Kutner et al. (2005) discussed an example in which human growth hormone was administered at a clinical research center to short prepubescent children. The investigator was studying the effects of gender and bone development levels on the rate of growth induced by hormone administration. Three children were randomly selected from each gender-bone development group, but 4 of the 18 children dropped out of the yearlong study. The data are as follows:

Bone development Gender Severely Moderately Mildly depressed depressed depressed Male 1.3 Use a SAS program with a proc glm step to this program to perform the computations described below. Use the usual two-way classification model for this analysis.

a. Use proc means to obtain estimates of the cell means μij . Construct a two-way table of gender by bone development levels showing the growth rate cell means.

b. Obtain an interaction plot using proc gplot of the growth rate cell means with bone development levels on the x -axis. Join the points for each gender by line segments. Use colors and line types to identify gender.

c. Obtain the least squares estimates of μ, αi, βj , and γij for i = 1, 2 and j = 1, 2, 3 computed by proc glm.

d. Construct an analysis of variance table to test main effects and interaction for these data. Use the values output from proc glm and write your own complete ANOVA table. Using the p-values with α = 0.05, make conclusions from each test.

e. Use lsmeans statements to obtain 90% confidence intervals on pairwise differences in bone development means adjusted for multiple testing using the Tukey method. What do you conclude from these intervals?

f. Kutner et al. (2005) tested the hypothesis whether the average growth rate of children with only mildly depressed bone development is significantly larger than zero. Add an estimate statement to obtain a t-statistic to test this one-sided hypothesis.

g. Test the hypothesis that the growth rates of children with severely depressed bone development are different in males and females using an appropriate contrast statement.