Statistics and Design of experiments TX00DJ57-3002 13.01.2020-08.05.2020 5 credits(KEM18, ...)+-
Learning outcomes of the course
The student realizes the importance of the measurement uncertainty, unavoidable in every measurement, and is able to take that into account in decision making. The student is able to visualize and interpret statistical data. The student knows confidence intervals, statistical tests, and regression analysis, and can apply them in solving typical simple applications of his or her own field.
The student masters the basics of statistical design of experiments (DOE), and is able to design efficient series of experiments in research and development projects. The student is able to analyze results obtained from designed experiments in order to meet with the objectives of quality control, optimization or of designing systems.
Prerequisites and co-requisites
Math and Science Basics 1
Math and Science Basics 2
Math and Science Basics 3
1. The concept and the basic laws of probability, and random variables and their most common distributions.
2. Measurement uncertainty and propagation of errors.
3. Visualization of statistical data and basic statistics.
4. Confidence intervals and statistical tests, and their applications in statistical inference.
5. Regression analysis and applications in student’s own filed of specialization.
6. Basic concepts of DOE; model and variable types.
7. The most common designs related to qualitative and quantitative variables.
8. Analyzing experimental results using analysis of variance or regression analysis.
9. Experimental optimization and response surfaces (the Box-Wilson strategy).
10. Visualising the results of statistical analyses by families of curves and response surfaces.
11. Using Excel or statistical software in statistical analyses and DOE.
1. The student can calculate probabilities in elementary applications, and name some of the most common distributions and calculate probabilities related to them. The student can estimate probabilities related to the standard normal distribution.
2. The student is able to apply the laws of propagation of errors to elementary applications related to replicate measurements.
3. The student is able to make a histogram and calculate basics statistics of given data using some statistical software.
4. The student is able to calculate confidence limits for expected values and for standard deviations, and is able to make conclusions in statistical tests based on the p-value of the test.
5. The student is able use linear regression analysis in elementary calibration problems.
6. The student can list the basic principles of design of experiments; the student can explain the difference between empirical and mechanistic models, and he or she is able to formulate linear models of several variables.
7. The student is able to create factorial designs, and especially 2N factorial designs.
8. The student is able to carry out multiple linear regression analyses.
9. The student takes part into the computer labs and carries out the given exercises acceptably.
1. The student is able to use laws of probability in statistical inference, and he or she is able to find an appropriate distribution in typical applications.
2. The student can approximate the standard measurement uncertainty of nonlinear expressions.
3. The student is able to draw conclusions based on graphs and statistics of a given data.
4. The student is able to apply confidence intervals in statistical inference, and he or she is able to formulate statistical hypotheses into a given problem.
5. The student is able to interpret basic regression statistics.
6. The student is able to apply the basic principles of DOE in simple practical cases; the student is able to formulate models used in analysis of variance.
7. The student is able to create CC designs and fractional 2N designs.
8. The student is able to choose and carry out analysis variance in a given simple problem.
9. The student is able to conclude when a 2N design requires supplementary experiments.
10. The student is able to create response surfaces.
11. The student is able to use his or hers computer skills in practical cases of experimental design.
1. The student is able to apply his knowledge about statistical distributions and Monte Carlo simulation to statistical tests or measurement uncertainty estimation.
2. The student is able to describe the nature of given statistical data using several different visualization and computational tools.
3. Using literature and other available information, the student is able to choose and use statistical tests in new applications.
4. The student is able to transform typical expressions of his or hers field of specialization into the linear regression form.
5. The student is able to classify categorical factors and, based on that, choose on an appropriate empirical model.
6. The student is able to choose a design of an appropriate resolution for a given case.
7. The student is able to assess the reliability of empirical models in several different ways.
8. The student is able to calculate gradients and design new experiments in their direction.
9. The student is able to use graphical visualization techniques in empirical optimization.