-
SAS Commands for the Analysis of
an RCBD with a Split Plot
Arrangement options pageno=1; data spplot; input
A $ B $ rep yield; datalines; a0 b0 1 13.8 a0 b1 1 15.5 a0 b2 1 21
a0 b3 1 18.9 a1 b0 1 19.3 a1 b1 1 22.2 a1 b2 1 25.3 a1 b3 1 25.9 a0
b0 2 13.5 a0 b1 2 15 a0 b2 2 22.7 a0 b3 2 18.3 a1 b0 2 18 a1 b1 2
24.2 a1 b2 2 24.8 a1 b3 2 26.7 a0 b0 3 13.2 a0 b1 3 15.2 a0 b2 3
22.3 a0 b3 3 19.6 a1 b0 3 20.5 a1 b1 3 25.4 a1 b2 3 28.4 a1 b3 3
27.6 ;; ods graphics off; ods rtf file='split_plot.rtf'; proc
anova; class rep a b; model yield=rep a rep*a b a*b; test h=a
e=rep*a; means a/lsd e=rep*a; means b/lsd; means a*b; title 'ANOVA
for the RCBD with a Split Plot Arrangement'; run; ods rtf
close;
-
ANOVA for the RCBD with a
Split Plot Arrangement
The ANOVA Procedure
Class Level Information
Class Levels Values
rep 3 1 2 3 A 2 a0
a1 B 4 b0 b1 b2 b3
Number of Observations Read 24
Number of Observations Used 24
-
ANOVA for the RCBD with a
Split Plot Arrangement
The ANOVA Procedure Dependent
Variable: yield
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 11 508.8812500 46.2619318
76.69 F
rep 2 7.8658333 3.9329167 6.52
0.0121 A 1 262.0204167
262.0204167 434.39
-
ANOVA for the RCBD with a
Split Plot Arrangement
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 2 Error Mean Square
2.517917 Critical Value of t 4.30265
Least Significant Difference 2.7873
Means with the same letter are
not significantly different.
t Grouping Mean N A
A 24.0250 12 a1
B 17.4167 12 a0
-
ANOVA for the RCBD with a
Split Plot Arrangement
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 12 Error Mean Square
0.603194 Critical Value of t 2.17881
Least Significant Difference
0.977
Means with the same letter are
not significantly
different.
t Grouping Mean N B
A 24.0833 6 b2
B 22.8333 6 b3
C 19.5833 6 b1
D 16.3833 6 b0
-
ANOVA for the RCBD with a
Split Plot Arrangement
The ANOVA Procedure
Level of A
Level of B N
yield
Mean Std Dev
a0 b0 3 13.5000000 0.30000000
a0 b1 3 15.2333333 0.25166115
a0 b2 3 22.0000000 0.88881944
a0 b3 3 18.9333333 0.65064071
a1 b0 3 19.2666667 1.25033329
a1 b1 3 23.9333333 1.61658075
a1 b2 3 26.1666667 1.95021366
a1 b3 3 26.7333333 0.85049005
-
SAS Commands for the
Analysis of an RCBD with a
Split-‐split Plot Arrangement
options pageno=1; data spspplot; input A B C rep Yield;
datalines; 0 0 0 1 25.7 0 0 1 1 31.8 0 0 2 1 34.6 0 1 0 1 27.7 0 1
1 1 38 0 1 2 1 42.1 1 0 0 1 28.9 1 0 1 1 37.5 1 0 2 1 38.4 1 1 0 1
38 1 1 1 1 36.9 1 1 2 1 44.2 2 0 0 1 23.4 2 0 1 1 25.3 2 0 2 1 29.8
2 1 0 1 20.8 2 1 1 1 29 2 1 2 1 36.6 0 0 0 2 25.4 0 0 1 2 29.5 0 0
2 2 37.2 0 1 0 2 30.3 0 1 1 2 40.6 0 1 2 2 43.6 1 0 0 2 24.7 1 0 1
2 31.5 1 0 2 2 32.5 1 1 0 2 31 1 1 1 2 31.9 1 1 2 2 41.6 2 0 0 2
24.2 2 0 1 2 27.7 2 0 2 2 29.9 2 1 0 2 23 2 1 1 2 32 2 1 2 2 37.8 0
0 0 3 23.8 0 0 1 3 28.7 0 0 2 3 29.1
-
0 1 0 3 30.2 0 1 1 3 34.6 0 1 2 3 44.6 1 0 0 3 27.8 1 0 1
3 31 1 0 2 3 31.2 1 1 0 3 29.5 1 1 1 3 31.5 1 1 2 3 38.9 2 0 0 3
21.2 2 0 1 3 23.7 2 0 2 3 24.3 2 1 0 3 25.2 2 1 1 3 26.5 2 1 2 3
34.8 0 0 0 4 22 0 0 1 4 26.4 0 0 2 4 23.7 0 1 0 4 33.2 0 1 1 4 31 0
1 2 4 42.7 1 0 0 4 23.4 1 0 1 4 27.8 1 0 2 4 29.8 1 1 0 4 30.7 1 1
1 4 35.9 1 1 2 4 37.6 2 0 0 4 20.9 2 0 1 4 24.3 2 0 2 4 23.8 2 1 0
4 23.1 2 1 1 4 31.2 2 1 2 4 40.2 ;; ods graphics off; ods rtf
file='split_split_plot.rtf'; proc anova; class rep a b c; model
yield=rep a rep*a b a*b rep*a*b c a*c b*c a*b*c; test h=a e=rep*a;
test h=b a*b e=rep*a*b; means a/lsd e=rep*a; means b/lsd e=rep*a*b;
means c/lsd; means a*b a*c b*c a*b*c; title 'ANOVA for the RCBD
with a Split-split Plot Analysis';
-
run; ods rtf close;
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
Class Level Information
Class Levels Values
rep 4 1 2 3 4 A 3
0 1 2 B 2 0 1 C
3 0 1 2
Number of Observations Read 72
Number of Observations Used 72
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure Dependent
Variable: Yield
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 35 2672.107778 76.345937 16.31
F
rep 3 143.4561111 47.8187037 10.22
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
t Tests (LSD) for Yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 6 Error Mean Square
18.62634 Critical Value of t 2.44691
Least Significant Difference 3.0485
Means with the same letter are
not significantly
different.
t Grouping Mean N A
A 33.008 24 1
A
A 32.354 24 0
B 27.446 24 2
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
t Tests (LSD) for Yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 9 Error Mean Square
8.704722 Critical Value of t 2.26216
Least Significant Difference
1.5731
Means with the same letter are
not significantly
different.
t Grouping Mean N B
A 34.0694 36 1
B 27.8028 36 0
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
t Tests (LSD) for Yield
Note:
This test controls the Type I
comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 36 Error Mean Square
4.680509 Critical Value of t 2.02809
Least Significant Difference 1.2666
Means with the same letter are
not significantly
different.
t Grouping Mean N C
A 35.3750 24 2
B 31.0125 24 1
C 26.4208 24 0
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
t Tests (LSD) for Yield
Level of A
Level of B N
Yield
Mean Std Dev
0 0 12 28.1583333 4.60265898 0
1 12 36.5500000 6.06907212 1
0 12 30.3750000 4.45831705 1
1 12 35.6416667 4.72179826 2
0 12 24.8750000 2.90458102 2
1 12 30.0166667 6.42761561
Level of A
Level of C N
Yield
Mean Std Dev
0 0 8 27.2875000 3.75858541 0
1 8 32.5750000 4.83462216 0
2 8 37.2000000 7.60263112 1
0 8 29.2500000 4.45517356 1
1 8 33.0000000 3.39369163 1
2 8 36.7750000 5.13051097 2
0 8 22.7250000 1.61842075 2
1 8 27.4625000 3.08773495 2
2 8 32.1500000 6.15838569
Level of B
Level of C N
Yield
Mean Std Dev
0 0 12 24.2833333 2.43229534 0
1 12 28.7666667 3.85871701 0
2 12 30.3583333 4.87320285 1
0 12 28.5583333 4.86872362 1
1 12 33.2583333 4.02367049 1
2 12 40.3916667 3.22813155
-
ANOVA for the RCBD with a
Split-‐split Plot Analysis
The ANOVA Procedure
t Tests (LSD) for Yield
Level of A
Level of B
Level of C N
Yield
Mean Std Dev
0 0 0 4 24.2250000 1.70171482
0 0 1 4 29.1000000
2.22860195 0 0 2 4 31.1500000
6.00583050 0 1 0 4
30.3500000 2.24870333 0 1 1 4
36.0500000 4.16773320 0 1 2
4 43.2500000 1.09087121 1 0
0 4 26.2000000 2.57811301 1
0 1 4 31.9500000 4.04680944
1 0 2 4 32.9750000
3.78098312 1 1 0 4 32.3000000
3.85486705 1 1 1 4
34.0500000 2.74893919 1 1 2 4
40.5750000 2.93527398 2 0 0
4 22.4250000 1.62557682 2 0
1 4 25.2500000 1.76162803 2
0 2 4 26.9500000 3.35509563
2 1 0 4 23.0250000
1.79698822 2 1 1 4 29.6750000
2.46762369 2 1 2 4
37.3500000 2.26495033
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SAS Commands for the RCBD with a Split Block Arrangement
options pageno=1; data spblk; input Horiz $ Vert $ Rep yield;
datalines; a0 b0 1 13.8 a0 b1 1 15.5 a0 b2 1 21 a0 b3 1 18.9 a1 b0
1 19.3 a1 b1 1 22.2 a1 b2 1 25.3 a1 b3 1 25.9 a0 b0 2 13.5 a0 b1 2
15 a0 b2 2 22.7 a0 b3 2 18.3 a1 b0 2 18 a1 b1 2 24.2 a1 b2 2 24.8
a1 b3 2 26.7 a0 b0 3 13.2 a0 b1 3 15.2 a0 b2 3 22.3 a0 b3 3 19.6 a1
b0 3 20.5 a1 b1 3 25.4 a1 b2 3 28.4 a1 b3 3 27.6 ;; ods graphics
off; ods rtf file='split_block.rtf'; proc anova; class horiz vert
rep; model yield=rep horiz rep*horiz vert rep*vert horiz*vert; test
h=horiz e=rep*horiz; test h=vert e=rep*vert; means horiz/lsd
e=rep*horiz; means vert/lsd e=rep*vert; means horiz*vert; title
'ANOVA for the RCBD in a Split Block Arrangement'; run; ods rtf
close;
-
ANOVA for the RCBD in a
Split Block Arrangement
The ANOVA Procedure
Class Level Information
Class Levels Values
Horiz 2 a0 a1 Vert 4 b0
b1 b2 b3 Rep 3 1 2
3
Number of Observations Read 24
Number of Observations Used 24
-
ANOVA for the RCBD in a
Split Block Arrangement
The ANOVA Procedure Dependent
Variable: yield
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 17 511.3587500 30.0799265
37.91 0.0001 Error 6 4.7608333
0.7934722 Corrected Total 23
516.1195833
R-‐Square Coeff Var Root MSE
yield Mean
0.990776 4.298913 0.890771 20.72083
Source DF Anova SS Mean Square
F Value Pr > F
Rep 2 7.8658333 3.9329167 4.96
0.0536 Horiz 1 262.0204167
262.0204167 330.22 F
Vert 3 215.2612500 71.7537500 173.77
-
ANOVA for the RCBD in a
Split Block Arrangement
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 2 Error Mean Square
2.517917 Critical Value of t 4.30265
Least Significant Difference 2.7873
Means with the same letter are
not significantly different.
t Grouping Mean N Horiz
A 24.0250 12 a1
B 17.4167 12 a0
-
ANOVA for the RCBD in a
Split Block Arrangement
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 6 Error Mean Square
0.412917 Critical Value of t 2.44691
Least Significant Difference 0.9078
Means with the same letter are
not significantly different.
t Grouping Mean N Vert
A 24.0833 6 b2
B 22.8333 6 b3
C 19.5833 6 b1
D 16.3833 6 b0
-
ANOVA for the RCBD in a
Split Block Arrangement
The ANOVA Procedure
Level of Horiz
Level of Vert N
yield
Mean Std Dev
a0 b0 3 13.5000000 0.30000000
a0 b1 3 15.2333333 0.25166115
a0 b2 3 22.0000000 0.88881944
a0 b3 3 18.9333333 0.65064071
a1 b0 3 19.2666667 1.25033329
a1 b1 3 23.9333333 1.61658075
a1 b2 3 26.1666667 1.95021366
a1 b3 3 26.7333333 0.85049005
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SAS Commands for the Combined ANOVA Across Locations for
an RCBD with Factorial Arrangement of A and B (locations are random
and A and B are both fixed effects) options pageno=1; data cmbloc;
input Loc $ A B rep yield; datalines; A 0 0 1 25.7 A 0 1 1 31.8 A 0
2 1 34.6 A 1 0 1 27.7 A 1 1 1 38 A 1 2 1 42.1 A 0 0 2 25.4 A 0 1 2
29.5 A 0 2 2 37.2 A 1 0 2 30.3 A 1 1 2 40.6 A 1 2 2 43.6 A 0 0 3
23.8 A 0 1 3 28.7 A 0 2 3 29.1 A 1 0 3 30.2 A 1 1 3 34.6 A 1 2 3
44.6 A 0 0 4 22 A 0 1 4 26.4 A 0 2 4 23.7 A 1 0 4 33.2 A 1 1 4 31 A
1 2 4 42.7 B 0 0 1 28.9 B 0 1 1 37.5 B 0 2 1 38.4 B 1 0 1 38 B 1 1
1 36.9 B 1 2 1 44.2 B 0 0 2 24.7 B 0 1 2 31.5 B 0 2 2 32.5 B 1 0 2
31 B 1 1 2 31.9 B 1 2 2 41.6 B 0 0 3 27.8
-
B 0 1 3 31 B 0 2 3 31.2 B 1 0 3 29.5 B 1 1 3 31.5 B 1 2 3
38.9 B 0 0 4 23.4 B 0 1 4 27.8 B 0 2 4 29.8 B 1 0 4 30.7 B 1 1 4
35.9 B 1 2 4 37.6 C 0 0 1 23.4 C 0 1 1 25.3 C 0 2 1 29.8 C 1 0 1
20.8 C 1 1 1 29 C 1 2 1 36.6 C 0 0 2 24.2 C 0 1 2 27.7 C 0 2 2 29.9
C 1 0 2 23 C 1 1 2 32 C 1 2 2 37.8 C 0 0 3 21.2 C 0 1 3 23.7 C 0 2
3 24.3 C 1 0 3 25.2 C 1 1 3 26.5 C 1 2 3 34.8 C 0 0 4 20.9 C 0 1 4
24.3 C 0 2 4 23.8 C 1 0 4 23.1 C 1 1 4 31.2 C 1 2 4 40.2 ;; ods
graphics off; ods rtf file='cmb_loc_anova.rtf'; proc sort; by loc;
proc anova; by loc; class rep a b; model yield=rep a b a*b; title
'ANOVA for Each Individual Location'; run;
-
proc anova; class loc rep a b; model yield=loc rep(loc) a
loc*a b loc*b a*b loc*a*b; test h=a e=loc*a; test h=b e=loc*b; test
h=a*b e=loc*a*b; means a/lsd e=loc*a; means b/lsd e=loc*b; title
'Combined ANOVA Across locations Assuming Location is a Random
Effect and A and B are Both Fixed Effects'; run;
-
ANOVA for Each Individual Location
The ANOVA Procedure
Loc=A
Class Level Information
Class Levels Values
rep 4 1 2 3 4 A 2
0 1 B 3 0 1 2
Number of Observations Read 24
Number of Observations Used 24
-
ANOVA for Each Individual Location
The ANOVA Procedure Dependent
Variable: yield
Loc=A
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 8 929.323333 116.165417 13.26
F
rep 3 71.2512500 23.7504167 2.71
0.0820 A 1 422.5204167
422.5204167 48.23
-
ANOVA for Each Individual Location
The ANOVA Procedure
Loc=B
Class Level Information
Class Levels Values
rep 4 1 2 3 4 A 2
0 1 B 3 0 1 2
Number of Observations Read 24
Number of Observations Used 24
-
ANOVA for Each Individual Location
The ANOVA Procedure Dependent
Variable: yield
Loc=B
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 8 579.1450000 72.3931250 21.22
F
rep 3 153.8816667 51.2938889 15.04
-
ANOVA for Each Individual Location
The ANOVA Procedure
Loc=C
Class Level Information
Class Levels Values
rep 4 1 2 3 4 A 2
0 1 B 3 0 1 2
Number of Observations Read 24
Number of Observations Used 24
-
ANOVA for Each Individual Location
The ANOVA Procedure Dependent
Variable: yield
Loc=C
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 8 641.6083333 80.2010417 18.72
F
rep 3 30.0812500 10.0270833 2.34
0.1146 A 1 158.6204167
158.6204167 37.02
-
Combined ANOVA Across locations Assuming
Location is a Random Effect and
A and B are Both Fixed
Effects
The ANOVA Procedure
Class Level Information
Class Levels Values
Loc 3 A B C rep 4
1 2 3 4 A 2 0 1 B
3 0 1 2
Number of Observations Read 72
Number of Observations Used 72
-
Combined ANOVA Across locations Assuming
Location is a Random Effect and
A and B are Both Fixed
Effects
The ANOVA Procedure
Dependent Variable: yield
Source DF Sum of Squares Mean
Square F Value Pr > F
Model 26 2593.765278 99.760203 18.19
F
Loc 2 443.6886111 221.8443056 40.44
-
Combined ANOVA Across locations Assuming
Location is a Random Effect and
A and B are Both Fixed
Effects
The ANOVA Procedure
Dependent Variable: yield
Tests of Hypotheses Using the
Anova MS for Loc*A*B as an
Error Term
Source DF Anova SS Mean Square
F Value Pr > F
A*B 2 127.8308333 63.9154167 5.81
0.0656
-
Combined ANOVA Across locations Assuming
Location is a Random Effect and
A and B are Both Fixed
Effects
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 2 Error Mean Square
20.34375 Critical Value of t 4.30265
Least Significant Difference 4.5742
Means with the same letter are
not significantly
different.
t Grouping Mean N A
A 34.069 36 1
B 27.803 36 0
-
Combined ANOVA Across locations Assuming
Location is a Random Effect and
A and B are Both Fixed
Effects
The ANOVA Procedure
t Tests (LSD) for yield
Note: This test controls the Type
I comparisonwise error rate, not
the experimentwise error rate.
Alpha 0.05 Error Degrees of
Freedom 4 Error Mean Square
3.277431 Critical Value of t 2.77645
Least Significant Difference 1.451
Means with the same letter are
not significantly
different.
t Grouping Mean N B
A 35.3750 24 2
B 31.0125 24 1
C 26.4208 24 0