DESIGNS FOR CROP SEQUENCE EXPERIMENTS: A CASE ... - IASRI

DESIGNS FOR CROP SEQUENCE EXPERIMENTS:
A CASE STUDY
Rajender Parsad and V.K. Gupta
I.A.S.R.I., Library Avenue, Pusa, New Delhi – 110 012
rajender@iasri.res.in; vkgupta@iasri.res.in
1. Introduction
In Indian National Agricultural Research System (NARS), many experiments are conducted for
cropping systems research wherein a crop sequence of two crops is grown; one in Kharif season
followed by another in Rabi season. More than two crops may also be grown in crop sequence
experiment, but we focus our attention to only two crops grown in the sequence. The extension
to three crops would follow naturally. In these experiments two different sets of treatments are
applied in succession with one set applied in Kharif crop and the other set applied in Rabi crop.
The observations are recorded in both the crop seasons. In two-crop sequence experiments, the
interest of the experimenter is in direct effects of treatments applied in Kharif and Rabi season
and residual effects of Kharif treatments. The interaction between the residual effect of Kharif
crop treatments and the direct effect of Rabi crop treatments may or may not be of interest to the
experimenter. These experiments may be run in a block design to account for the variability in
the experimental material.
Crop sequence experiments run in block designs can be viewed as block designs with factorial
structure of treatments. For example if m treatments are applied in the Kharif crop and n
treatments are applied in the Rabi crop, then on the application of n treatments in the Rabi crop, a
maximum of mn treatment combinations may appear and the treatment structure is factorial in
nature. These experiments are classified into two broad categories. Category I experiments are
those in which all the possible mn treatment combinations applied in both the crops are taken for
experimentation; in other words, one has a complete factorial experiment run in a block design.
In these experiments, the interaction between the residual effect of Kharif crop treatments and
the direct effect of Rabi crop treatments are also of interest to the experimenter. Category II
experiments are similar to the category I experiments with the difference that after the
application of n treatments in the second crop, all the mn treatment combinations do not appear.
In other words, it is a fractional factorial plan rather than a complete factorial experiment run in a
block design. Further, the interaction between residual effect of Kharif treatments and direct
effect of Rabi treatments is not of interest to the experimenter.
Experimental Situation 1: An experiment on Rice-Wheat sequence was conducted in the Division
of Agronomy, IARI, New Delhi. During the Karif crop (Rice), 5 herbicidal treatments, denoted as
1, 2, 3, 4, 5 were applied. On the following Rabi crop (Wheat), 4 herbicidal treatments, denoted as
a, b, c, d, were given. The purpose of the experiment was (i) to compare direct effects of Kharif
and Rabi treatments, (ii) residual effects of Kharif treatments, and (iii) interaction between residual
effects of Kharif and direct effects of Rabi treatments.
The design recommended and adopted was a resolvable rectangular design with v = 5×4 (=20), b
= 6, r = 3 and k = 10. Blocks 1 and 2 form first replication, blocks 3 and 4 form the second
replication and blocks 5 and 6 form the third replication. This design has a factorial treatment

Designs for Crop Sequence Experiments: A Case Study
structure with two factors, one at 5 levels and the other at 4 levels. Relative efficiencies of main
effect of first factor (residual effect of Kharif treatments), main effect of second factor (direct
effect of Rabi treatments) and interaction of first and second factors as compared to the
randomized complete block design are ∈(10)=1, ∈(01)=2/3, ∈(11) = 1, respectively. The layout
of the design is
Replication I Replication II Replication III
Block 1 Block 2 Block 3 Block 4 Block 5 Block 6
1a 1c 1a 1b 1b 1a
2a 2c 2a 2b 2b 2a
3a 3c 3a 3b 3b 3a
4a 4c 4a 4b 4b 4a
5a 5c 5a 5b 5b 5a
1b 1d 1d 1c 1d 1c
2b 2d 2d 2c 2d 2c
3b 3d 3d 3c 3d 3c
4b 4d 4d 4c 4d 4c
5b 5d 5d 5c 5d 5c
The analysis of the data generated from such an experiment is:
ANOVA for resolvable design (YEAR I)
Kharif Season
Rabi Season
Source DF Source DF
Between Blocks 5 Between Blocks 5
Kharif Treatments 4 Residual (Kharif Treatments) 4
Error 50 Direct (Rabi Treatments) 3
Total 59 Residual * Direct 12
Error 35
Total 59
If same randomization on same experimental area is followed in second year, then one can
analyze the data as
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Designs for Crop Sequence Experiments: A Case Study
ANOVA for resolvable design (YEAR II)
Kharif Season
Rabi Season
Source DF Source DF
Between Blocks 5 Between Blocks 5
Residual (RabiTreatments) 3 Residual (Kharif Treatments) 4
Direct (Kharif Treatments) 4 Direct (Rabi) 3
Residual * Direct 12 Residual * Direct 12
Error 35 Error 35
Total 59 Total 59
The best treatment can be picked through the usual block design analysis as below. The steps for
analysis of data on test weight of wheat crop is given as:
data egdgopi;
input rep blk kh rabi $ trt tw;
/*rep=replication, blk=block, kh=kharif, rabi=Rabi, trt=treatment, tw=test
weight of wheat*/
cards;
1 1 3 a 9 40.33
1 1 4 b 14 40.8
1 1 1 b 2 40.66
1 1 5 a 17 40.22
1 1 2 b 6 39.9
1 1 5 b 18 41.3
1 1 4 a 13 40.2
1 1 2 a 5 41.15
1 1 1 a 1 41.2
1 1 3 b 10 40.75
1 2 2 a 5 39.9
1 2 3 c 11 41.75
1 2 1 a 1 38.48
1 2 5 a 17 40.04
1 2 4 c 15 40.72
1 2 5 c 19 41.15
1 2 1 c 3 41.76
1 2 2 c 7 41.03
1 2 3 a 9 39.44
1 2 4 a 13 39.4
2 3 4 d 16 39.03
2 3 2 a 5 40.2
2 3 5 a 17 40.12
2 3 5 d 20 40
2 3 3 d 12 38.78
2 3 3 a 9 40.55
2 3 1 a 1 40
2 3 2 d 8 38.89
2 3 1 d 4 39.27
2 3 4 a 13 39.32
2 4 3 b 10 41
2 4 4 c 15 42.8
2 4 2 b 6 41.26
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Designs for Crop Sequence Experiments: A Case Study
2 4 1 b 2 39.95
2 4 5 b 18 40.65
2 4 5 c 19 41.25
2 4 2 c 7 41.4
2 4 3 c 11 40.95
2 4 4 b 14 40.83
2 4 1 c 3 41.44
3 5 1 b 2 40.7
3 5 3 b 10 40.18
3 5 2 d 8 37.62
3 5 2 b 6 40.46
3 5 4 d 16 38.96
3 5 4 b 14 39.8
3 5 1 d 4 37.36
3 5 3 d 12 39.00
3 5 5 b 18 40.52
3 5 5 d 20 38.1
3 6 1 d 4 39.15
3 6 4 d 16 39.1
3 6 2 c 7 42.6
3 6 3 c 11 41.92
3 6 2 d 8 39.96
3 6 3 d 12 38.77
3 6 1 c 3 41.07
3 6 4 c 15 43.54
3 6 5 d 20 39.22
3 6 5 c 19 40.05
;
proc glm;
class rep blk trt kh rabi;
model tw = rep blk(rep) kh rabi kh*rabi/ss3;
means kh rabi kh*rabi/lsd;
lsmeans rabi rabi kh*rabi/pdiff lines;
lsmeans rabi rabi kh*rabi/pdiff slice =rabi;
run;
proc glm;
class rep blk trt kh rabi;
model tw = rep blk(rep) trt/ss3;
means kh rabi kh*rabi/lsd;
lsmeans rabi rabi kh*rabi/pdiff lines;
lsmeans rabi rabi kh*rabi/pdiff slice =rabi;
run;
The data on next year rice and wheat can also be analysed similarly.
Some References
Gupta, V.K. and Parsad, Rajender (2009). Block Designs for Cropping Systems Research.
NAAS News. 8(2), 3-7.
Parsad, Rajender, Gupta, V.K. and Srivastava, R. (2007). Designs for cropping systems research.
Journal of Statistical Planning and Inference, 137, 1687-1703.
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