An unbalanced two-way ANOVA was conducted to compare ethics scores on an exam (Y) among

members of the U.S. Coast Guard. The factors were Gender (X1=1 if Male, -1 if Female) and Rank (X2=1

if Officers, -1 if Enlisted). The sample sizes were: M/O = 72, M/E = 180, F/O = 15, F/E =32. Four

regressions models were fit:

^

0 1 1 2 2 3 1 2 1 1 1 2 1 2

^

0 1 1 2 2 2 2 1 2

0 2 2 3 1 2

Model 1: 42088 36.35 2.40 3.85 0.50

Model 2: 42122 36.23 2.21 3.52

Model 3:

ijk ijk ijk ijk ijk

ijk ijk ijk

ijk ijk ijk ijk

E Y X X X X SSE Y X X X X

E Y X X SSE Y X X

E Y X X X

^

3 3 2 1 2 SSE 42873 Y 34.75 3.30X 0.39X X

a. Test whether there is an interaction between Gender and Rank. H0: ____________ HA:

___________

Test Statistic _______________________

Rejection Region _______________________

P-value > 0.05 or < 0.05

b. Test whether there is main effect for Gender. H0: ____________ HA: ___________

Test Statistic _______________________

Rejection Region _______________________

P-value > 0.05 or < 0.05

c. Based on Model 2, give the predicted scores for all combinations of Gender and Rank.

Gender\Rank Officer Enlisted

Male

Female

5. A published report, based on a balanced 1-Way ANOVA reports means (SDs) for the three treatments as: Trt 1: 70 (8) Trt 2: 75 (6) Trt 3: 80 (10)

Tragically, the authors fail to give the treatment sample sizes.

a. The Treatment degrees of freedom is the same for each sample size. The error degrees of freedom are:

dfTRTS = __________ ri = 2: dfERR = __________ ri = 6: dfERR = ___________ ri = 10: dfERR = __-_________

b. Complete the following table, given arbitrary levels of the number of replicates per treatment:

R

SSTrt

SSErr

MSTrt

MSErr

F_obs

F(0.05)

2

6

10

c. The smallest ri, so that these means are significantly different is:

i) ri <= 2 ii) 2 < ri <= 6 iii) 6 < ri <= 10 iv) ri > 10