1. Problem 18.6 : Refer to the Rehabilitation therapy problem 16.9.

(a) Obtain the residuals and prepare aligned residual dot plots by factor level. What departures from ANOVA model (16.2) can be studied from these plots? What are your findings?

(b) (* = changed slightly from the textbook) Prepare a normal probability plot of the residuals. Does the normality assumption appear to be reasonable here ?

(c) The observations within each factor level are in time order. Prepare residual sequence plots and analyze them. What are your findings ?

(d*) (* = changed slightly from the textbook) Obtain the studentized residuals and prepare aligned residual dot plots by factor levels.

2. Problem 18.12 : Refer to the Rehabilitation therapy problem 16.9. Examine by means of the Brown-Forsythe test whether or not the treatment error variances are equal. Use α = 0.10. State the alternatives, decision rule and conclusion. What is the P-value of the test ?

3. Problem 18.15 : Helicopter service. An operations analyst in a sheriff's department studied how frequently their emergency helicopter was used during the past year, by time of day (shift 1: 2 AM - 8 AM; shift 2: 8 AM - 2 PM; shift 3: 2 PM to 8 PM; shift 4: 8 PM - 2 AM). Random samples of size 20 for each shift were obtained.

Since the data are counts, the analyst was concerned about the normality and equal variance assumptions of ANOVA model (16.2).

(a) Obtain the fitted values and residuals for ANOVA model (16.2).

(b) Prepare suitable residual plots to study whether or not the error variances are equal for the four shifts. What are your findings ?

(c) Test by means of Brown-Forsythe test whether or not the treatment error variances are equal. Use α = 0.10. What is the (approximate) P-value of the test ? Are your results consistent with your diagnosis in part (b)?

(d) For each shift, calculate Y i· and si. Examine the three relations found in the table on page 791 and determine the transformation that is most appropriate here. What do you conclude ?

(e) Use the Box-Cox procedure to find an appropriate power transformation of Y , first adding the constant 1 to each Y observation. Evaluate SSE for the values of λ given in Table 18.6. Does λ = 0.5, a square-root transformation, appear to be reasonable, based on the Box-Cox procedure?

(f*) (additional question) Test by means of Hartley test whether or not the treatment error variances are equal. Use α = 0.05.