Final Exam In-class Part:
Name:___________________________________
ID:______________________________________
I.
Write TRUE or FALSE for the following with your reasoning. (30 points, 3 points each)
1. RCBD are always more efficient than the corresponding CRD.
2. We test for block effect for a RCBD and find that it is not significant. We put the block effect in
the error (in our model) and then it is correct to call our design CRD.
3. Since Latin Square allows for incorporation of two blocking effects it is a design more commonly
used than the RCBD.
4. The three basic designs CRD, RCBD and Latin Square all use the three basic tenets of design:
randomization, replication and local control.
5. We are interested in 3 different brands of cake mixes and we will bake each cake mix at three
randomly selected temperatures (between 300 and 400). Since we are NOT interested in the
temperature values per se, its correct to call the temperature a “blocking factor”.
6. We have three brands of dog food and for each feed we have a three measures (lo= ½ cup,
med= ¾ cup, hi=1 cup). We are interested in the gain in the BMI of the dogs. Here the factor
“measure” is nested within the brand.
7. Since the randomization is more constrained in repeated measures design, one can never
analyze repeated measures as a split plot design.
8. A completely Randomized design using a two-way structure cannot be analyzed if the number of
observations per treatment combination is not the same.
9. We run an experiment using a CRD with three treatments (4 replicates each within the
treatments) and the ANOVA table shows that SSE=0. This indicates that all the treatments have
equal means.
10. If we fail to reject the null hypothesis for a specific test. Then we have proved that the null
hypothesis is true.
II. Short Answers: (25 points, 5 points each)
1. Explain why we test the H0: a=0 vs Ha: a>0 when A is a random effect.
2. Write out the model for a Split Plot Design and explain the terms in the model.
3. You suspect interaction between the factors A and B. You construct the interaction plot and
get the following plot. The test for interaction has a p-value of .224. How do you explain
this?
Interaction Plot for Response Y for Trt A and B
Fitted Means
250.5
Trt B
1
2
3
250.0
Mean
249.5
249.0
248.5
248.0
247.5
247.0
1
2
Trt A
4. You are given the following plot. Comment about the plot and the diagnostic it is used for.
Normal Probability plot of the residuals
99.9
99
95
Percent
90
80
70
60
50
40
30
20
10
5
1
0.1
-40
-30
-20
-10
0
10
20
30
C2
5. Complete the following ANOVA table and discuss the design it represents:
Source
df
SS
A
1
743.8
Block
2
198.4
A*Block
2
60.6
B
5
8551.1
A*B
124.7
Error
20
Total
35
10790.1
MS
F