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QUEEN MARY, UNIVERSITY OF LONDON

MTH6116 Design of Experiments

Coursework for handing in 20 March 2012

This coursework should be submitted at the latest by Wednesday 28th March2012 at 12.00. You will hand in a maximum of one page per question. Itcounts for 10% of your overall marks, and all the questions are weighted equally.Make sure you have written your name and student number on your work.

1 Write a report summarizing your answer to Question 1 of Practical week 10(12th March 2012). Computations are to be performed by hand; also build andexplain Hasse diagrams for plots and for treatments and joint Hasse diagram forplots and treatments.

2 Write a brief summary of what you would answer to Problem 8.3 in RosemaryBaileys book (problem is shown below).

8.3 A cattle breeder wants to find a way of protecting his cattle

against a particular stomach disease. He wants to compare the effects

of

S: spraying the grass in the paddock with a special chemical

N: no spray.

He also wants to compare the effects of

+: injecting each animal with a special vaccine

-: no injection.

He has several paddocks. Each paddock contains 20 animals, labelled 1,...,20

with ear-tags. He wants to apply the treatments once. A month later he will

assess the amount of stomach disease in each animal by counting the number

of a certain type of bacterium in a sample from the stomach contents. The

logarithm of this number will be analysed. He wants to use two paddocks tofind out the effect of the spray, using S on one paddock and N on the other.

He wants to use another two paddocks to find out the effect of the injection,

using + on one paddock and - on the other. He asks you:

Since N and - are both no treatment, can I just use three paddocks, one for

S, one for + and one for no treatment?

How do you answer?

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3 Consider the rye grass experiment which was presented and described duringthe Module lectures (see also description in Chapter 1 of Rosemary Baileysbook).

The file RYEGRASS.DAT (in the module page) has the data corresponding tothe experiment. The first column in the data set gives the variety (coded as1-Cropper, 2-Melba, 3-Melle), while the second column contains the amountsof fertilizer (coded as 1-0 t/ha, 2-80 t/ha, 3-160 t/ha, 4-240 t/ha). The thirdcolumn gives the percentage of dry matter in the harvested grass. The first 12values in the data set are from the first field, while the remaining are from thesecond field. Within each field, varieties are applied to whole strips.

Write your summary of the following analysis.

(a) Build and interpret Hasse diagrams for plots and for treatments and jointHasse diagram for plots and treatments.

(b) Assuming the classic split-plot design structure, analyze the design. Note

that your computations have to be performed by hand.

4 Hand in your solution for Question 3 ofAssignment 5 (17th February 2012).

5 Write a brief report summarizing your answers to Question 1 parts a), b),c), d) and e) of Practical week 8 (27th February 2012). As part of your solution,build and explain Hasse diagrams for plots and for treatments and Hasse diagramfor plots and treatments.

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