1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Computer science and econometrics - drugiego stopnia z tyt. magistra
5. Experimental Design

Wygeneruj PDF dla tej strony

Experimental Design - opis przedmiotu

Cel przedmiotu

To introduce the students to the theoretical and practical foundations of experimental design.

Wymagania wstępne

Zapisz zmiany

Passing the lectures on probability theory and elements of mathematical statistics.

Zakres tematyczny

Lecture

1. Linear model, matrix notation (2 hours)

2. Distributions related to normal distribution (Student's t, Chi-square and F-Snedecor) (2 hours)

3. Theorems on independence of linear and quadratic forms (2 hours)

4. The least squares (LS) method, normal equations, residuals (2 hours)

5. Theorem on the characterization of estimable functions, restrictions on parameters, generalized inverse matrices (2 hours)

6. Analysis of variance for testing linear hypotheses about model parameters. F test (2 hours)

7. Residuals and testing if distribution of the data deviates from a normal distribution (2 hours)

8. Checking the adequacy of the model (2 hours)

9. Mathematical definition of the experimental design and optimality criteria (2 hours)

10. The equivalence theorem (Kiefer and Wolfowitz), examples of optimal plans (2 hours)

11. Optimal plans for one-way, two-way and multi-way analysis of variance (2 hours)

12. Statistical analysis of the experimental results from point 11. (2 hours)

13. Latin squares, Graeco-Latin squares (2 hours)

14. 2^k factorial and fractional designs (2 hours)

15. Optimal plans for block designs (2 hours)

Laboratory

1. Writing a linear model for given design, using LS method to determine explicit formulas for estimators of the parameters of optimal models. Examples for points 11-15. from lectures (2 hours)

2. Analysis of variance tables for the above-mentioned models presented in examples and their interpretation (2 hours)

3. Repeat exercise for points 1-2. for models under block designs (2 hours)

4. Repeat exercise 1-2. for polynomial models (2 hours)

5. Passing self-prepared projects (7 hours)

Metody kształcenia

Traditional lecture (chalk and blackboard for the most important phrases only, computer examples), in laboratories, solving previously announced exercises (computation exercises, for given practical examples using using selected statistical packages).

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

1. Student's preparation for laboratories is verified by checking the knowledge (concept, properties, theorems) necessary to solve the next exercise on the list (lack of preparation for the laboratory is included in the final grade).

2. The final project to assess whether the student has achieved the learning outcomes to a minimum degree.

3. Oral exam (checking knowledge of the theory of experimental design).

The subject grade consists of the laboratory grade (40%, including the project grade) and the exam grade (60%).

The condition for taking the exam is a positive grade from the laboratory. The condition for passing the course is a positive exam grade.

Literatura podstawowa

1. C. R. Rao, Linear Statistical Inference and its Applications, Wiley, Canada 2002.
2. H. Scheffe, The Analysis of Variance, Wiley, New York, 1959.
3.  D. C. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, 1991

Literatura uzupełniająca

1. E. L. Lehmann, Testing statistical hypothesis, Second edition. Wiley, New York 1986.

Uwagi

Zmodyfikowane przez dr Ewa Synówka (ostatnia modyfikacja: 10-04-2024 21:23)