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Analysis of Data from Designed Experiments |
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Randomized Complete Block Design |
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Analysis Using SAS
To answer the
question whether the performance of check varieties is
significantly different from strains, treatment contrast analysis
is to be performed Therefore, for ease of
understanding, recode
the varieties from 1 to 24 as follows:
|
Strain |
Code |
Number Code |
|
RK-04-3 |
MCN-04-110 |
1 |
|
RK-04-4 |
MCN-04-111 |
2 |
|
RGN-124 |
MCN-04-112 |
3 |
|
HYT-27 |
MCN-04-113 |
4 |
|
PBR-275 |
MCN-04-114 |
5 |
|
HUJM-03-03 |
MCN-04-115 |
6 |
|
RGN-123 |
MCN-04-116 |
7 |
|
BIO-13-01 |
MCN-04-117 |
8 |
|
RH-0115 |
MCN-04-118 |
9 |
|
RH-0213 |
MCN-04-119 |
10 |
|
NRCDR-05 |
MCN-04-120 |
11 |
|
NRC-323-1 |
MCN-04-121 |
12 |
|
RRN-596 |
MCN-04-122 |
13 |
|
RRN-597 |
MCN-04-123 |
14 |
|
CS-234-2 |
MCN-04-124 |
15 |
|
RM-109 |
MCN-04-125 |
16 |
|
BAUSM-2000 |
MCN-04-126 |
17 |
|
NPJ-99 |
MCN-04-127 |
18 |
|
SWARNA JYOTI(ZC)
|
MCN-04-128 |
19 |
|
VARDAN (NC) |
MCN-04-129 |
20 |
|
PR-2003-27 |
MCN-04-130 |
21 |
|
VARUNA (NC) |
MCN-04-131 |
22 |
|
PR-2003-30 |
MCN-04-132 |
23 |
|
KRANTI-(NC) |
MCN-04-133 |
24 |
To test equality of treatment effects, analysis using SAS may be performed using the following steps:
Data
Input:
For
performing analysis, input the data in the following
format.
{Here we call the strain codes as treatments: TRT, strain number as Treatment Number: TRTN, Replication: REP. It may, however, be noted that one can retain the same name or can code in any other fashion}.
Prepare a SAS data file using
Data
rbd; /*one can enter any other name
for Data*/;
Input
TRT $ 11.
TRTN REP YIELD;
*here
11. represents that the value of the variable trt is upto 11
columns;
Cards;
MCN-04-110
1
1
1539.69
MCN-04-111 2
1
1261.85
MCN-04-112 3
1
1389.19
MCN-04-113 4
1
1192.39
MCN-04-114 5
1
1250.27
MCN-04-115 6
1
1296.58
MCN-04-116 7
1
1227.12
MCN-04-117 8
1
1273.43
MCN-04-118 9
1
1180.82
MCN-04-119 10
1
1296.58
MCN-04-120 11
1
1122.93
MCN-04-121 12
1
1250.27
MCN-04-122 13
1
1180.82
MCN-04-123 14
1
1146.09
MCN-04-124 15
1
1574.42
MCN-04-125 16
1
914.55
MCN-04-126 17
1
891.4
MCN-04-127 18
1
1227.12
MCN-04-128 19
1
1389.19
MCN-04-129 20
1
1331.31
MCN-04-130 21
1
1250.27
MCN-04-131 22
1
717.75
MCN-04-132 23
1
1169.24
MCN-04-133 24
1
1203.97
MCN-04-110 1
2
1412.35
MCN-04-111 2
2
1065.05
MCN-04-112 3
2
1516.54
MCN-04-113 4
2
1215.55
MCN-04-114 5
2
1203.97
MCN-04-115 6
2
1273.43
MCN-04-116 7
2
1018.74
MCN-04-117 8
2
1157.66
MCN-04-118 9
2
1203.97
MCN-04-119 10
2
1458.65
MCN-04-120 11
2
1065.05
MCN-04-121 12
2
926.13
MCN-04-122 13
2
1053.47
MCN-04-123 14
2
1180.82
MCN-04-124 15
2
1412.35
MCN-04-125 16
2
972.44
MCN-04-126 17
2
937.71
MCN-04-127 18
2
1203.97
MCN-04-128 19
2
1180.82
MCN-04-129 20
2
1157.66
MCN-04-130 21
2
1250.27
MCN-04-131 22
2
740.9
MCN-04-132 23
2
1157.66
MCN-04-133 24
2
1296.58
MCN-04-110 1
3
1319.73
MCN-04-111 2
3
1111.36
MCN-04-112 3
3
1203.97
MCN-04-113 4
3
1157.66
MCN-04-114 5
3
1366.04
MCN-04-115 6
3
1308.16
MCN-04-116 7
3
937.71
MCN-04-117 8
3
1088.2
MCN-04-118 9
3
1041.9
MCN-04-119 10
3
1250.27
MCN-04-120 11
3
1018.74
MCN-04-121 12
3
1030.32
MCN-04-122 13
3
717.75
MCN-04-123 14
3
856.67
MCN-04-124 15
3
1597.57
MCN-04-125 16
3
659.87
MCN-04-126 17
3
798.79
MCN-04-127 18
3
1389.19
MCN-04-128 19
3
1273.43
MCN-04-129 20
3
1180.82
MCN-04-130 21
3
1296.58
MCN-04-131 22
3
578.83
MCN-04-132 23
3
1111.36
MCN-04-133 24
3
1250.27
;
*To test the equality of treatment effects, one can perform the analysis of variance using the following statements;
PROC
ANOVA;
Class
REP TRTN;
Model YIELD = REP TRTN;
Run;
/*One can obtain means of treatments and all possible pair wise treatment comparisons can be performed using any of the multiple comparison procedures such as least significant difference, Duncan’s New Multiple range test, Tukey's Honest Significant difference test by using the following statements:*/
PROC
ANOVA;
Class
REP TRTN;
Model Yield = REP TRTN;
Means TRTN/LSD; /*performs all possible pairwise
treatment comparisons using LSD*/
Means TRTN/DUNCAN; /*performs all possible
pairwise treatment comparisons using Duncan's Multiple Range
Test*/
Means
TRTN/Tukey; /*performs
all possible pairwise treatment comparisons using Tukey's
HSD. For controlling the family error rate, it is advisable to perform these comparisons using Tukey's HSD*/;
Run;
/*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
(DUNCAN), Waller - Duncan (WALLER) test, Tukey’s Honest
Significant Difference (TUKEY). The LSD, DUNCAN and
TUKEY options takes level of significance ALPHA = 5% unless
ALPHA = options is specified. Only ALPHA = 1%, 5% and
10% are allowed with the Duncan’s test. 95%
Confidence intervals about means can be obtained using CLM
option under MEANS statement.
Contrast analysis can not be performed using PROC ANOVA, therefore, one has to use PROC GLM. This can be done using the following steps.
Note: Here we want to test
*/
* The following SAS statements can be made use of ;
PROC
GLM;
Class
REP TRTN;
Model YIELD = REP TRTN;
Contrast
'check vs varieties' TRTN 4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
-20
-20
4
-20
4
-20;
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)