Exercise 8.6.1 A study was performed to examine the effect of two factors on increasing muscle mass in weight lifters. The first factor was dietary protein level.

The levels were use of a relatively low protein diet (L) and use of a high protein diet

(H). The second factor was the use of anabolic steroids. The first level consisted of no steroid use (N) and the second level involved the use of steroids (S). Subjectswere chosen so that one subject was in each combination of four height groups (i ) and four weight groups ( j ). Treatments are identified as LN, LS, HN, and HS. The dependent variable is a measure of increase in muscle mass during the treatment period. The study was replicated in two different years. The height groups and weight groups changed from the first year to the second year. The design and data are listed below.

Heights are the columns of the squares and weights are the rows. Analyze the data.

Year 1 Weight Trt(yi jk) 1 2 3 4 1 LN(2.7) LS(4.6) HS(9.3) HN(0.0)

Height 2 LS(2.0) LN(5.0) HN(9.1) HS(4.5)

3 HN(6.4) HS(10.2) LS(6.1) LN(2.9)

4 HS(8.3) HN(6.3) LN(6.3) LS(0.9)

Year 2 Weight Trt(yi jk) 1 2 3 4 1 LN(8.6) LS(3.3) HN(7.6) HS(9.0)

Height 2 LS(8.9) HN(4.7) HS(12.2) LN(5.2)

3 HN(10.0) HS(7.6) LN(12.3) LS(5.4)

4 HS(10.0) LN(0.5) LS(5.0) HN(3.7)