The aim of the project is to

• plan,
• perform,
• analyse and
• report

the results from a self selected experiment. This will make up 20 % of the grade in TMA4267.

Guidance: When? Report back to reference group you opinion.

Submission: To lecturer. The report can preferably delivered ON PAPER in her mailbox at the Department of Mathematical Sciences, 7th floor of Sentralbygg II (this will ensure your anonymity), or at the lectures. It is also possible to send the report by email (but that is not the preferred way).

Identification: The report should be identified by CANDIDATE NUMBER, not name - and not student number. Why? So this can easily be merged with your exam results (handed in with candiate number). The candidate number is a number generated for each exam, and is 10000 or higher.

Submission dates: Before Easter, on Friday April 11 at 12.00 at the latest.

Collaboration: You can work up to 2 in collaboration.

Report: You shall write a report (preferably in English) on the work that is done. The report should be simple, and the structure may follow the main points made in the 'Keywords'. The length should be 6-7 pages, and preferably not exceed 10 pages. Since the report will not be returned to you, it may be useful to take a copy of it for personal use. 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!

Scoring: The submitted report will be graded and will count 20% of the grade for the course. This means that you will be given a mark in the interval 0-20. Note that both the obligatory exercise and exam needs to be passed in order to achieve the Passing grade of the subject, so you need at least a project score of 0.4*20=8.

The theme for the exercise is design of experiments (DOE). The purpose is to provide insight and training in planning, performing and analyzing a statistical experiment, as well as to report the results.

Carry out a k-factor two-level experiment where the goal is to determine how the various factors influence a response. You should yourself decide what kind of experiment to perform. This may be a laboratory experiment, or be from a problem in your daily life.

Alternatively, you may do a different statistical analysis, using multiple linear regression or another suitable method, using your own data. In this case you should present a brief sketch to the course teacher before the project starts.

IMPORTANT: you are strongly encouraged to collect at least 16 observations, for example in a full design with 4 factors or do two repetitions of 3 factors. Why? With as few as 8 observations we will seldom see significant effects, and that would make it difficult for you to write about in the report.

Keywords

1. Issues to be addressed:
   • Describe the problem you want to study.
   • Why is this interesting?
   • What prior knowledge do you have?
   • What do you want to achieve?
2. Selection of factors and levels:
   • Which factors do you think are relevant to the problem described above?
   • Do you expect an interaction between some of the factors?
   • Which levels should be used, and why do you think these are reasonable?
   • How can you control that the factors really are at the desired level?
3. Selection of response variable:
   • Which response variable will provide information about the problem described above?
   • Are there several response variables of interest?
   • How should the response be measured?
   • What can you say about the accuracy of these measurements?
4. Choice of design:
   • 2 k factorial,
   • 2 k-p fractional factorial or other design?
   • Desired resolution of the design?
   • Is it necessary or desirable to use a blocked design?
   • Is it necessary or desirable with replicates?
5. Implementation of the experiment:
   • Randomization.
   • Describe any problems with the implementation (maybe the randomization was not followed?)
6. Analysis of data
   • Calculation of effects and assessment of statistical significance.
   • Check the assumptions. Important: residual plots!
7. Conclusion and recommendations:
   • Which conclusions can you draw from the experiment?
   • Interpretation of significant effects, main and interaction plots.
   • Remember that plots are illustrative and very useful for demonstrations.

I have made available an R script for a DOE experiment "Running on a treadmill". Reponse is pulse, factors are A=backpack (no, yes), B=time (30s or 2 min), C=slope (0 or 5%), D=speed (10 or 16). This is a full two level experiment with 4 factors.

List of the project done in 2011: here and list for some of the projects in 2012: here from the TMA4255 course. You may of cause perform the same experiment as listed here!

Below are given some examples of problems that have been examined by former students:

• Baking of pie: Importance of the type of flour, type of berries and appearance (with or without cover), regarding taste, consistency and experience - rated by a taste panel

• Treatment of welding to avoid fatigue: The importance of voltage, frequency and hammering on the life of a welding

• Corona-based electric field probe: Importance of air flow across and through a probe that measures the electrical field, with application in warning systems for lightning in helicopters.

• Sound level for fireworks: Importance of quantity and fill volume of gunpowder, different mix ratio of gunpowder and wall thickness of the rockets, regarding sound level (dB)

• Maximum performance in weight-lifting: Importance of kreatin-intake, physical exhaustion, position and grip on the number of lifts.

• Yield of pyridin: Importance of pH,% methanol, the number of equivalents NaHSO 3 and t temperature on the yield of pyridin

• Optimizing the use of heat pump in propane-propene distillation: Importance of pressure in the column, reflux ratio and temperature change over the vessel on energy costs

• Perfect 'popping' of popcorn: Importance of the type of popcorn, the type and amount of oil in comparison to the amount of popcorn.

• Reaction speed in an S N 2-reaction between 1-brompropan and NaOH: Importance of reaction temperature, amount of solvent and start concentration of reactant on the reaction speed

• Purification of waste water: Meaning of focculation time, focculation intensity and sedimentation time for the remaining concentration of small particles in the cleaned water

• Basket ball shots: Importance of distance, type of defense and shot position on the number of points scored in basketball

• Study of line widths in photoresist: Importance of exposure, development and baking on the line width

• Development of fish food for use in conditioning of fish: Significance of the amount of alginat, the concentration of calcium chloride, stirring time after adding alginat and curing temperature on the consistency of fish

• Economic aspects of burning candles: Importance of price, style and color of the burning time

More examples from US course (pdf).