Statistics 106
Homework 5 Solutions
Due : Nov. 7, 2016, In Class
19.5
In a two-factor study, the treatment means
μ
i j
are as follows:
Factor
B
Factor
A
B
1
B
2
B
3
B
4
A
1
250
265
268
269
A
2
288
273
270
269
a. Obtain the factor
B
main e
ff
ects. 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
i j
and plot the transformed values to explore whether this
transformation is helpful in reducing the interactions. What are your findings?
Solution:

b. The treatment means plot is shown below:
1

c. The transformed treatment means plot is shown below:
2

19.8
Refer to Problem 19.5. 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?
Solution:

3

b.
E
{
MS AB
}
is substantially larger than
E
{
MS E
}
. This implies it is very likely that the interaction
e
ff
ects are present.
19.12
Eye contact e
ff
ect.
In a study of the e
ff
ect of applicant’s eye contact (factor
A
) and personnel o
ffi
cer’s
gender (factor
B
) on the personnel o
ffi
cer’s assessment of likely job success of applicant, 10 male and
10 female personnel o
ffi
cers 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 o
ffi
cers 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. The success ratings are saved in ”CH19PR12.txt”.
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