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Experimental Design - course description

General information
Course name Experimental Design
Course ID 11.1-WK-CSEEP-ED-S22
Faculty Faculty of Exact and Natural Sciences
Field of study computer science and econometrics
Education profile academic
Level of studies First-cycle studies leading to Bachelor's degree
Beginning semester winter term 2022/2023
Course information
Semester 6
ECTS credits to win 5
Available in specialities Statistics and econometrics
Course type optional
Teaching language english
Author of syllabus
  • prof. dr hab. Roman Zmyślony
  • dr Arkadiusz Kozioł
Classes forms
The class form Hours per semester (full-time) Hours per week (full-time) Hours per semester (part-time) Hours per week (part-time) Form of assignment
Lecture 30 2 - - Credit with grade
Laboratory 30 2 - - Credit with grade

Aim of the course

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

Prerequisites

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

Scope

Lecture

1. Univariate and multivariate normal distribution and related distributions. Random variable, random variable with normal distribution (repetition). Chi-square distribution of the quadratic form and theorems on the independence of linear and quadratic forms, Student's t distributions, F-Snedecor distributions (2 hours)

2. Linear model, definition and assumptions about the model (2 hours)

3. Estimators obtained using the least squares (LS) method and their relationship with estimability (2 hours)

4. Theorem on the characterization of estimable functions (2 hours)

5. Normal equations and properties of LS estimators (2 hours)

6. Probability distributions of LS estimators and their functions (2 hours)

7. Residuals in the linear model. Independence of the sum of squared residuals of LS estimators (2 hours)

8. Unbiased estimator for variance and its probability distribution (2 hours)

9. Theory of testing statistical hypotheses for linear functions of model parameters with the use of Student's t distribution (2 hours)

10. Analysis of variance table for testing complex hypotheses, F-Snedecor test (2 hours)

11. Confidence intervals for parametric functions, their interpretation (2 hours)

12. Prediction and confidence intervals of parametric functions and for prediction (2 hours)

13. Examples of optimal plans with a singular design matrix, linear restrictions on parameters (6 hours)

Laboratory

1. Repetition and development of knowledge about probability theory. Normal distribution and its properties. Multivariate normal distribution of random variables and its basic numerical characteristics. Functions of random variables and their distributions (2 hours)

2. Independence of variables. Determining and showing the independence of the mean and variance from a normal sample based on the theorem on the independence of linear and quadratic forms (2 hours)

3. Writing a linear model for one- and multivariate regression functions, using LS method to determine explicit formulas for estimating model parameters. Examples (4 hours)

4. Determination of the model residuals and the sum of squares of the residuals, as well as the variance estimator and confidence intervals for parameters and predictions (4 hours)

5. Analysis of variaance table for the above-mentioned model with an example (2 hours) Colloquium (2 hours)

6. Repeat exercise for points 3-5. for the one-way and multi-way analysis of variance model (10 hours)

7. Repeat the exercise from 3-5. for factorial designs 2^k (2 hours) Colloquium (2 hours)

Teaching methods

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).

Learning outcomes and methods of theirs verification

Outcome description Outcome symbols Methods of verification The class form

Assignment conditions

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, with varying degrees of difficulty, to assess whether the student has achieved the learning outcomes to a minimum degree.

3. A written project referring to concepts and theorems that check the understanding of the acquired knowledge based on this project

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

The condition for taking the project is a positive grade from the laboratory. The condition for passing the lecture is a positive project grade.

Recommended reading

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

Further reading

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

Notes


Modified by dr Ewa Synówka (last modification: 16-02-2024 17:40)