BIOM 602
SPLIT PLOT DESIGN AND ANALYSIS
In some experiments, we randomize levels of two or more factors on multiple "levels" of experimental units.
For two factors, experimental units are commonly referred to as the whole units and sub units (in field trials,
whole plots and sub plots). The sub units are within the whole units, and thus, are smaller than the whole units.
Each levels of experimental units is expected to have a different variance, larger units (whole units) generally
having greater variance than smaller units (sub units). Different sizes of units require that different experimental
errors be estimated. The treatment structure for a split plot is a factorial because at least one factor is assigned to
the whole units (whole plots) and one (or more) factor is assigned to the sub units (sub-plots). The sub unit
design is always like a block design, while the whole unit design may be any of the designs that we have studied
(e.g., CR, RCB, LS, etc.). The complete design name for split plot includes the identification of the whole plot
design. For example, if the whole plot treatment factor is assigned as an RCB, then the design would be called a
Randomized Complete Block Split-Plot Design.
MIXED syntax for Split Plot Analysis:
PROC MIXED ratio covtest;
CLASS <classification variables>;
MODEL <dep var> = <fixed sources>;
Specifies the fixed sources of variation. In
most cases this will be the sources of variation
representing the factorial treatment structure.
RANDOM <random sources>;
Specifies the random sources of variation. In
most cases this will be any blocking factors,
plus the whole and sub unit error terms. It is
the correct identification of the whole and sub
unit error terms that make the analysis a split
plot.
LSMEANS <fixed sources>/pdiff;
ESTIMATE . . .
CONTRAST . . .
The MIXED procedure uses the expected
mean squares to compute the correct standard
error of the difference for any of the mean
comparison procedures, ESTIMATE, and
CONTRAST statements.
ODS . . .
3/26/02
1
Split-plot
The SAS program and Output for a CRD Split-plot Example:
OPTIONS LS=75 PS=500 NOCENTER NODATE PAGENO=1;
TITLE1 ANALYZING CRD SPLIT-PLOT DESIGNS;
TITLE2 Whole Plot Treatments Are 6 Combinations of 3 Ozone & 2
RainpH Levels Assigned as A CRD;
TITLE3 The sub-plot Treatments are 3 Genotypes;
DATA A;
INPUT O3$ RAINPH$ REP GENOTYPE LEAFAGE AN;
DATALINES;
Data lines entered here
RUN;
The data are from a research on the effects of simulated ozone and
acid rain on net photosynthesis (An) of one-year-old needles in
seedlings of 3 ponderosa pine genotypes. Air pollution treatments
consisted of a factorial combination of 3 ozone (filtered, ambient, and
twice ambient) and two rain pH (3, 5.1) levels. This produced 6
treatment combinations, each of which replicated four times. Air
pollution treatments were applied using exposure chambers that
served as whole plots, within each the three genotypes were assigned
as sub-plots.
PROC PRINT;
RUN;
ANALYZING CRD SPLIT-PLOT
The Whole Plot Treatments Are 6 Combinations of 3 Ozone & 2 Rain pH Levels
The Sub-plot Treatments are 3 Genotypes
Obs
1
2
3
4
5
6
.
44
45
46
47
48
.
67
68
69
70
71
72
3/9/16
O3
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Rain
pH
3.0
3.0
3.0
3.0
3.0
3.0
rep
1
1
1
2
2
2
Genotype
1
2
3
1
2
3
Leaf
Age
1
1
1
1
1
1
An
7.6149
6.6716
5.2160
5.6866
6.7961
4.0350
Filtered
Filtered
Filtered
Filtered
Filtered
5.1
5.1
5.1
5.1
5.1
3
3
4
4
4
2
3
1
2
3
1
1
1
1
1
9.5690
7.5071
5.5003
7.3806
9.1482
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
5.1
5.1
5.1
5.1
5.1
5.1
3
3
3
4
4
4
1
2
3
1
2
3
1
1
1
1
1
1
4.5229
6.8610
6.5856
5.7229
5.0970
6.6198
2
Split Plot
PROC MIXED DATA=A;
CLASS O3 RAINPH REP GENOTYPE;
MODEL AN=O3|RAINPH|GENOTYPE/DDFM=KR;
RANDOM REP*O3*RAINPH;
RUN;
The MODEL statement identifies the fixed sources of variation; in this case,
ozone, rain ph, genotype, and their interactions. The RANDOM statement
identifies the random sources of variation, which is replication*ozone*rainph
interaction. This is the whole plot MSe. The default residual becomes the sub
plot MSe.
ANALYZING CRD SPLIT-PLOT DESIGNS
The Whole Plot Treatments Are 6 Combinations of 3 Ozone & 2 Rain pH Levels
The sub-plot Treatments are 3 Genotypes
The Mixed Procedure
Model Information
Data Set
WORK.A
Dependent Variable
An
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method
Profile
Fixed Effects SE Method
Model-Based
Degrees of Freedom Method
Containment
Class Level Information
Class
O3
RainpH
rep
Genotype
Levels
3
2
4
3
Values
Ambient Filtered TwiceAmb
3.0 5.1
1 2 3 4
1 2 3
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
Observations Used
Observations Not Used
Total Observations
3/9/16
2
48
24
1
72
72
0
72
3
Split Plot
Iteration History
Evaluations
-2 Res Log Like
1
222.57320081
1
221.51041731
Iteration
0
1
Criterion
0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm
O3*RainpH*rep
Residual
Estimate
0.3309
1.9436
These are the variance component (VC) estimates for the random effects. In
this case the residual VC is the largest. the VC for residual is the sub-plot
MSe. However, the VC for O3*RainpH*rep is not the MSe for the whole plots.
The whole plot MSe is the sub plot VC + 3* whole plot VC [1.9436 +
3(0.3309)=2.9363], where 3 is the number of sub plots per whole plots.
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
BIC (smaller is better)
Effect
Type 3 Tests of Fixed Effects
Num
Den
DF
DF
F Value
O3
RainpH
O3*RainpH
Genotype
O3*Genotype
RainpH*Genotype
O3*RainpH*Genotype
3/9/16
221.5
225.5
225.7
227.9
2
1
2
2
4
2
4
18
18
18
36
36
36
36
29.75
0.56
0.65
0.03
0.97
0.32
0.66
Pr > F
<.0001
0.4644
0.5337
0.9695
0.4349
0.7271
0.6257
These are the test of hypotheses for the main and interactive effects of the
fixed factors. The only significant effect is the main effect of ozone. Note that
the denominator degrees of freedoms (error dfs) are different for ozone, Rain
pH, and their interaction versus those for genotype and interactions involving
genotype. This is because of having two different error terms for the wholeand sub-plots.
4
Split Plot
Suppose that in the previous study, the researcher was also interested
in examining the An response of two needle age classes (conifers
usually maintain several needle age classes). So the fixed factors of
interests were factorial combinations of ozone and rain ph assigned to
main plots (whole plot factors), genotype within ozone and rain ph
combination (sub-plot factor), and needle age class within genotype
(sub-sub-plot factor). This setting produces a design named Splitsplit-plot design. There are three different kinds of experimental
units, and thus, three different random error terms should be identified
and used.
The SAS program and Output for a CRD Split-split-plot Example:
OPTIONS LS=75 PS=500 NOCENTER NODATE PAGENO=1;
TITLE1 ANALYZING CRD SPLIT-SPLIT-PLOT DESIGNS;
DATA B;
INPUT O3$ RAINPH$ REP GENOTYPE LEAFAGE AN;
DATALINES;
Data lines entered here
RUN;
PROC PRINT DATA=B;
RUN;
ANALYZING CRD SPLIT-PLOT
The Whole Plot Treatments Are 6 Combinations of 3 Ozone & 2 Rain pH Levels
The Sub-plot Treatments are 3 Genotypes
Obs
1
2
3
4
5
6
7
8
9
10
.
133
134
135
136
137
138
139
140
141
142
143
144
3/9/16
O3
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Ambient
Rain
pH
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
rep
1
1
1
1
1
1
2
2
2
2
Genotype
1
1
2
2
3
3
1
1
2
2
Leaf
Age
1
2
1
2
1
2
1
2
1
2
An
7.6149
5.6383
6.6716
3.3239
5.2160
4.1720
5.6866
3.6622
6.7961
4.3654
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
TwiceAmb
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
3
3
3
3
3
3
4
4
4
4
4
4
1
1
2
2
3
3
1
1
2
2
3
3
1
2
1
2
1
2
1
2
1
2
1
2
4.5229
2.0557
6.8610
3.8902
6.5856
4.7786
5.7229
4.1057
5.0970
3.1993
6.6198
3.5799
5
Split Plot
PROC MIXED DATA=B;
CLASS O3 RAINPH REP GENOTYPE LEAFAGE;
MODEL AN=O3|RAINPH|GENOTYPE|LEAFAGE/DDFM=KR;
RANDOM REP*O3*RAINPH REP*GENOTYPE*O3*RAINPH;
RUN;
The MODEL statement identifies the fixed sources of variation; in this case,
ozone, rain ph, genotype, leaf age, and their interactions. The RANDOM
statement identifies the random sources of variation consisting of 1)
rep*O3*rainph interaction, which is the whole plot MSe, 2)
rep*genotype*O3*rainph interaction, which is the sub-plot (genotype) MSe,
and 3) the default residual, which becomes the sub-sub-plot (leaf age) MSe.
ANALYZING CRD SPLIT-SPLIT-PLOT DESIGNS
The Mixed Procedure
Model Information
Data Set
WORK.B
Dependent Variable
An
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method
Profile
Fixed Effects SE Method
Prasad-Rao-JeskeKackar-Harville
Degrees of Freedom Method
Kenward-Roger
Class Level Information
Class
O3
RainpH
rep
Genotype
LeafAge
Levels
3
2
4
3
2
Values
Ambient Filtered TwiceAmb
3.0 5.1
1 2 3 4
1 2 3
1 2
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
Observations Used
Observations Not Used
Total Observations
3/9/16
3
144
96
1
144
144
0
144
6
Split Plot
Iteration History
Iteration
Evaluations
0
1
-2 Res Log Like
Criterion
413.45258995
389.88307775
0.00000000
1
1
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm
Estimate
O3*RainpH*rep
0.1702
O3*RainpH*rep*Genoty
0.8244
Residual
0.7014
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
BIC (smaller is better)
Type 3 Tests of Fixed Effects
Num
Effect
DF
O3
2
RainpH
1
O3*RainpH
2
Genotype
2
O3*Genotype
4
RainpH*Genotype
2
O3*RainpH*Genotype
4
LeafAge
1
O3*LeafAge
2
RainpH*LeafAge
1
O3*RainpH*LeafAge
2
Genotype*LeafAge
2
O3*Genotype*LeafAge
4
RainpH*Genoty*LeafAg
2
O3*Rainp*Genot*LeafA
4
3/9/16
These are the variance component (VC) estimates for the random effects.
Remember that except for the residual VC these are not MSes.
389.9
395.9
396.1
399.4
Den
DF
18
18
18
36
36
36
36
54
54
54
54
54
54
54
54
F Value
56.71
2.18
0.56
0.35
0.88
0.44
0.37
101.79
0.54
1.15
0.53
0.84
0.58
0.01
1.32
Pr > F
<.0001
0.1575
0.5822
0.7036
0.4882
0.6447
0.8268
<.0001
0.5843
0.2891
0.5942
0.4377
0.6758
0.9860
0.2752
These are the test of hypotheses for the main and interactive effects of the
fixed factors. The only significant effects are the main effect of ozone and .
needle age. Note the differences in the denominator degrees of freedoms
(error dfs), indicating different error terms for the whole-, sub-, and sub-subplots.
7
Split Plot
SAS program and listing RCBD split plot example
The SAS program and Output for the RCBD Split-plot Example:
1
2
3
4
5
6
7
8
9
10
11
TITLE1 'LAB#9:
ANALYZING RCBD SPLIT PLOT DESIGNS';
OPTIONS LS=66 PS=54 PAGENO=1;
TITLE2 'The Whole Plot Design is a Randomized Complete Block';
TITLE3 'The Whole Plot Treatment is Irrigated vs Non-irrigated';
TITLE4 'The Sub Plot Trt is Level of Nitrogen (0, 40, 80, 160)';
TITLE5 'The data are expressed in yield per hectare';
DATA sp;
INPUT blk ig$ nit yield;
LINES;
This experiment is a randomized complete block split plot with
four blocks. The whole plot treatment is irrigated or nonirrigated and the sub plot treatment is level of nitrogen (0,
40, 80 or 160), making the treatment structure a 2x4
factorial. The dependent variable is crop yield per hectare.
Data lines entered here
45 RUN;
NOTE: The data set WORK.SP has 32 observations and 4 variables.
47
48
49
3/9/16
TITLE5 'Print of data file';
PROC PRINT DATA=sp;
QUIT;
8
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Print of data file
3/9/16
OBS
BLK
IG
NIT
YIELD
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
.
.
.
25
26
27
28
29
30
31
32
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
N
N
N
N
Y
Y
Y
Y
N
N
N
N
Y
Y
Y
Y
0
40
80
160
0
40
80
160
0
40
80
160
0
40
80
160
26
31
33
25
32
41
49
46
22
29
35
24
31
29
38
44
4
4
4
4
4
4
4
4
N
N
N
N
Y
Y
Y
Y
0
40
80
160
0
40
80
160
13
24
20
15
20
25
33
32
9
Split Plot
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
66
TITLE5 'Mixed model analysis of varaince';
TITLE6 'Orthogonal polynomial contrasts, Nit
interaction';
PROC MIXED DATA=sp RATIO COVTEST;
CLASS blk ig nit;
MODEL yield = ig nit ig*nit;
RANDOM blk blk*ig;
CONTRAST 'Nitrogen linear'
nit -7 -3 1
CONTRAST 'Nitrogen quadratic' nit 7 -4 -8
CONTRAST 'Nitrogen cubic'
nit -3 8 -6
CONTRAST 'Ig*Nit linear'
ig*nit -7 -3 1
CONTRAST 'Ig*Nit quadratic' ig*nit 7 -4 -8
CONTRAST 'Ig*Nit cubic'
ig*nit -3 8 -6
LSMEANS ig nit ig*nit / PDIFF;
ODS exclude listing lsmeans;
ODS output LSMEANS=lsm;
ODS exclude listing diffs;
ODS output DIFFS=diffs;
QUIT;
and IG*Nit
The MODEL statement identifies the fixed sources of variation.
In this case the 2x4 factorial structure. The RANDOM statement
identifies the random sources of variation, which are block
and the block*irrigation interaction. The block*irrigation
interaction is the whole plot MSe, while the residual is the
sub plot MSe. Since the nitrogen treatment is quantitative, I
have included a number of orthogonal polynomial contrasts.
These contrasts should identify the form of the regression
equation that would best describe these data. Because of the
multiple random variances, it is difficult to correctly
analyze data from split plot designs using simple regression
techniques.
9;
5;
1;
9 7 3 -1 -9;
5 -7 4 8 -5;
1 3 -8 6 -1;
NOTE: The data set WORK.LSM has 14 observations and 8 variables.
NOTE: The data set WORK.DIFFS has 35 observations and 10
variables.
3/9/16
10
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Mixed model analysis of varaince
Orthogonal polynomial contrasts, Nit and IG*Nit interaction
The Mixed Procedure
Model Information
Data Set
Dependent Variable
WORK.SP
yield
Class Level Information
Class
blk
ig
nit
Levels
4
2
4
Values
1 2 3 4
N Y
0 40 80 160
Dimensions
Observations Used
32
Iteration History
Iteration
Evaluations
-2 Res Log Like
Criterion
0
1
1
1
175.73630999
151.89110756
0.00000000
Convergence criteria met.
3/9/16
11
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Mixed model analysis of varaince
Orthogonal polynomial contrasts, Nit and IG*Nit interaction
Covariance Parameter Estimates
Ratio
Estimate
Standard
Error
Z
Value
Pr Z
3.1785
0.6532
1.0000
36.7292
7.5486
11.5556
34.5144
8.5764
3.8519
1.06
0.88
3.00
0.1436
0.1894
0.0013
Cov Parm
blk
blk*ig
Residual
These are the variance component (VC) estimates for the random
effects. In this case the block VC is the largest, followed
by the sub plot VC and then the whole plot VC. Remember these
are variance components and not MS for the whole unit or
block. In fact the whole unit variance (MS) would be the sub
unit VC + 4 * whole unit VC [MSw = 11.56 + 4(7.55)=41.76],
where the four is the number of sub units per whole unit.
Type 3 Tests of Fixed Effects
Effect
Num
DF
Den
DF
F Value
Pr > F
ig
nit
ig*nit
1
3
3
3
18
18
13.04
17.86
4.98
0.0365
<.0001
0.0109
These are the test of hypotheses for the fixed effects. Note
that although the F ratio is quite large for irrigation, it is
barely significant due to the small number of degrees of
freedom. This is the price the researcher frequently pays for
using a split plot design; a large reduction in the
sensitivity for tests concerning the whole plot treatment
factor. On the other hand, tests at the sub plot level are
sometimes more sensitive.
Contrasts
Label
Nitrogen linear
Nitrogen quadratic
Nitrogen cubic
Ig*Nit linear
Ig*Nit quadratic
Ig*Nit cubic
68
69
70
71
72
3/9/16
Num
DF
Den
DF
F Value
Pr > F
1
1
1
1
1
1
18
18
18
18
18
18
24.93
28.59
0.05
13.12
0.79
1.02
<.0001
<.0001
0.8298
0.0020
0.3860
0.3252
The polynomial contrasts indicate that the nitrogen response
contains both a linear and quadratic component and that the
two response lines differ in the linear component (slope).
TITLE5 'Print of main effect and treatment means';
PROC PRINT DATA=lsm;
FORMAT Estimate StdErr 6.1;
VAR EFFECT IG NIT Estimate StdErr;
QUIT;
12
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Print of main effects and treatment means
Obs
Effect
ig
nit
Estimate
StdErr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
74
75
76
77
78
79
3/9/16
ig
ig
nit
nit
nit
nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
N
Y
N
N
N
N
Y
Y
Y
Y
_
_
0
40
80
160
0
40
80
160
0
40
80
160
23.9
32.1
20.7
28.7
32.5
30.0
18.2
27.0
28.0
22.2
23.2
30.5
37.0
37.7
These are the broad sense estimates of the standard errors of
the treatment means. That is they are estimates of the
variation that would be expected in repetitions of the
experiment based on random samples of other blocks from the
same population of blocks as was sampled for the current
experiment.
3.43
3.43
3.40
3.40
3.40
3.40
3.74
3.74
3.74
3.74
3.74
3.74
3.74
3.74
TITLE5'Print of differences and tests of differences';
PROC PRINT DATA=diffs;
FORMAT DIFF StdErr 6.1 Probt 6.3;
WHERE ig=_IG or nit=_NIT;
VAR Effect ig nit _IG _NIT DIFF StdErr DF Probt;
QUIT;
13
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Print of differences and tests of differences
Obs
Effect
1
2
3
4
5
6
7
8
9
10
11
15
16
18
21
24
29
30
31
32
33
34
35
ig
nit
nit
nit
nit
nit
nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig*nit
ig
N
N
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
Y
Y
nit
_ig
_nit
Estimate
Y
_
40
80
160
80
160
160
40
80
160
0
80
160
40
160
80
160
40
80
160
80
160
160
-8.2
-8.0
-11.8
-9.3
-3.8
-1.3
2.5
-8.8
-9.8
-4.0
-5.0
-1.0
4.7
-3.5
5.8
-9.0
-15.5
-7.3
-13.8
-14.5
-6.5
-7.3
-0.7
_
0
0
0
40
40
80
0
0
0
0
40
40
40
80
80
160
0
0
0
40
40
80
N
N
N
Y
N
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
StdErr
2.3
1.7
1.7
1.7
1.7
1.7
1.7
2.4
2.4
2.4
3.1
2.4
2.4
3.1
2.4
3.1
3.1
2.4
2.4
2.4
2.4
2.4
2.4
DF
3
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
Probt
Note that there are four different standard errors of the
differences. These reflect the comparisons of means that are
based on whole plot variance, sub plot variance or a combination
of the two, as well as differences in replication between main
effect means and two-way means. If one uses the polynomial
contrast to interpret the nitrogen effect then these mean
comparisons should only be used to examine the differences
between irrigated and non-irrigated at a given nitrogen level.
0.036
0.000
0.000
0.000
0.041
0.472
0.159
0.002
0.001
0.113
0.123
0.682
0.064
0.272
0.028
0.009
0.000
0.007
0.000
0.000
0.015
0.007
0.759
81
82
83
DATA lsm;
SET lsm;
IF Effect='ig*nit';
The ODS statement in the MIXED procedure generated an output
data set containing the treatment means. Only the interaction
means (IG*NIT) are retained, to plot the data.
84
85
nitrogen = nit*1;
RUN;
The variable nitrogen is generated, which is the same as nit to
give the variable actual name to appear in the plot.
NOTE: There were 14 observations read from the dataset WORK.LSM.
NOTE: The data set WORK.LSM has 8 observations and 9 variables.
87
88
89
90
91
TITLE5 'Plot of trt means for examination of interaction effect';
The PLOT procedure is used to construct a crude plot of the
PROC PLOT DATA=lsm VPERCENT=70;
treatment means to examine the irrigation by nitrogen
FORMAT Estimate 5.0;
interaction. The VAXIS option determines the placement of tick
PLOT Estimate*nitrogen=ig / VAXIS=0 TO 40 BY 10;;
marks on the vertical axis.
QUIT;
3/9/16
14
Split Plot
LAB#9: ANALYZING RCBD SPLIT PLOT DESIGNS
The Whole Plot Design is a Randomized Complete Block
The Whole Plot Treatment is Irrigated vs Non-irrigated
The Sub Plot Treatment is Level of Nitrogen (0, 40, 80, 160)
Plot of trt means for examination of interaction effect
Plot of Estimate*nitrogen. Symbol is value of ig.
40 +
|
Y
|
Y
|
|
|
30 +
Y
|
N
|
N
Estimate |
| Y
|
N
20 +
| N
|
|
|
|
10 +
|
|
|
|
|
0 +
+-+------------+------------+------------+------------+-0
40
80
120
160
The interaction can be seen as an increasing difference
between irrigated and non-irrigated as the nitrogen level
increases. In addition, very little increase in yield is seen
as nitrogen is increased from 80 to 160 units under
irrigation, while yields of non-irrigated plots decreased at
the highest level of nitrogen.
nitrogen
3/9/16
15
Split Plot