Split plot worksheet
The data present below was originally analyzed by Yates (1935). The experiment was conducted to
assess the effects on yield of three oat varieties (Golden Rain, Marvellous and Victory) with four levels of
nitrogen application (0, 0.2, 0.4 and 0.6 cwt/acre). The field layout consisted of six blocks. The three
varieties were randomly allocated to the three whole-plots while the four levels of nitrogen application
were randomly assigned to the four sub-plots within each whole-plot.
Block
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
Variety
GR
GR
GR
GR
M
M
M
M
V
V
V
V
GR
GR
GR
GR
M
M
M
M
V
V
V
V
GR
GR
GR
GR
M
M
M
M
V
V
V
V
GR
GR
Nitro
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
yield
111
130
157
174
117
114
161
141
105
140
118
156
61
91
97
100
70
108
126
149
96
124
121
144
68
64
112
86
60
102
89
96
89
129
132
124
74
89
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
GR
GR
M
M
M
M
V
V
V
V
GR
GR
GR
GR
M
M
M
M
V
V
V
V
GR
GR
GR
GR
M
M
M
M
V
V
V
V
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0
0.2
0.4
0.6
81
122
64
103
132
133
70
89
104
117
62
90
100
116
80
82
94
126
63
70
109
99
53
74
118
113
89
82
86
104
97
99
119
121
a. Write the split plot model (assume Variety and Nitrogen are fixed effects).
b. Fit the model in part a, and perform appropriate hypotheses.
c. Assume Nitrogen is a random effect and rewrite the model and redo the analysis (perform
appropriate hypothesis test, use the default method, REML). Give the estimates of covariance.
2.
There are three bacterial inoculation treatments applied to two cultivars of grasses (A and B)
and the dry weight yield is recorded as the response. The factor CULT (cultivar) is applied to the
main plot and the factor INOC (inoculation) is applied randomly to the subplots. The levels of
INOC are CON for control, LIV for live and DEA for dead. The data is shown below.
Block
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
CULT
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
B
B
B
INOC
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
CON
DEA
LIV
DRYWT
27.4
29.7
34.5
29.4
32.5
34.4
28.9
28.7
33.4
28.7
32.4
36.4
28.6
29.7
32.9
27.2
29.1
32.6
26.7
28.9
31.8
26.8
28.6
30.7
d. Write the split plot model (assume INOC and CULT are fixed effects).
e. Fit the model in part a, and perform appropriate hypotheses.
f. Assume CULT is a random effect and rewrite the model and redo the analysis (perform
appropriate hypothesis test, use the default method, REML). Give the estimates of covariance.