 |
Analysis of Data from Designed Experiments |
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|
Partially Confounded Factorial Experiment |
Analysis Using SPSS
Analysis Using SAS
To test the equality of treatment combinations and identification of best treatment combination requires analysis to be performed on treatment combinations. Therefore, 27 treatment combinations are recoded as:
|
V |
N |
P |
Treatment
(renumbered) |
|
V |
N |
P |
Treatment
(renumbered) |
|
1 |
1 |
1 |
1 |
2 |
2 |
3 |
15 |
|
|
1 |
1 |
2 |
2 |
2 |
3 |
1 |
16 |
|
|
1 |
1 |
3 |
3 |
2 |
3 |
2 |
17 |
|
|
1 |
2 |
1 |
4 |
2 |
3 |
3 |
18 |
|
|
1 |
2 |
2 |
5 |
3 |
1 |
1 |
19 |
|
|
1 |
2 |
3 |
6 |
3 |
1 |
2 |
20 |
|
|
1 |
3 |
1 |
7 |
3 |
1 |
3 |
21 |
|
|
1 |
3 |
2 |
8 |
3 |
2 |
1 |
22 |
|
|
1 |
3 |
3 |
9 |
3 |
2 |
2 |
23 |
|
|
2 |
1 |
1 |
10 |
3 |
2 |
3 |
24 |
|
|
2 |
1 |
2 |
11 |
3 |
3 |
1 |
25 |
|
|
2 |
1 |
3 |
12 |
3 |
3 |
2 |
26 |
|
|
2 |
2 |
1 |
13 |
3 |
3 |
3 |
27 |
|
|
2 |
2 |
2 |
14 |
|
|
|
|
The analysis of the data is performed using PROC GLM of SAS. The SAS commands are given in the sequel.
Data
Input:
For performing analysis, input the data in the following format.
{Here Replication is termed as REP, block as blk, three factors as V, N and P and treatment as TRT. It may, however, be noted that one can retain the same name or can code in any other fashion}.
data
confound; /*one
can enter any other name for data*/
input
rep blk v n p trt yield;
cards;
1
1
2
1
2
1
0.50
1
1
1
2
2
2
0.97
1
1
2
2
3
3
0.75
1
1
3
1
3
4
1.21
1
1
1
3
3
5
1.23
1
1
3
2
1
6
0.98
1
1
2
3
1
7
1.10
1
1
3
3
2
8
1.00
1
1
1
1
1
9
0.50
1
2
2
1
1
10
0.49
1
2
1
2
1
11
0.97
1
2
2
2
2
12
0.98
1
2
3
1
2
13
0.81
1
2
1
3
2
14
1.13
1
2
3
2
3
15
1.67
1
2
2
3
3
16
1.40
1
2
3
3
1
17
1.00
1
2
1
1
3
18
0.73
1
3
2
1
3
19
0.60
1
3
1
2
3
20
1.10
1
3
2
2
1
21
0.70
1
3
3
1
1
22
0.74
1
3
1
3
1
23
1.08
1
3
3
2
2
24
1.40
1
3
2
3
2
25
1.35
1
3
3
3
3
26
2.00
1
3
1
1
2
27
0.60
2
1
1
1
1
1
0.48
2
1
1
2
3
2
1.25
2
1
2
3
1
3
0.93
2
1
3
3
3
4
2.00
2
1
1
3
2
5
1.35
2
1
3
2
1
6
1.30
2
1
2
1
3
7
0.64
2
1
2
2
2
8
0.85
2
1
3
1
2
9
1.16
2
2
2
1
2
10
0.50
2
2
2
3
3
11
1.45
2
2
1
3
1
12
1.32
2
2
1
1
3
13
0.85
2
2
2
2
1
14
0.70
2
2
3
2
3
15
1.92
2
2
3
3
2
16
2.00
2
2
3
1
1
17
1.07
2
2
1
2
2
18
1.00
2
3
1
2
1
19
0.87
2
3
1
1
2
20
0.65
2
3
3
1
3
21
1.30
2
3
1
3
3
22
1.55
2
3
2
1
1
23
0.45
2
3
3
2
2
24
1.85
2
3
3
3
1
25
2.00
2
3
2
2
3
26
1.25
2
3
2
3
2
27
1.40
;
/*If one is interested in answering first two questions, then there is no need of recoding the treatment combinations and adding the variable TRT in input.
For
testing significance of main effects and interaction effects
and performing pairwise comparison of single factor level
means and means of 2- factors and 3-factors, use the
following steps:
proc glm;
class rep blk v n p;
model yield =rep blk(rep) v n
p v*n v*p n*p v*n*p;
means v n p v*n v*p n*p v*n*p/lsd;
lsmeans v n p v*n v*p n*p v*n*p/pdiff;
run;
/*Here, the main effects are not confounded, therefore, LSD for means of single factor level comparisons has been obtained. In the absence of knowledge of confounded or unconfounded factorial effects, one may directly perform pair wise effect comparisons using LSMEANS statement alongwith pdiff option.
LSD option under means statement gives LSD value only for comparing single factor level means and not for the means of the level combination of 2 or 3 factors. For performing such comparisons LSMEANS statement with PDIFF option may be used.
One
may use a host of multiple comparison procedures under the
options in MEANS statement viz. Least Significant
Difference (LSD), Duncan’s New multiple - range test (
For testing the significance of treatment combination, identification of best treatment combination and for contrast analysis one may use the following: */
proc glm;
class rep blk trt;
model yield= rep blk(rep) trt;
lsmeans trt/pdiff;
run;
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For exposure on SAS, SPSS,
MINITAB, SYSTAT and
MS-EXCEL for analysis of
data from designed experiments:
Please see Module I of Electronic Book II: Advances in Data Analytical Techniques
available at Design Resource Server (www.iasri.res.in/design)