| 11. Special Topics | ||||
| Questionairre | ||||
| Stability Analysis (excel) | ||||
Before combining locations, do you test for homogeneity of error terms?
LOCATION*TRT INTERACTIONS:
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 27 4182.666667 154.913580 49.11 <.0001
Error 32 100.933333 3.154167
Corrected Total 59 4283.600000
R-Square Coeff Var Root MSE yield Mean
0.976437 4.826080 1.775997 36.80000
Source DF Type I SS Mean Square F Value Pr > F
loc 3 3132.933333 1044.311111 331.09 <.0001
rep(loc) 8 121.066667 15.133333 4.80 0.0006
nrate 4 484.933333 121.233333 38.44 <.0001
loc*nrate 12 443.733333 36.977778 11.72 <.0001
Source DF Type III SS Mean Square F Value Pr > F
loc 3 3132.933333 1044.311111 331.09 <.0001
rep(loc) 8 121.066667 15.133333 4.80 0.0006
nrate 4 484.933333 121.233333 38.44 <.0001
loc*nrate 12 443.733333 36.977778 11.72 <.0001
Level of --------------MP------------- ------------yield------------
loc N Mean Std Dev Mean Std Dev
1 15 26.4666667 6.08119662 26.6000000 4.59502837
2 15 38.1333333 8.30547725 39.2666667 6.38599658
3 15 42.8666667 3.54293395 46.5333333 3.31375201
4 15 32.8666667 4.96943036 34.8000000 3.05193147
Level of --------------MP------------- ------------yield------------
nrate N Mean Std Dev Mean Std Dev
20 12 30.0000000 10.1533693 33.4166667 11.0161727
40 12 31.1666667 7.3587713 33.7500000 7.6767062
60 12 36.6666667 6.9718047 37.1666667 7.8836232
80 12 38.5833333 7.4767316 39.0833333 7.6450618
100 12 39.0000000 6.7823300 40.5833333 6.6668561
Level of Level of --------------MP------------- ------------yield------------ loc nrate N Mean Std Dev Mean Std Dev
1 20 3 20.3333333 3.51188458 21.0000000 1.00000000 1 40 3 21.6666667 1.52752523 24.0000000 1.00000000 1 60 3 27.0000000 5.56776436 26.6666667 3.05505046 1 80 3 30.3333333 4.72581563 28.3333333 2.51661148 1 100 3 33.0000000 3.60555128 33.0000000 2.64575131 2 20 3 29.6666667 6.80685929 32.0000000 1.73205081 2 40 3 29.3333333 5.50757055 33.0000000 1.73205081 2 60 3 40.3333333 0.57735027 39.6666667 0.57735027 2 80 3 45.3333333 1.15470054 44.6666667 0.57735027 2 100 3 46.0000000 1.73205081 47.0000000 2.64575131 3 20 3 44.0000000 3.60555128 50.0000000 1.00000000 3 40 3 39.0000000 3.60555128 44.0000000 4.00000000 3 60 3 43.0000000 1.73205081 46.6666667 3.51188458 3 80 3 44.3333333 4.50924975 46.0000000 3.46410162 3 100 3 44.0000000 3.00000000 46.0000000 2.64575131 4 20 3 26.0000000 6.08276253 30.6666667 2.08166600 4 40 3 34.6666667 1.15470054 34.0000000 1.73205081 4 60 3 36.3333333 3.51188458 35.6666667 2.51661148 4 80 3 34.3333333 4.04145188 37.3333333 2.51661148 4 100 3 33.0000000 3.00000000 36.3333333 2.08166600
1. Test Treatment Significance of Potential Covariate If TRT effect is not significant using the potential covariate (MP) as a dependent variable it can be used as a covariate in AOV
Dependent Variable: MP
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 27 3936.583333 145.799383 15.35 <.0001
Error 32 304.000000 9.500000
Corrected Total 59 4240.583333
R-Square Coeff Var Root MSE MP Mean
0.928312 8.785388 3.082207 35.08333
Source DF Type I SS Mean Square F Value Pr > F
loc 3 2235.650000 745.216667 78.44 <.0001
rep(loc) 8 289.333333 36.166667 3.81 0.0031
nrate 4 855.333333 213.833333 22.51 <.0001
loc*nrate 12 556.266667 46.355556 4.88 0.0002
Source DF Type III SS Mean Square F Value Pr > F
loc 3 2235.650000 745.216667 78.44 <.0001
rep(loc) 8 289.333333 36.166667 3.81 0.0031
nrate 4 855.333333 213.833333 22.51 <.0001
loc*nrate 12 556.266667 46.355556 4.88 0.0002
2. Enter Covariate as independent effect in the model, but do not include
it in the classes statements (not an effect we are controlling)
Use LSMEANS (adjusted means)
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 28 4198.509956 149.946784 54.63 <.0001
Error 31 85.090044 2.744840
Corrected Total 59 4283.600000
R-Square Coeff Var Root MSE yield Mean
0.980136 4.502054 1.656756 36.80000
Source DF Type I SS Mean Square F Value Pr > F
loc 3 3132.933333 1044.311111 380.46 <.0001
rep(loc) 8 121.066667 15.133333 5.51 0.0002
nrate 4 484.933333 121.233333 44.17 <.0001
loc*nrate 12 443.733333 36.977778 13.47 <.0001
MP 1 15.843289 15.843289 5.77 0.0225
Source DF Type III SS Mean Square F Value Pr > F
loc 3 270.9265184 90.3088395 32.90 <.0001
rep(loc) 8 48.2687576 6.0335947 2.20 0.0555
nrate 4 78.3412862 19.5853215 7.14 0.0003
loc*nrate 12 150.5722362 12.5476864 4.57 0.0003
MP 1 15.8432895 15.8432895 5.77 0.0225
The GLM Procedure
Least Squares Means
loc yield LSMEAN
1 28.5670943
2 38.5703838
3 44.7564803
4 35.3060417
nrate yield LSMEAN
20 34.5771382
40 34.6441338
60 36.8052083
80 38.2843202
100 39.6891996
loc nrate yield LSMEAN
1 20 24.3672697
1 40 27.0628838
1 60 28.5120066
1 80 29.4177083
1 100 33.4756031
2 20 33.2365680
2 40 34.3126645
2 60 38.4681469
2 80 42.3266996
2 100 44.5078399
3 20 47.9644189
3 40 43.1058662
3 60 44.8593750
3 80 43.8883224
3 100 43.9644189
4 20 32.7402961
4 40 34.0951206
4 60 35.3813048
4 80 37.5045504
4 100 36.8089364
3. Plot covariate versus dependent variable (simple linear model)
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 3660.722778 3660.722778 340.87 <.0001
Error 58 622.877222 10.739262
Corrected Total 59 4283.600000
R-Square Coeff Var Root MSE yield Mean
0.854590 8.905112 3.277081 36.80000
Source DF Type I SS Mean Square F Value Pr > F
MP 1 3660.722778 3660.722778 340.87 <.0001
Source DF Type III SS Mean Square F Value Pr > F
MP 1 3660.722778 3660.722778 340.87 <.0001
Standard
Parameter Estimate Error t Value Pr > |t|
Intercept 4.203462574 1.81551271 2.32 0.0242
MP 0.929117456 0.05032392 18.46 <.0001
Plot of yield*MP. Symbol used is 'x'.
yield ‚
‚
51 ˆ x
50 ˆ x x x x
49 ˆ x x
48 ˆ x
47 ˆ x
46 ˆ x
45 ˆ x x
44 ˆ x x x x
43 ˆ x
42 ˆ
41 ˆ
40 ˆ x x x x
39 ˆ x
38 ˆ x x
37 ˆ x x
36 ˆ x
35 ˆ x x x x
34 ˆ x x x x
33 ˆ x x x
32 ˆ x
31 ˆ x x
30 ˆ x x x x
29 ˆ x
28 ˆ x
27 ˆ
26 ˆ x x
25 ˆ x
24 ˆ x
23 ˆ x
22 ˆ x
21 ˆ x
20 ˆ x
‚
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15 20 25 30 35 40 45 50
MP
NOTE: 5 obs hidden.