Printout of 3-factor Data 1
09:06 Wednesday, November 6, 2002
Obs rep a b c yield
1 1 0 0 0 25.7
2 2 0 0 0 25.4
3 3 0 0 0 23.8
4 4 0 0 0 22.0
5 1 0 0 1 31.8
6 2 0 0 1 29.5
7 3 0 0 1 28.7
8 4 0 0 1 26.4
9 1 0 0 2 34.6
10 2 0 0 2 37.2
11 3 0 0 2 29.1
12 4 0 0 2 23.7
13 1 0 1 0 27.7
14 2 0 1 0 30.3
15 3 0 1 0 30.2
16 4 0 1 0 33.2
17 1 0 1 1 38.0
18 2 0 1 1 40.6
19 3 0 1 1 34.6
20 4 0 1 1 31.0
21 1 0 1 2 42.1
22 2 0 1 2 43.6
23 3 0 1 2 44.6
24 4 0 1 2 42.7
25 1 1 0 0 28.9
26 2 1 0 0 24.7
27 3 1 0 0 27.8
28 4 1 0 0 23.4
29 1 1 0 1 37.5
30 2 1 0 1 31.5
31 3 1 0 1 31.0
32 4 1 0 1 27.8
33 1 1 0 2 38.4
34 2 1 0 2 32.5
35 3 1 0 2 31.2
36 4 1 0 2 29.8
37 1 1 1 0 38.0
38 2 1 1 0 31.0
39 3 1 1 0 29.5
40 4 1 1 0 30.7
41 1 1 1 1 36.9
42 2 1 1 1 31.9
43 3 1 1 1 31.5
44 4 1 1 1 35.9
45 1 1 1 2 44.2
46 2 1 1 2 41.6
47 3 1 1 2 38.9
48 4 1 1 2 37.6
49 1 2 0 0 23.4
50 2 2 0 0 24.2
51 3 2 0 0 21.2
52 4 2 0 0 20.9
53 1 2 0 1 25.3
54 2 2 0 1 27.7
55 3 2 0 1 23.7
Printout of 3-factor Data 2
09:06 Wednesday, November 6, 2002
Obs rep a b c yield
56 4 2 0 1 24.3
57 1 2 0 2 29.8
58 2 2 0 2 29.9
59 3 2 0 2 24.3
60 4 2 0 2 23.8
61 1 2 1 0 20.8
62 2 2 1 0 23.0
63 3 2 1 0 25.2
64 4 2 1 0 23.1
65 1 2 1 1 29.0
66 2 2 1 1 32.0
67 3 2 1 1 26.5
68 4 2 1 1 31.2
69 1 2 1 2 36.6
70 2 2 1 2 37.8
71 3 2 1 2 34.8
72 4 2 1 2 40.2
ANOVA for A whole plot, BxC factorial arrangement forsubplot 3
All factors fixed
09:06 Wednesday, November 6, 2002
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 72
ANOVA for A whole plot, BxC factorial arrangement forsubplot 4
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 26 2593.765278 99.760203 18.19 <.0001
Error 45 246.840833 5.485352
Corrected Total 71 2840.606111
R-Square Coeff Var Root MSE yield Mean
0.913103 7.570709 2.342083 30.93611
Source DF Anova SS Mean Square F Value Pr > F
rep 3 143.4561111 47.8187037 8.72 0.0001
a 2 443.6886111 221.8443056 40.44 <.0001
a(rep) 6 111.7580556 18.6263426 3.40 0.0076
b 1 706.8800000 706.8800000 128.87 <.0001
c 2 962.3352778 481.1676389 87.72 <.0001
a*b 2 40.6875000 20.3437500 3.71 0.0323
a*c 4 13.1097222 3.2774306 0.60 0.6663
b*c 2 127.8308333 63.9154167 11.65 <.0001
a*b*c 4 44.0191667 11.0047917 2.01 0.1098
Tests of Hypotheses Using the Anova MS for a(rep) as an Error Term
Source DF Anova SS Mean Square F Value Pr > F
a 2 443.6886111 221.8443056 11.91 0.0081
ANOVA for A whole plot, BxC factorial arrangement forsubplot 5
All factors fixed
09:06 Wednesday, November 6, 2002
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 A whole plot, BxC factorial arrangement for subplot 6
All factors fixed
09:06 Wednesday, November 6, 2002
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 45
Error Mean Square 5.485352
Critical Value of t 2.01410
Least Significant Difference 1.1119
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 A whole plot, BxC factorial arrangement for subplot 7
All factors fixed
09:06 Wednesday, November 6, 2002
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 45
Error Mean Square 5.485352
Critical Value of t 2.01410
Least Significant Difference 1.3617
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 A whole plot, BxC factorial arrangement for subplot 8
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Level of Level of ------yield------
a b N 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 Level of ------yield------
a c N 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 Level of ------yield------
b c N 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
Level of Level of Level of ------yield------
a b c N 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
ANOVA for A whole plot, BxC factorial arrangement for subplot 9
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Level of Level of Level of ------yield------
a b c N Mean Std Dev
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
ANOVA for AxB factorial arrangment for whole plot, Csuplot. 10
All factors fixed
09:06 Wednesday, November 6, 2002
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 72
ANOVA for AxB factorial arrangement for whole plot, C subplot. 11
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 35 2672.107778 76.345937 16.31 <.0001
Error 36 168.498333 4.680509
Corrected Total 71 2840.606111
R-Square Coeff Var Root MSE yield Mean
0.940682 6.993279 2.163448 30.93611
Source DF Anova SS Mean Square F Value Pr > F
rep 3 143.4561111 47.8187037 10.22 <.0001
a 2 443.6886111 221.8443056 47.40 <.0001
b 1 706.8800000 706.8800000 151.03 <.0001
a*b 2 40.6875000 20.3437500 4.35 0.0204
a*b(rep) 15 190.1005556 12.6733704 2.71 0.0072
c 2 962.3352778 481.1676389 102.80 <.0001
a*c 4 13.1097222 3.2774306 0.70 0.5969
b*c 2 127.8308333 63.9154167 13.66 <.0001
a*b*c 4 44.0191667 11.0047917 2.35 0.0725
Tests of Hypotheses Using the Anova MS for a*b(rep) as an Error Term
Source DF Anova SS Mean Square F Value Pr > F
a 2 443.6886111 221.8443056 17.50 0.0001
b 1 706.8800000 706.8800000 55.78 <.0001
a*b 2 40.6875000 20.3437500 1.61 0.2335
ANOVA for AxB factorial arrangement for whole plot, C subplot. 12
All factors fixed
09:06 Wednesday, November 6, 2002
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 15
Error Mean Square 12.67337
Critical Value of t 2.13145
Least Significant Difference 2.1904
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 AxB factorial arrangement for whole plot, C subplot. 13
All factors fixed
09:06 Wednesday, November 6, 2002
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 15
Error Mean Square 12.67337
Critical Value of t 2.13145
Least Significant Difference 1.7885
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 AxB factorial arrangement for whole plot, C subplot. 14
All factors fixed
09:06 Wednesday, November 6, 2002
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 AxB factorial arrangement for whole plot, C subplot. 15
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Level of Level of ------yield------
a b N 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 Level of ------yield------
a c N 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 Level of ------yield------
b c N 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
Level of Level of Level of ------yield------
a b c N 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
ANOVA for AxB factorial arrangement for whole plot, C subplot. 16
All factors fixed
09:06 Wednesday, November 6, 2002
The ANOVA Procedure
Level of Level of Level of ------yield------
a b c N Mean Std Dev
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