TMA 4255 Applied Statistics

1. TMA 4255Applied Statistics Spring 2010

2. About the course Learning outcome The objective of the course is to give the students a solid foundation for use of basic statistical methods in science and technology. In addition the students shall be capable of planning collection of data and to use statistical software for analysing data. Learning methods and activities Lectures and exercises with the use of a computer (computing programme MINITAB). The lectures may be given in English. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination 80% and selected parts of the exercises 20%. The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. Compulsory assignments Exercises Recommended previous knowledge The course is based on ST0103 Statistics with Applications/TMA4240 Statistics/TMA4245 Statistics, or equivalent.

3. Contents (preliminary list) Hypotheses testing, simple and multiple linear regression, residual plots and selection of variables, transformations, design of experiments, 2^k experiments and fractions of these. Special designs. Graphical methods. Error propagation formula. Analysis of variance, statistical process control, contingency tables and nonparametric methods. Use of statistical computer package, MINITAB. Lecturer Professor Bo Lindqvist, Room 1129, Sentralbygg II, NTNU Gløshaugen Telephone: (735) 93532 Email: bo@math.ntnu.no Teaching assistant Stipendiat Håkon Toftaker, Room 1036, Sentralbygg II, NTNU Gløshaugen Telephone (735) 91681 Email: toftaker@math.ntnu.no

4. Teaching material Main book: Walpole, Myers, Myers and Ye: "Probability and Statistics for Engineers and Scientists". Eighth Edition. Pearson International Edition. Tables: ”Tabeller og formler i statistikk”, 2. utgave. Tapir 2009. MINITAB: Information is found on http://www.ntnu.no/adm/it/brukerstotte/programvare/minitab.

5. Weekly meetings Lectures Tuesdays 12.15 – 14.00 H3 Thursdays 12.15 – 14.00 S4 Exercises Mondays 17.15 – 18.00 in H3 or a computer lab

6. Tuesdays 12.15 – 14.00 H3 Thursdays 12.15 – 14.00 S4 Preliminary curriculum, lecturing and progress plan Preliminary curriculum, lecturing and progress plan

15. The compulsory project: Example

18. Introduction to course TMA 4240/45 Statistics and ST 0103: Probability theory + simple statistics TMA 4255 (this course): A little probability + APPLICABLE and APPLIED statistics The ”classical” statistical methods: • Regression analysis • Design of experiments • Analysis of variance (ANOVA) • Analysis of discrete data (contingency tables) • Nonparametric methods

19. Why is statistics important in science and industry? The book emphasizes ”the Japanese industrial miracle”: Use of statistical methods in design and production Statistical thinking in all parts of the production In 2000, the highly reputated international medical journal New England Journal of Medicine appointed Use of statistical methods as one of the 11 most important medical advances throughout time

21. Originally:Statistics = ”collection and presentation of data” • Today much more: • Design and collection of data from statistical investigations • Modeling of the stochastic mechanisms behind the data • Drawing conclusions about these mechanisms, based on the data • Evaluation of the strength of the conclusions (variance, confidence interval, • test power) • Basic tool: Probability theory

22. Statistical investigations can be divided into two main types: • Experimental studies based on design of experiments (DOE): Experiments are done under controlled conditions. • Observational studies: When control of conditions are not possible.

23. Eksperimental studies: Clinical trials Comparison of drugs A og B Trial group of n persons r drawn at random are given A s drawn at random are given B n-r-s (rest) get Placebo Blind test: Patient does not know kind of drug Double blind: Examining doctor does not know either Observational studies: Epidemiological experiments Smoking and cancer Diet and coronary diseases Cannot control the conditions; e.g. cannot force people to smoke/not smoke. Difficulty in interpretation: May be unknown underlying causes which make the results biased (”confounding”). For example: A gene which increases the need for smoking, and at the same time influences chance of getting cancer. Statistical studies

24. Statistics in scientific investigations: • Generate hypotheses • Derive consequences • See whether these are fulfilled in observations • Generate new hypotheses • Etc.

25. Particular matters for statistics in industry: Product and process engineer: Off-line: Controlled experiments aiming at optimizing production Production: Register production data; use them to control production.

26. MINITAB 15: Rocket fuel exampleStat > Basic Statistics > Display Descriptive Statistics

27. Stat > Basic Statistics > Graphical Summary

28. More plots: Rocket fuel data

31. Statistical inference with MINITAB: Rocket fuel dataStat > Basic Statistics > 1-Sample ZAssume known standard deviation sigma=2 One-Sample Z: X Test of mu = 40 vs not = 40 The assumed standard deviation = 2 Variable N Mean StDev SE Mean 95% CI Z P X 10 40,560 1,991 0,632 (39,320; 41,800) 0,89 0,376 One-Sample Z: X Test of mu = 40 vs > 40 The assumed standard deviation = 2 95% Lower Variable N Mean StDev SE Mean Bound Z P X 10 40,560 1,991 0,632 39,520 0,89 0,188

32. Stat > Basic Statistics > 1-Sample tAssume unknown standard deviation sigma One-Sample T: X Test of mu = 40 vs not = 40 Variable N Mean StDev SE Mean 95% CI T P X 10 40,560 1,991 0,629 (39,136; 41,984) 0,89 0,397 One-Sample T: X Test of mu = 40 vs > 40 95% Lower Variable N Mean StDev SE Mean Bound T P X 10 40,560 1,991 0,629 39,406 0,89 0,198

34. One and two sample tests concerning means

35. Example: The industrial experment An experiment was performed on a manufacturing plant by making in sequence 10 batches using the standard production method (A), followed by 10 batches of a modified method (B). The results from these trials are given in the table on the next slide. What evidence do the data provide that method B is better than method A?

38. (Assuming equal variances:)

39. (Not assuming equal variances:)

40. Two sample t-test

41. Paired observations (example)

46. Regression analysis Goal: Describe Y as function of the xi,

47. Linear Regression

48. Typical data

49. EXAMPLE Connection between stiffness (stivheit) and density (tettleik) of a tree product.

50. Plot of stiffness versus density