Experiments in Engineering (E362701)

Departments: | ústav přístrojové a řídící techniky (12110) | ||

Abbreviation: | Approved: | 28.01.2011 | |

Valid until: | ?? | Range: | 1P+0C+2L |

Semestr: | * | Credits: | 3 |

Completion: | KZ | Language: | EN |

Annotation

The course provides an introduction to Design of Experiments in the field of engineering. The concept of measurement is presented as a key method for information acquisition which together with correct interpretation allow understanding of not only engineering phenomena. Provided is an introduction to applied mathematical statistic and up-to-date data analysis with computer support. During exercises students master design of effective experiments and get skilled with MATLAB environment especialy with tools for data analysis.

Structure

1. Research project. Population and sample, Deduction and induction, A Characteristic, Design of a research project, Data acquisition, Interpretation of the results

2. Probability theory - an introduction. Rules of probability, Bayes theorem, ROC curve, Odds, probability, likelihood

3. Probability distribution. Discrete and continuous random variable, Probability and relative frequency, Normal distribution, Binomial distribution, Poisson distribution, Sample and descriptive statistics, Measures of central tendency, Mean, modus, median, Measures of variation, Range, Variation, Standard deviation, Quantiles

4. Estimates of probability, Distribution of a sample mean, Interval estimate of a mean, Sample size

5. Hypothesis testing. Null and alternative hypothesis, The type I. and II. errors

6. Two samples comparison. Mean comparison, Pair comparison

7. Non-parametric methods. Quantile, median and sign tests, Wilcoxon's pair test, Mann-Whitney's test

8. Nominal data. Chi-square test, Contingency tables

9. Linear regression and correlation

10. Analysis of variance. Mean comparison for 3+ groups, Model condition verification, Multiple comparison

2. Probability theory - an introduction. Rules of probability, Bayes theorem, ROC curve, Odds, probability, likelihood

3. Probability distribution. Discrete and continuous random variable, Probability and relative frequency, Normal distribution, Binomial distribution, Poisson distribution, Sample and descriptive statistics, Measures of central tendency, Mean, modus, median, Measures of variation, Range, Variation, Standard deviation, Quantiles

4. Estimates of probability, Distribution of a sample mean, Interval estimate of a mean, Sample size

5. Hypothesis testing. Null and alternative hypothesis, The type I. and II. errors

6. Two samples comparison. Mean comparison, Pair comparison

7. Non-parametric methods. Quantile, median and sign tests, Wilcoxon's pair test, Mann-Whitney's test

8. Nominal data. Chi-square test, Contingency tables

9. Linear regression and correlation

10. Analysis of variance. Mean comparison for 3+ groups, Model condition verification, Multiple comparison

Structure of tutorial

1. Visualising a random process . Random numbers generation, Creating a plot, Computation of the probability of random processes, Conditional probability computation, Testing the dependence of random processes, Calculating probabilities using Bayes' theorem (Matlab)

2. Calculation of the sensitivity and selectivity of a test. Construction of the ROC curve (Matlab)

3. Calculation of odds, probabilities and likelihoods

4. Construction of the probability distribution function and the distribution function for discrete and continuous random variable (Matlab)

5. Visualising the probability density. Calculating probabilities (Matlab)

6. Calculation of the descriptive characteristics. Plotting the histogram, the percentile plot, box plot, normal plot (Matlab)

7. Visualising the probability distribution of the sample mean (Matlab)

8. Hypothesis testing. Carrying out one sample t-test, two sample t-test, comparison of the population probabilities, Evaluation of the pair measurement, Carrying out non-parametric tests, quantile test, median test, sign test, Wilcoxon's test, Mann-Whitney's test

9. Categorial data. Carrying out chi-square test, Evaluation of the contingency table (Matlab)

10. Carrying out linear regression and correlation (Matlab)

11. Carrying out analysis of variance

12. Execution of an experiment

13. Presentation of the results of the experiment

2. Calculation of the sensitivity and selectivity of a test. Construction of the ROC curve (Matlab)

3. Calculation of odds, probabilities and likelihoods

4. Construction of the probability distribution function and the distribution function for discrete and continuous random variable (Matlab)

5. Visualising the probability density. Calculating probabilities (Matlab)

6. Calculation of the descriptive characteristics. Plotting the histogram, the percentile plot, box plot, normal plot (Matlab)

7. Visualising the probability distribution of the sample mean (Matlab)

8. Hypothesis testing. Carrying out one sample t-test, two sample t-test, comparison of the population probabilities, Evaluation of the pair measurement, Carrying out non-parametric tests, quantile test, median test, sign test, Wilcoxon's test, Mann-Whitney's test

9. Categorial data. Carrying out chi-square test, Evaluation of the contingency table (Matlab)

10. Carrying out linear regression and correlation (Matlab)

11. Carrying out analysis of variance

12. Execution of an experiment

13. Presentation of the results of the experiment

Literarture

1. Experiments in Engineering subject web, http://pmo.fs.cvut.cz/tex

2. Bernard, J., Technický experiment, ČVUT Praha 1999

3. Novovičová, J., Pravděpodobnost a matematická statistika, ČVUT Praha 1999

4. Beneš, V., Pravděpodobnost a matematická statistika, ČVUT Praha 1995

5. Zvárová, J., Introduction to Statistics for Biomedical Domains, Karolinum Praha 1998, http://pmo.fs.cvut.cz/biostat-en

6. MATLAB Statistics Toolbox, http://www.mathworks.com/help/toolbox/stats

2. Bernard, J., Technický experiment, ČVUT Praha 1999

3. Novovičová, J., Pravděpodobnost a matematická statistika, ČVUT Praha 1999

4. Beneš, V., Pravděpodobnost a matematická statistika, ČVUT Praha 1995

5. Zvárová, J., Introduction to Statistics for Biomedical Domains, Karolinum Praha 1998, http://pmo.fs.cvut.cz/biostat-en

6. MATLAB Statistics Toolbox, http://www.mathworks.com/help/toolbox/stats