Experimental designs and data analysis in the field of soil science by making use of sophisticated software

Experimental designs and data
analysis in the field of soil science by
making use of sophisticated software
Dr K.B Singh
Principal Soil Physicist

Experimental designs play an important role in research. To analyse data
with different statistical designs, package of computer programs named
'CPCS1', has been used. CPCS1 includes the programs for the analysis of
the following experimental designs.
a) Completely Randomised Designs (CRD)
b) Randomised Block Designs (RBD)
c) Split Plot Designs (SPD)
d) Factorial Experiments in CRD/RBD
e) Factorial Experiments in SPD
f) RBD with missing data

The source programs of CPCS1 have been written in FORTRAN 77
computer language and compiled on an IBM compatible Personal
Computer (PC).This package can be run on an IBM compatible PC. CPCS1
includes the following files.
Data input/output file name:
When you get the message on the screen
• GIVE DATA FILE NAME
Type your data file name along with its source i.e. drive/ directory name.
For example, if you have a data file named HSC1.DAT on the hard disc C in
the directory named DAT, then type
C:DATHSC1.DAT and press 'Enter' key

This will be followed by the message on the screen
GIVE FILE/DEVICE NAME FOR OUTPUT
You can opt for any one of the three devices used for output viz.
console/screen, printer or file on a particular disc drive.
a) If the output is to be obtained on the screen
type CON and press 'Enter' key
Note: If the output is of more than 23 lines, the last 23 lines will be
displyed on the screen and the rest would be lost while screen will scroll.
If the output is to be obtained directly on the printer
type PRN and press 'Enter' key
Note: Before typing PRN the printer should be ready with paper properly
in place.

c) If the output is to be written on to a file on a hard disc type a new file
name along with its source i.e. drive/directory name.
Any number of data sets of similar type can be punched in one data file.
Output of all the data sets can be obtained by executing the program once
if data is punch correctly according to the format of the design used.
The values of the input parameters pertaining to whole numbers must be
non-negative integers without decimal point e.g. in case of RBD if there
are fifteen treatments, the value of the parameter NT (number of
treatments) must be entered 15 and not 15. or 15.0

Analysis of Completely Randomised Design
The program computes necessary statistics concerning analysis of
variance for Completely Randomised Designš(CRD) with equal or unequal
number of replications. Analysis of the data pooled over environments is
also provided.
Data can be analysed using arcsine, square root, natural logarithm or
kilograms per plot to quintals per hactare transformations, if desired. The
program can also be used for t©test.
Format of data input:
Perform the following steps to punch/record data in a file on a
floppy/hard disc. This file is called data file or data input file.

Case I For equal number of replications
Step 1 Identification of the data set : First line of the
data is provided for identification of the data
set of which first 80 columns will be reproduced
as such in the output.
Step 2 Parameters of the data set : Values of the
following parameters are to be supplied in
second line of the data set in the given order with at least one blank among
them
NR = Number of replications
NT = Number of treatments
NE = Number of environments (NE = 1, when pooled
analysis is not required)
JT = 0, when transformation is not required
= 1, for transformation from kg/plot to q/ha
= 2, for arcsine transformation
= 3, for square root (n+1) transformation
= 4, for natural logarithmic transformation
PS = Area of plot in square metres when JT = 1
= 0, otherwise

Step 3 From third line onwards, environment wise data of the set are to be
supplied for all treatments giving serial number and values of all the
replications for each treatment in one line.
Step 4 Repeat steps 1 to 3 for more sets of data.
Case II For unequal number of replications
Step 1 Same as that of case I
Step 2 Same as that of case I except that the value of the parameter
NR = 0 in this case
step 3 From third line onwards data of the set are to be supplied for all the
treatments giving serial number, number of replications and values of all
the replications for each treatment in one line.

Experimental designs and data analysis in the field of soil science by making use of sophisticated software

For unequal number of replications
Given below are the data of an experiment conducted
in CRD having eight treatments with 2, 4, 3, 5, 4, 3, 5
and 4 number of replications šrespectively.
Contents of data input file :
SET 1
0 8 1 0 0
1 2 15 17.2
2 4 21.2 22 19.1 20.5
3 3 13.6 14.1 17
4 5 12.0 10.9 13 11.7 14.4
5 4 9.8 11.5 11.2 10.5
6 3 17.2 16.4 19
7 5 11.6 9.8 12.4 10.8 14
8 4 8.8 11 9.2 10

Contents of the output :
SET 1
Analysis of CRD with unequal no. of replications
TREATMENT MEANS
1 16.100000 20.700000 14.900000 12.40¬0000 10.750000
6 17.533330 11.720000 9.7500000
ANOVA TABLE
SOURCE d.f. M.S. F-Ratio S/NS(5%) G.M. C.V.
Treatments 7 54.384070 30.46 S
Error 22 1.7852230 13.830000 9.66
Note: The calculation of C.D.(5%) has been avoided for the
case of unequal replications as C.D. changes with
the change in pair of treatment šmeans.

Application of the program for t-test
Example
For a random sample of 10 pigs fed on diet A and an
other random sample of 12 pigs fed on diet B, the following increase in
the weight was recorded. Test whether diet
A differs significantly from diet B.
Contents of data input file :
Data on increase in weight for t©test
0 2 1 0 0
1 10 15 9 8 14 12 13 16 17 10 6
2 12 21 23 10 17 18 8 12 14 7 13 22 15
Contents of output :
SOURCE d.f. M.S. F-Ratio S/NS(5%) G.M. C.V.
Treatments 1 49.090820 2.26 NS
Error 20 21.700000 13.636360 34.16

Analysis of Randomised Block Design
Step 1 Identification of the data set : First line of the data is provided for identification
of the data set of which first 80 columns will be reproduced as such in the output.
Step 2 Parameters of the data set : Values of the following parameters are to be
supplied in second line of the data set in the given order with at least one blank among
them.
NR = Number of replications
NT = Number of treatments
NE = Number of environments (NE = 1, when pooled
analysis is not required)
JT = 0, when transformation is not required
= 1, for transformation from kg/plot to q/ha
= 2, for arcsine transformation
= 3, for square root (n+1) transformation
= 4, for natural logrithmic transformation
PS = Area of plot in square metres when JT = 1 = 0, otherwise
Step 3 From third line onwards, environment wise data of the set are to be supplied
for all treatments giving serial number and values of all the replications for each
treatment in one line.

Example
The data on blood pressure of 12 patients before and after administering a stimulus was
recorded. Can it be concluded that the stimulus has a significant effect on the change in blood
pressure.
Data on blood pressure for paired t-test
12 2 1 0 0
1 75 80 77 85 82 79 78 83 85 86 90 82
2 80 82 85 88 81 79 84 81 84 91 90 86
Data on blood pressure for paired t-test
NR =12 NT = 2 NE = 1
Analysis of RBD
TREATMENT MEANS
1 81.833340 84.250000
REPLICATION MEANS
1 77.500000 81.000000 81.000000 86.50¬0000 81.500000
6 79.000000 81.000000 82.000000 84.50¬0000 88.500000
11 90.000000 84.000000
ANOVA TABLE
SOURCE d.f. M.S. F-Ratio CD(5%) G.M. C.V.
Replicates 11 28.406250 5.44 5.02763
Treatments 1 35.052080 6.71 2.05252
Error 11 5.2225380 83.041660 2.75

Analysis of Split Plot Designs
The program facilitates to perform the analysis for single split plot, double split plot
etc. upto a maximum of five split plot designs. Analysis of the data pooled over en-
vironments can also be carried out by taking environments as levels of the main factor
and increasing the number of factors by one in the data input. Data can be analysed
using arcsine, square root, natural logarithm or kil¬lograms per plot to quintels per
hactare transformations if
desired.
Perform following steps
Step 1 Identification of the data set : First line of the data is provided for identification
of the data set of which first 80 columns will be reproduced as such in the output.
Step 2 Parameters of the data set : Values of the following parameters are to be
supplied in second line of the data set in the given order with at least one blank among
them. NR = Number of replications, NF = Number of factors
NL(J) = Number of levels of J th factor ( J = 1,2,3,...,NF)
JT = 0, when transformation is not required, =1, for transformation from kg/plot to
q/ha, = 2, for arcsine transformation, = 3, for square root (n+1) transformation
= 4, for natural logrithmic transformation
PS = Area of plot in square metres when JT = 1 and = 0, otherwise

Step 3 From third line onwards, data of the set are to be supplied for all treatment
combinations starting with first level of each factor and varying all levels of last factor
first, then the last but one factor and so on, giving serial number and values
of all the replications for each treatment combination in one line.
Example In an experiment on mustard using split plot design, two levels of irrigation
in main plots and three levels of fertilizer in sub plots with three replications, the data
on yield for two years are given below.
Yield data (q/ha) on Mustard (year1)
3 2 2 3 0 0
11 7.7 6.3 3.5
12 9.0 10.2 8
13 15.1 16.2 14
21 6.8 3.3 3.2
22 14.5 9.5 11
23 19.5 15 17
Year 2
3 2 2 3 0 0
11 4.8 4.7 4.3
12 6.2 6.7 5.8
13 14.5 12.8 14.8
21 6.3 3.7 4.8
22 12.3 11. 10.8

23 18.3 16 14.2
Pooled over two years
3 3 2 2 3 0 0
11 7.7 6.3 3.5
12 9.0 10.2 8
13 15.1 16.2 14
21 6.8 3.3 3.2
22 14.5 9.5 11
23 19.5 15 17
11 4.8 4.7 4.3
12 6.2 6.7 5.8
13 14.5 12.8 14.8
21 6.3 3.7 4.8
22 12.3 11. 10.8
23 18.3 16 14.2

Contents of output :
Yield data (q/ha) on Mustard (year1)
No. of reps.= 3 No. of factors= 2
Analysis of Split Plot Design
TREAT. COMBINATION MEANS
1 5.8333330 9.0666670 15.100000 4.433¬3330 11.666670
6 17.166670
FACTOR MEANS
1 10.000000 11.088890
2 5.1333330 10.366670 16.133330
ANOVA TABLE
SOURCE d.f. M.S. F-Ratio CD(5%) C.V.
Reps. 2 11.490520 1.31
A 1 5.3355310 .61 NS
Error a 2 8.7904850 28.12
B 2 181.64220 281.01 1.07063
AB 2 7.0755620 10.95 1.51410
Error b 8 .64638160 7.62
---------------------------------------------------------------------------

Year 2
1 4.6000000 6.2333340 14.033330 4.9333330 11.366670
6 16.166670
FACTOR MEANS
1 8.2888890 10.822220
2 4.7666670 8.8000000 15.100000
ANOVA TABLE
Reps. 2 3.2105920 1.68
A 1 28.879900 15.11 NS
Error a 2 1.9117770 14.47
B 2 162.73560 224.13 1.13472
AB 2 8.8199770 12.15 1.60474
Error b 8 .72608740 8.92
---------------------------------------------------------------------------

Pooled over years
1 5.8333330 9.0666670 15.100000 4.4333330 11.666670
6 17.166670 4.6000000 6.2333340 14.033330 4.9333330
11 11.366670 16.166670
FACTOR MEANS
1 10.544450 9.5555550
2 9.1444440 10.955560
3 4.9500000 9.5833330 15.616670
ANOVA TABLE
Reps. 2 13.293860 9.45
A 1 8.8021370 6.26 NS
Error a 2 1.4070360 11.80
B 1 29.522190 5.52 NS
AB 1 4.6930890 .88 NS
Error b 4 5.3512110 23.02
C 2 343.29350 500.25 .716619
AC 2 1.0841060 1.58 NS
BC 2 14.707310 21.43 1.01345
ABC 2 1.1882930 1.73 NS
Error c 16 .68624850 8.24

Use of Excel Sheet for analysis

Experimental designs and data analysis in the field of soil science by making use of sophisticated software

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