Explain how you would perform ANOVA on a single replicate 26-2 design.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1.

a)

Explain how you would perform ANOVA on a single replicate 26-2 design.

5 marks

b)

Explain the difference between a fixed effects and random effects model.

6 marks

c)

Explain why Blocking is used in experimental design. Give an example.

5 marks

d) Consider a 27 fractional factorial design with the generators D = ABC, E = AC,

F=BC and G=AB.

i) Write out the sign table (design matrix) for the factors A, B, C, D, E, F ii) Write out the complete defining relation for this design.

and G.

4 marks

6 marks

iii) What two Interactions are confounded with the main effect of Factor D? What Factor including two factor Interactions are confounded with the Interaction BG?

2.

iv) Identify the resolution of this design. Explain your answer.

6 marks

2 marks

a) An experiment was conducted to determine whether the type of plastic has any effect on the bursting strength. Four types of plastic were chosen. The experimenter was unable to obtain equal numbers of each type of plastic but decided to conduct the experiment nonetheless. The data presented is the bursting load.

A

B

23

19

25

20

24

18

21

22

11

TITT

Plastic Type C

D

22

13

21

12

23

13

20

14

i)

Use one-way ANOVA to test for significant differences between the plastic types at the 1% level. Explain the meaning of your answer.

10 marks

ii) Is one compound significantly worse than the rest? Choose a significance level at which to evaluate. Explain your answer.

11 marks

b). The accompanying data results from an experiment on bacterial growth.

No. of Days growth (x)

2

2.5

Bacteria growth (y)

15

22

34 40 100

6

1100

i) By using the transformation y=ae, show how linear regression techniques can applied to the above data.

4 marks

ii) Determine the parameters of a suitable regression model and use this to predict the bacteria growth after 5 days.

8 marks

 

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