Exercise 6

 

 

 

1.The following experiment was designed to find out to what extent a particular type of fabric gave homogeneous results over its surface for a standard wear test. In a single run the test machine could accommodate four samples of fabric, at positions 1, 2, 3, and 4. On a large sheet of the fabric four areas A, B, C, and D were marked out at random at different places over the surface. From each area 4 samples were taken, and the 16 samples thus obtained were compared in the machine with the followihg results, diven in milligrams of wear:

 

 

run

   

I

II

III

IV
 

1

A 26.1

D 20.0

C 32.4

B 20.7

position

2

B 22.3

A 26.9

D 21.5

C 35.0
 

3

C 29.0

B 22.4

A 26.3

D 22.8
 

4

D 30.6

C 28.8

B 25.2

A 26.4

 

 

What type of design is this? Analyze the data, stating carefully your assumptions.

 

 

2.Samples of four different metals were subjected to corrosive solutions, and their corrosion rates were measured. The experimenter calculated the following analysis of variance table for the data:

 

Source of variation

Sum of squares

Degrees of freedom

Mean square

Ratio

Average

213,363.33

1

    

Between treatments

77.58

3

25.86

  

Within treatments

59.09

26

2.27

11.38

Total

213,500.00

30

    

 

 

  1. How should this experiment have been conducted to allow valid inferences to be made from this analysis?

  2. The treatment averages are as follows:

 

 

 

 

 

 

 

Metal

Average

Number of samples

 

A

YbarA = 86.143

 

7

 

B

YbarB = 85.750

 

8

 

C

YbarC = 82.625

 

8

 

D

YbarD = 82.857

 

7

 

 

Make an appropriate reference distribution diagram.

 

(c) Metals A and B are of one alloy, and C and D of another. This statistic is calculated:

 

0.5 (YbarA + YbarB ) – 0.5 (YbarC + YbarD )

 

What inferences can you draw about the corresponding parameter? What can you conclude about the performance of the two alloys?

 

 

3. (a) Develop a design suitable for evaluating three different instruments ( I, II, III ) for obtaining bacteria counts on three different types of floor tile (A, B, C ). A reasonable trial is 1 day for setting up three test tiles, coating them with a standard solution, and obtaining the three bacteria counts.

  1. Set out a detailed schedule of how the experiment is to be conducted.

  2. Illustrate with constructed data precisely how the analysis is to be conducted.

  3. List in detail all the assumptions you make and questions you would need to ask.

 

4. (a) Write a 6x6 Latin square design.

(b) What is the usual model employed in the analysis of data from such a design? State all assumptions.

(c) Describe a situation in which this design could be used.

(d) In what way(s) might the model and assumptions listed in (b) be violated in this situation?