Question

Four different designs for a digital computer circuit are being studied in order to compare the amount of noise present. Determine whether the amount of noise present is the same for all four design based on the following data.
Circuits		Noise Observed
1	19	20	19	21	24
2	40	41	43	46	40
3	28	26	25	31	20
4	79	68	77	78	67

ANOVA

1. What type of experimental design is employed in this problem?

2. Identify the treatments and the dependent variable (Response).

3. Use a multiple boxplot in order to compare responses between different levels.

a.

Are there differences between the mean of the responses in at least two of the levels?

b. Do you think this is the result of within-group variation or between-group variation?

4. State clearly the hypothesis that we are testing in this problem.

a.

Set up the null and alternative.

5. Run ANOVA on the data and generate the output with plots.

a.

Comment on the degree of freedom values for each source of variation. How do you

calculate them?

b. Do we reject the hypothesis that we are testing? Why or why not?

i. If you reject, can you tell which level(s) is probably the one(s) that has the

different mean? (Hint: use the boxplots from part 1a)

ii. If you are suspicious of only one level, repeat the ANOVA without that level and

see if you fail to reject the null in the test.

c.

Use the histogram of residuals to comment on the normality of error term (residuals) in

this ANOVA model.

Answer 1

1.

This is a completely randomized design. The effects of the factor (circuit design) are fixed since they were specified by the experimenter rather than being selected at random.

The statistical model we would use to analyze this data is a one-factor fixed effect model described by the equation:

Yij = μ +τ i + ε ij , i = 1,2,3,4 , j = 1,...,5

Where μ is the overall mean yield i

τ is the effect of the i th circuit design

εij is the random or experimental error

Please raise separate request for other parts.