ST 524
NCSU - Fall 2008
Homework 1
Due: September 11, 2008
1. Description
A plant scientist measured the concentration of a particular virus in plant sap
using ELISA (enzyme-linked immunosorbent assay) (Novy 1992). The study
included 13 potato clones:: 2 commercial cultivars, 5 somatic hybrids, 5 progeny
of the somatic hybrids, and one clone of Solanum etuberosum (a species related to
potato). Of the 5 progeny of the somatic hybrids, two were classified as
susceptible and three as resistant to the virus. The scientist wants to understand
the resistance to the virus among these 13 clones. Plant sap was taken from 5
inoculated plants of each clone, for a total of 65 measurements of titer. One
measurement was lost during processing of the samples.
Reference : Yandell (2001)
Data
clone reps titer code type
1
1 1302
a susc
1
2 1717
a susc
1
3 1321
a susc
1
4 1358
a susc
1
5 1093
a susc
2
1
32
b etb
2
2
12
b etb
2
3
25
b etb
2
4
61
b etb
2
5
93
b etb
3
2 1846
c cult
3
3 1745
c cult
3
4 1814
c cult
3
5 1752
c cult
4
1
197
d res
4
2
380
d res
4
3
280
d res
4
4
112
d res
4
5
355
d res
5
1
529
e par
5
2
396
e par
5
3
629
e par
5
4
261
e par
5
5
325
e par
6
1
931
f par
6
2
791
f par
6
3
57
f par
6
4
706
f par
6
5
742
f par
7
1 1361
g cult
7
2
363
g cult
7
3
418
g cult
7
4
579
g cult
7
5 1660
g cult
clone reps titer code type
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
12
12
13
13
13
13
13
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
361
113
338
283
301
594
173
526
58
88
644
680
663
780
965
549
603
229
398
252
1185
1105
1196
949
906
214
351
564
98
417
h
h
h
h
h
i
i
i
i
i
j
j
j
j
j
k
k
k
k
k
l
l
l
l
l
m
m
m
m
m
res
res
res
res
res
par
par
par
par
par
odd
odd
odd
odd
odd
par
par
par
par
par
susc
susc
susc
susc
susc
res
res
res
res
res
Objective: Checking assumptions. Decide whether a common residual variance is a
good fit in model.
1) Write statistical linear model.
2) Run an analysis of variance in Proc GLM. Analysis of Variance Table.
3) Graph standardized residuals (StudentResid) vs predicted (mean value) for
each clone. Summarize findings.
Friday September 5, 2008
1
ST 524
NCSU - Fall 2008
4) Run homogeneity of variance test. Use Brown-Forsythe’s and Bartlett tests.
Indicate hypothesis and conclusions. Use = 0.05.
5) Study the need to fit separate variances for each type level.
6) Select the best model to be fitted.
a. Test whether a model with a common residual variance is preferred to a
model with separate variances. Use a likelihood ratio test, and  = 0.05.
b. Check residual plot and normality test for standardized residuals in selected
model.
c. Write down the final model. Test of hypothesis. Conclusions. Use = 0.05.
7) Explain any limitations to the final selected model.
2. A study will be carried out in the greenhouse on the effects of 2 methods of obtaining
cuttings (M1, M2) on the growth of 5 cultivars of an ornamental shrub (V1, V2, V3, V4,
V5). Identify uniquely each method by cultivar combination from T1 through T10. Use
PROC PLAN to obtain:
1) a randomization plan for an CRD with 4 pots per cutting method and cultivar
combination, with three cuttings per plot. These pots for 10 methods by cultivar
treatment combinations will be randomly distributed along four selected benches in
the greenhouse. Sketch a plan for the layout in the greenhouse indicating the position
of each treatment combination. Assume each bench will contain a single row of 10
pots.
2) a randomization plan for an RCBD with 4 blocks corresponding to 4 benches in the
greenhouse, and all 10 methods by cultivar treatment combinations represented once
in each block. Sketch a plan for the layout in the greenhouse indicating the position of
each treatment combination in each block. Assume each block will contain a single
row of 'plots'.
Friday September 5, 2008
2