Problem 1- In a two-factor study, the treatment means µ_ij are as follows:

a. Obtain the factor B main effects. What do your results imply about factor B?

b. Prepare a treatment means plot and determine whether the two factors interact. How can you tell that interactions are present? Are the interactions important or unimportant?

c. Make a logarithmic transformation of the µ_ij and plot the transformed values to explore whether this transformation is helpful in reducing the interactions. What are your findings?

Problem 2- Refer to Problem 1. Assume that σ = 4 and n = 6.

1. Obtain  E{MS E} and E{MS AB}.

2. Is  E{MS AB} substantially larger than E{MS E}? What is the implication of this?

Problem 3-  Eye contact effect. In a study of the effect of applicant's eye contact (factor A) and personnel officer's gender (factor B) on the personnel officer's assessment of likely job success of applicant, 10 male and 10 female personnel officers were shown a front view photograph of an applicant's face and were asked to give the person in the photograph a success rating on a scale of 0 (total failure) to 20 (outstanding success). Half of the officers in each gender group were chosen at random to receive a version of the photograph in which the applicant made eye contact with the camera lens. The other half received a version in which there was no eye contact.

a. Obtain the fitted values for ANOVA model.

b. Obtain the residuals. Do they sum to zero for each treatment?

c. Prepare aligned residual dot plots for the treatments. What departures from ANOVA model can be studied from these plots? What are your findings?

d. Prepare a normal Q-Q plot of the residuals. Does the normality assumption appear to be reasonable here?

e. The observations for each treatment were obtained in the order shown. Prepare residual sequence plots and interpret them. What are your findings?

Problem 4- Refer to Eye contact effect Problem 3. Assume that ANOVA model is applicable.

a. Prepare an estimated treatment means plot. Does it appear that any factor effects are present? Explain.

b. Set up the analysis of variance table. Does anyone source account for most of the total variability in the success ratings in the study? Explain.

c. Test whether or not interaction effects are present; use α = .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

d. Test whether or not eye contact and gender main e ffects are present. In each case, use α = .01 and state the alternatives, decision rule, and conclusion. What is the P-value of each test?

e. Do the results in parts (c) and (d) confirm your graphic analysis in part (a)?