Name:____________________________________________ ID:_________________________________
Stat 512 Exam 1:
Total points 100
A. State True or False with Reasons for the following: (30 points)
1. If we have a sufficient number of replicates (say 100 per treatment) it is not required to
randomize the units to the treatments.
2. The smaller the p-value, the greater your belief in the null hypothesis.
3. Any symmetric distribution can be assumed to be normal.
4. CRD are always better than RCBD.
5. We are interested in the polluting effects of a factory on a river. A random sample of 5 units is
taken from the river water 2 miles upstream and a random sample of 5 units are taken from a
site 2 miles downstream after the factory. The means are compared for upstream and
downstream. This is an example of paired samples and warrants the use of paired t test.
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Name:____________________________________________ ID:_________________________________
6. We are interested in one way ANOVA. We have three treatments and 6 replicates for each
treatment. Our degrees of freedom for error are 10.
7. We have a factorial design with two factors, A and B, one fixed and one random. The interaction
effect is fixed in for the effect AB.
8. You are testing for normality and your p-value for the test for normality is .005. This indicates
the normality assumption is correct.
9. For pairwise comparisons with equal sample sizes for the treatments, its best to use Fisher’s
LSD.
10. You are checking for assumptions and find that the equal variance assumption is violated, but
normality seems valid. Since normality is the most crucial assumption, this means your ANOVA
F test is valid.
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Name:____________________________________________ ID:_________________________________
B. Short Answers: (30 points)
1. The main assumptions for ANOVA are:
2. What is the relationship between Normal, Chi-square and F distributions?
3. Complete the following ANOVA table for a one-way ANOVA:
Source
df
SS
MS
Treatment
F
4
Error
400
Total
14
800
4. You run a diagnostic and get the following plots. Comment on the plots and your conclusions
from these.
Normal Probability Plot
Versus Fits
(response is resp)
(response is resp)
99
40
95
30
90
20
70
60
50
40
30
Residual
Percent
80
0
20
10
-10
5
-20
1
-30
3
10
-20
-10
0
10
Residual
20
30
40
10
15
20
25
Fitted Value
30
35
40
Name:____________________________________________ ID:_________________________________
5. Write down the model for 2-way ANOVA mixed model (CRD) with interactions and the relevant
hypothesis for the model.
6. Comment on the following plot:
Interaction Plot for resp
Fitted Means
40
35
Mean
30
25
20
15
10
20
40
factor2
60
C. ANSWER THESE FROM THE PROBLEMS YOU HAVE ALREADY COMPLETED:
17.18 (3+5+4)
a. Model:
b. Write down the ANOVA table and mark the ones that are significant.
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Name:____________________________________________ ID:_________________________________
c. Comment on the assumptions using diagnostics.
17.27 (5+5+4)
a. Model:
b. ANOVA table
c. Your conclusions:
5
Name:____________________________________________ ID:_________________________________
17.29 (5+5+4)
a. Model
b. ANOVA Table
c. Conclusions using the Data from 17.30
6