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20 May 2013

Examples in SPSS and SAS for oil palm fertilizer experimental design and analysis - Part B


This section continues from Part A which discusses Example 2 on pages 267-268 of the publication Oil Palm: Management for Large and Sustainable Yields.

B1 Example 4 (page 271)

Data file for SPSS and SAS

The contents of the data file (contained in a *.dat format) is given below showing (from left to right) the plotnumber (plot), applied level of N (n), applied level of P (p), yield (yield), and block number (block )

Plot number (plotnr)
Applied level of N (n)
Applied level of P (p)
Yield
Block number (block)
21
0
0
73.60
2
33
0
0
79.90
3
26
0
0
80.00
3
16
0
0
75.20
2
6
0
1
93.80
1
19
0
1
87.00
2
15
0
1
86.90
2
12
0
1
95.70
1
29
0
2
92.00
3
5
0
2
93.70
1
3
0
2
94.60
1
30
0
2
88.10
3
28
1
0
84.00
3
4
1
0
90.00
1
2
1
0
88.50
1
32
1
0
87.50
3
20
1
1
88.90
2
34
1
1
98.30
3
36
1
1
98.60
3
14
1
1
88.50
2
10
1
2
97.00
1
24
1
2
86.50
2
13
1
2
90.90
2
11
1
2
95.50
1
7
2
0
90.90
1
18
2
0
79.00
2
23
2
0
83.60
2
8
2
0
89.40
1
27
2
1
95.40
3
1
2
1
100.40
1
9
2
1
97.50
1
31
2
1
95.90
3
22
2
2
88.20
2
35
2
2
92.10
3
25
2
2
96.30
3
17
2
2
88.20
2

B2 Analysis with SPSS


The command file for SPSS is (*.sps) is as follows.

COMPUTE n1 = n * 2 .
EXECUTE .
COMPUTE p1 = p * 2 .
EXECUTE .
COMPUTE n2 = n1 * n1 .
EXECUTE .
COMPUTE p2 = p1 * p1 .
EXECUTE .
COMPUTE n1p1 = n1 * p1 .
EXECUTE .
COMPUTE b1 = 0 .
EXECUTE .
COMPUTE b2 = 0 .
EXECUTE .
COMPUTE b3 = 0 .
EXECUTE .
IF (block = 1) b1 = 1 .
EXECUTE .
IF (block = 2) b2 = 1 .
EXECUTE .
IF (block = 3) b3 = 1 .
EXECUTE .
REGRESSION
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI BCOV R ANOVA
/CRITERIA=PIN(.05) POUT(.10) CIN(95)
/NOORIGIN
/DEPENDENT yield
/METHOD=ENTER b1 b2 n1 p1 n2 p2 n1p1
/SAVE PRED MCIN RESID .

B3 Output with SPSS

The output of this SPSS program provides the following information:



- Multiple R 0.97366

- R Square 0.94802

- Adjusted R Square 0.93502

- Standard Error 1.68051


Analysis of Variance:
Degrees of Freedom
Sums of Squares
Mean Square
Regression
7
1442.18476
206.02639
Residual
28
79.07524
2.82412

F = 72.95253; Signif F = 0.0000




Variable
B
Std. Error B
95% C.I.
B
T
Sig T
B1
2.780952
0.721884
1.302240
4.259665
3.852
0.0006
B2
-5.966667
0.686066
-7.372008
-4.561325
-8.697
0.0000
N1
3.760714
0.657923
2.413020
5.108409
5.716
0.0000
P1
8.787798
0.657923
7.440103
10.135492
13.357
0.0000
N2
-0.531250
0.148538
-0.835515
-0.226985
-3.577
0.0013
P2
-1.553125
0.148538
-1.857390
-1.248860
-10.456
0.0000
N1P1
-0.230357
0.112284
-0.460360
-3.54136E-04
-2.052
0.0497
(Const.)
80.548810
0.830192
78.848238
82.249381
97.024
0.0000


B4 Calculation of eigenvalues and stationary point with SPSS

These commands cannot be given by clicking in the menus, but must be typed in the Syntax window.



MATRIX.
COMPUTE B= {3.760714 ; 8.787798} .
COMPUTE A= {-0.531250 , -0.1151785 ;
-0.1151785 , -1.553125 }.
COMPUTE STAT_P= - INV(A) * B/2 .
PRINT STAT_P .
COMPUTE EIGVALS= EVAL(A) .
PRINT EIGVALS .
END MATRIX.

The corresponding SAS command file (*.sas) contains the following code, where the data file is called: "quadr_ex.dat":


data;
infile 'c:\quadr_ex.dat';
input plotnr n yield;
n1 = n .
n2 = n * n;
run;
proc print;
run;
proc reg;
model yield= n1 n2 /p i clm ;
run;

B5 Output for calculation of eigenvalues and stationary point with SPSS

The output of these SPSS commands is:



Run MATRIX procedure:
STAT_P
2.973950337
2.608524015
EIGVALS
-.518428762
-1.565946238
------ END MATRIX -----

B6 Analysis with SAS

Assumed is that the data are in the file “ exam_np.dat ” .


data;
infile 'c:\ppi\exam_np.dat';
input plot n p yield block;
n1= 2*n ;
p1= 2*p;
n2=n1*n1;
p2=p1*p1;
n1p1=n1*p1;
if block =1 then b1=1;
else b1=0;
if block =2 then b2=1;
else b2=0;
if block =3 then b3=1;
else b3=0;
run;
proc print ;
run;
proc rsreg;
model yield = b1 b2 n1 p1 /covar=2;
run;

B7 Output with SAS

All relevant information can be found in the output as follows:

Coding Coefficients for the Independent Variables:


Factor
Subtracted off
Divided by
N1
2.000000
2.000000
P1
2.000000
2.000000

Response Surface for Variable YIELD:


- Response Mean 89.766667

- Root MSE 1.680511

- R-Square 0.9480

- Coef. of Variation 1.8721

Regression
d.f.
Type I SoS
R-Square
F-Ratio
Prob > F
Covariates
2
523.611667
0.3442
92.704
0.0000
Linear
2
561.800417
0.3693
99.5
0.0000
Quadratic
2
344.886250
0.2267
61.061
0.0000
Crossproduct
1
11.886429
0.0078
4.209
0.0497
Total Regress
7
1442.184762
0.9480
72.953
0.0000


d.f.
SoS
Mean Square
Total Regress
28
79.075238
2.824116


d.f.
Parameter estimate
Standard Error
T for H0 Parameter= 0
Prob>|T|
INTERCEPT
1
80.548810
0.830192
97.0
0.0000
N1
1
3.760714
0.657923
5.716
0.0000
P1
1
8.787798
0.657923
13.357
0.0000
N1*N1
1
-0.531250
0.148538
-3.577
0.0013
P1*N1
1
-0.230357
0.112284
-2.052
0.0497
P1*P1
1
-1.553125
0.148538
-10.456
0.0000
B1
1
2.780952
0.721884
3.852
0.0006
B2
1
-5.966667
0.686066
-8.697
0.0000


Factor
df
SoS
MS
F-ratio
Prob>F
N1
3
180.551429
60.183810
21.311
0.0000
P1
3
749.908095
249.969365
88.512
0.0000


Canonical Analysis of Response Surface (based on coded data):


Critical value
Factor
Coded
Uncoded
N1
0.486975
2.973950
P1
0.304262
2.608524

Predicted value at stationary point: 96.540583


Canonical Analysis of Response Surface (based on coded data):


Eigenvectors
Eigenvalues
N1
P1
-2.073715
0.993861
-0.110633
-6.263785
0.110633
0.993861

Stationary point is a maximum.



The illustration for Example 2 from the book is discussed in Part A.

The information on these pages were kindly provided by Dr Rob Verdooren, Statistical Advisor of Numico-Research B.V. For further information on the statistical aspects of the experiments, please email Dr Verdooren directly.

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