TMA4255 Applied Statistics

Spring 2010



26.05  Here is solution for today’s exam. Exercise in English and Norwegian.


03.05  Meeting times before exam:


Wednesday  May 12: 13:00 -15:00  Bo Lindqvist, office 1138 in Sentralbygg II

Thursday      May 20: 13:00 -15:00  Bo Lindqvist

Friday           May 21: 13:00 -15:00  Håkon Toftaker, office 1036, Sentralbygg II

Monday        May 24: 13:00 - 15:00  Håkon Toftaker

Tuesday       May 25: 13:00 -15:00   Bo Lindqvist


03.05  Here is Final Syllabus for the course.


21.04  The results of the obligatory project are now available at the Exercise website.


15.04  The last topic of the course is Chapter 16.1-16.3. (So slides pages 56-59 will not be used). After having gone through 16.1-16.3, I will go through earlier exams. Will give list of exercises later.


12.03  Starting Monday March 15, 18:15 – 19:00 in H3, Håkon Toftaker will go through exercises from the weekly sets. See Exercise website for information.


10.03  Here are two examples of earlier obligatory projects: One in English, one (old) in

Norwegian. Note that you will be rewarded for the contents and not for the layout! Thus a handwritten report may be as good as a nicely printed one! Also: Pictures are of course nice to have, but not needed if you can explain things without them!


09.03 This message is copied from the Exercise website: (02.03) To run MiniTab you need a new licence file. You can find it by connecting to\progdist. When you start MiniTab choose "Specify the licence file" and browse to\progdist\campus\MiniTab. The new licence file is called minitab.lic .


24.02  There will be NO LECTURES March 2 and 4. (Work with the obligatory project!)


18.02 The obligatory exercise will start in Week 9 (March 1), and deadline for submitting the report is Thursday March 25 at 12 Noon. An updated version of the information about the exercise can now be downloaded under “Exercises” below. There will be no new exercises in Weeks 9 and 10 (March 1 and 8), instead you may consult the teaching assistant in the regular exercise hours these weeks, and in addition on Thursday March 4 at 16:15 – 17:00.

12.02  Starting Monday 15.02 the exercises in Vegas computer lab will be from 16.15 to 18.00 (see message on Exercise website).

14.01  For those using 7th edition of book: The (very few!) changes in chapter numbers of the curriculum are given in the course webpage for 2008.

11.01  Lectures start tomorrow January 12 at 12:15 in H3. First Exercise meeting is Monday January 18. See EXERCISE WEBSITE.

About the course


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.

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


Recommended previous knowledge

The course is based on ST0103 Statistics with Applications/TMA4240 Statistics/TMA4245 Statistics, or equivalent.

Credit: 7.5 stp.

  • Duration: 1 semester (fall)
  • Lecturing: 4 hours a week
  • Exercises: 1 hour a week
  • Special activity: A compulsory project counts 20 % for the exam.
  • Exam: Written, 4 hours.



Professor Bo Lindqvist, Room 1129, Sentralbygg II, NTNU Gløshaugen
Telephone: (735) 93532
Office hours: To be announced

Teaching assistant

Stipendiat Håkon Toftaker, Room 1036, Sentralbygg II, NTNU Gløshaugen

Telephone (735) 91681



Student assistant

Stud. Håkon Kile


Reference group

Ingeborg Engh (Biology). Email:

Tom Ivar Pedersen (PuP/IPK). Email:

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: Some information is found on


Recommended literature that can be useful to read as a supplement to the book is Box, Hunter og Hunter (1978, 2005): "Statistics for Experimenters". Wiley.


Tuesdays  12.15 – 14.00 H3

Thursdays 12.15 – 14.00 S4

Preliminary curriculum, lecturing and progress plan



Chapter (WMMY)



Introduction, motivation and repetition. Descriptive measures and graphs. Normal plot.

(1-10) Particularly 8.1-8.7



Two-sample case. Comparing variances. F-distribution.

Simple linear regression,

8.8, 9.8, 9.13, 10.8, 10.13, 10.18.


(11.1-11.5) 11.6 – 11.12




Multiple linear regression

12.1 -12.7, 12.9-12.10

12.11: Only Cp



2k experiment and fractions thereof

BHH 10 and 12
Alternatively, WMMY 15




No lectures


Work with project



Analysis of variance




Statistical process control



13-14 (Tuesd)

Easter vacation




Chi-square tests and Contingency tables








Nonparametric statistics




Earlier exam exercises




Earlier exams




Mondays 17.15 – 18.00 in Vegas computer lab and 18.15 – 19.00 in H3 (see information on EXERCISE WEBSITE from week to week).

The teaching assistant will on this time be available for supervising exercises or answering other relevant questions.

Exercises with the aim to get a deeper insight into lectured material are given each week. These can be found on the EXERCISE WEBSITE. These exercises are voluntary but are a part of the curriculum. Solutions will be put on the exercise website.
Most of the exercises require the use of the statistical software MINITAB, see for instance NTNU has bought an unlimited site licence for Windows and Macintosh for installation of MINITAB on campus and private machines of students and faculty. MINITAB is also available on several of the data labs on campus.

One of the exercises is compulsory and will be more comprehensive. Here the students shall plan, perform, analyse and report a self selected experiment, or do another statistical analysis that needs to be approved by the lecturer of the course. This will count 20 % on the exam. A description of this exercise is given here
(English). Some examples of earlier experiments performed in the course are also given there. An older version of the description in Norwegian is also available. Some examples of experiments conducted in a similar course in USA are given here. Here are two complete examples of earlier obligatory projects at NTNU: One in English, one (old) in Norwegian. Note that you will be rewarded for the contents and not for the layout! Thus a handwritten report may be as good as a nicely printed one! Also: Pictures are of course nice to have, but not needed if you can explain things without them!



The obligatory exercise will start in Week 9 (March 1), and deadline for submitting the report is Thursday March 25 at 12 Noon. There will be no new exercises in Week 9 and 10 (March 1 and 8), instead you may consult the teaching assistant in the regular exercise hours these weeks. There will also be scheduled additional times for consulting with teaching assistant and lecturer.



Wednesday May 26, 2010 at 09:00. Written exam. Durance 4 hours.

Obligatory exercise counts 20% of the exam mark.
Permitted help: All printed or hand written material. Simple, specified calculator.


Earlier exams in TMA4255 and similar courses:


Exam Dec 2008 is found in Norwegian here and in English here. Solution is found here.

Exam August 2007 in English is here (no solution).

Exam May 2007 is found in Norwegian here and in English here. Solution is found here.
Exam May 2006 w/solution is
here (in Norwegian). Exercise in English is here.

Exam June 2005 w/solution is here (in Norwegian)
Exam August 2005 is
here, with solution here (all in Norwegian)
Exam December 2005 is
here with last pages of the solution here (all in Norwegian)

Exam August 2004 in English is here (no solution).
Some earlier exams w/solution are found on this old
homepage (all in Norwegian).


27.04  Last lecture: Exam exercises


22.04  Earlier exam exercises – today and 27.04: Will do the following exercises in the given order:


December 2008: 1 a b (c is not in syllabus of 2010)

May 2007: 1

May 2007: 2

December 2008: 2

December 2008: 4


20.04  Continue 16.2: Signed-Rank. Then 16.3, Wilcoxon Rank-Sum Test for two independent samples.


15.04 Chapter 16 (Nonparametric statistics). 16.1: Sign test. Started to look at 16.2: Signed-Rank Test (Wilcoxon one-sample test). Slides are found here  (part 2, pages 52-59). (Only 52-55 are relevant)


13.04 Contingency tables and tests for independence and homogeneity: Chapter 10.15-10.16. Simpson’s paradox. Same slides as for 08.04.


08.04 Started by going through main properties of the multinomial distribution (end of Chapter 5.3). Chi-square tests for multinomial data. Model testing: Chapter 10.14. Slides are found here  (part 2, pages 44-51).


30.03, 01.04, 06.04 NO LECTURES (Easter vacation)


25.03 Complete chapter 17. Note that 17.6 is not in the curriculum.


23.03 Did 13.13 (random effects models, but not the last part of 13.13 with two random effects). Then started chapter 17, Statistical process control – 17.1-17.4. Slides from chapter 17 are found here (part 2, pages 37-43).


18.03 Went through main topics from 14.1-14.3, mostly via slides.

A proof of Theorem 13.2 can be downloaded here.


16.03 Started with 13.6, then 13.8-13.10 (13.11-13-12 are not in curriculum, will take 13.13 later). Same slides as for 09.03.


11.03 Continued with chapter 13: 13.4 and 13.6 (13.5 and 13.7 are not in curriculum). Same slides as for 09.03.


09.03 One-way ANOVA: Chapter 13.1-13.3. Slides for chapters 13 and 14 are here: (part 2, pages 1-36).






25.02  Finish with fractional factorial designs


23.02  Fractional factorial designs. You may download book chapter. Slides: pages 135-145.


18.02  Will finish note on Factorial Experiments at two levels: Significance testing, blocking. Slides up to 134.


16.02  Continued DOE, in particular estimation of sigma. Centered around slides 110-113 and pages 7-12 in note.


11.02 Design of experiments (DOE): Download note: “Factorial Experiments at Two Levels”. Slides for the next lectures can be downloaded here (pages 92-145). Went through slides 92-107 (or to mid of page 7 in note). You may also download a Chapter on DOE from the MINITAB manual.


09.02  Rest of Chapter 12: Testing groups of variables, more on residuals and transformations, multicollinearity, polynomial regression. If time: Start treatment of Design of Experiments.


04.02  Completed most of Chapter 12. (Stepwise regression, best subsets regression, residual plots). Same slides as for 26.01.


02.02. Continue Multiple linear regression: 12.3 -12.6. Same slides as for 26.01.


28.01 Prediction (Ch. 11.6). Multiple linear regression (Chapter 12): Went through 12.1-12.2, started on 12.3.


26.01 Linear regression – Chapter 11.1-11.5 Slides can be downloaded here (pages 46-91).


21.01 Comparison of variances for two samples. Fisher-distribution. F-test and confidence interval for sigma1/sigma2. Slides as for 19.01.


19.01 One-sample and two-sample t-tests. Pooled variance estimator. Slides can be downloaded here (pages 34-45). Tables copied from the book for normal, t, chi-square and F distributions, are found here in pdf-format. (Will be used in lectures).


14.01 Descriptive measures and graphs (e.g. normal plot). One sample from normal distribution: sampling distributions, inference with known sigma. Use same slides as last time.


12.01 Introduction and repetition of probability theory and some very basic concepts of statistical models and statistical inference. Slides can be downloaded here (pages 1-33)


Here are some examples and notes that have been used in earlier years, most of them in Norwegian. The relevant parts are covered in the slides and notes that you find under “Progress” above.

Notat om faktorielle forsøk og blokkdeling
Bokkapitel om fraksjonelle forsøk

Notat om Variansstabiliserande transformasjonar

Approksimasjon av forventing og varians
Eksempel i ikkje parametrisk statistikk
Forsøksplanlegging med senterpunkt, CCD
Stivheit og tettleik til treprodukt
Eksempel på approksimasjon av forventing og varians  


Last updated: 26 May at 15:09