRACTICE
Phases of analytical process, sampling strategies, basic principles of good laboratory practice, quality assurance program, internal and external quality control methods (control charts, proficiency testings and collaborative trials).

Exercises:

10 points (2 hours a week)

Syllabus:

1. Introduction tŢ software packages for statistical analysis.
2. Calculation of descriptive statistics. Evaluation of errors and measurement uncertainty. Error propagation and uncertainty of derived results. Significant figures and proper display of measurement results.
3. Essential characteristics of binomial, normal, and Student’s distribution.
4. Detection of gross errors and non-standard observations in analytical measurements. Testing the accuracy and precision of analytical measurements using a battery of parametric significance tests.
5. Comparison of measurements from multiple laboratories, analysts or analytical methods using analysis of variance.
6. Significance of various factors on the results of chemical analysis (two-factor analysis of variance).
7. Comparison of analytical methods for accuracy, precision, and presence of trends in analytical data using a battery of non-parametric tests.
8. Calibration and linear regression using the least-squares method. Determination of unknown concentration and its error. Comparison of analytical methods by linear regression. Method of standard addition.
9. Curvilinear regression - a selection of the best fit.
10. Validation and verification of analytical methods (linearity, accuracy, repetitiveness, within laboratory reproducibility, reproducibility, limits of detection and quantification).
11. Elements of quality control and quality assurance (control charts, estimation of uncertainty, collaborative studies and proficiency testing).

Labwork:

10 points (3 hours a week)

Syllabus:

Laboratory and theoretical practice follow the plan and content of the lectures so that a student, through practical work, acquires necessary skills for statistical data processing in analytical chemistry.

Semester papers:

20 points

Written exam:

50 points