G. K. Bose D. N. R. Paul and K. Rahim

Ann. Bangladesh Agric.5(1) ^: 23-26, 1995

DISTRIBUTION PATTERN OF COEFFICIENT OF VARIATION OF SOMB BIOMETRIC CHARACTERS OF RICE

G. K. Bose D. N. R. Paul and K. Rahim

A g ricultural Statistics Division Banghdesh Rice Research lnstitute

Gazipur- I 70 l, Bangladesh

Abstract

Coefficient

of

variation

(Cv) of grain yield from

preliminary

yield trial

^(PYT)'

secondary

yield trial (SyT)

and regional

yield trial

(RYT)

of

varietal experiment ^and

grain

yield, straw yield, ^panicles

per

square meter,

tillers per

square meter and ^plant height

from fertilizer trials

were included

in this

study. 'l'hree tests

of

normality ^were employed

on

original

CV

and

CV

transformed

to

logarithmic scale. The tests were

a6;

fqr

skewness, Geary's

'a' for

^kurtosis

and

Shapiro-Wilk

W'test of

normality.

It

was observed

that CV for

grain yield

of

varietal

trial

^was lower than

that of

fertilizer trial.

Smallest

Cv

was observed

for plant

height. Results obtained

form the three

tests revealed

that for

the stated biometric characters

of

rice, the distribution

of

original ^CV was

very well to normal distribution

indicating

that the distribution of CV

^follows

lognormal.

Coefficient of CV). Distribution and Normalit

Introduction

In Agricultural ^research, coefficient of

variation, (CV) is widely

used

by

^the

researchers as a measure of reliability of ^{their ""}

experiments. By definition, CV ^is the standard

deviation as a

percentage

of

mean. In

experimental design it

expresses ^the experimental error as percentage of mean.

It

is

inversely related

to the reliability of

^the

experiment

i.

e., higher the value of CV, the

lower is the reliability

of

the experiment. In agricultural research, one

of

the objective of

the researchers

is

to compare the treatment means.

The CV

indicates

the

degree

of

precision with which treatments are compared (Gomez and Gomez,1984). CV is also used in growth and trend analysis of ^time series data for measuring variability and instability. Mitra

( 1989) used

CV

as an index

of

^measuring

instability of

agricultural prices

in

^West

Bengal. Singh (1989) used CV for ^measuring yield variability

of

main crops is India. ^For measuring variability of commercial ^{crops in} India CV was also employed by Kandaswamy

( r e88).

r

ts

The magnitude

of

CV depends on the type of experiment (e. g. varietal trial, fertilizer trial, insecticide trial), the crop grown (e. g.

wheat, pulses), growing season (e.g., aus, aman and boro in case of rice crop) and the

plant character meastired (e.g. yield, grain number, plant height). Our experience with the

field experiments with rice in the Bangladesh Rice Research Institute (BRRI) is that even fbr same type

of

experiments there exist ^wide variability of CV for a particular character

of rice plant. This

study was undertaken to investigate the extent of variations o CV and its probability distribution for some biometric characters of rice plant.

Methodology

Coefficient of variarion (CV)

for different rice plant characters were collected from the documentation files of Agricultural Statistics Division, BRRI.

For

the present study, data from varietal trials and fertilizer trials were considered. These were mainly experiments

of Plant

Breeding

and

Soil Chemistry Divisions.

A total

of

194 CVs for measuring grain yield

in

varietal trials were examined. These

' included 30 fiom preliminary yield trial (pyT), 87 from secondary yield rrial (SYT) and 77 from regional yield rrial (RyT).

A

total of 56

CV

was considered

for

measuring yields in fertilizer trials. CVs for.straw yield, panicles per square meter, tillers p€r sQusre meter and

plant height were examined from 34, 34, 39

and

25

cases, respectiyely, coming from fertilizer trials.

'

The

following

tests

of

normality on

original CV and CV transformed

to Iogarithmic scale were performed to identify the distribution of

CV.

^{f 'rt}

l.

Test of skewness and kurtosis

Let x _| , x2 ....xn be a random sampte of size n.

If

we define the

'' ' !*.

;r'*--,

Jnoments of the ohservation as

E t (;.-f)s

^r

$q '' %-', E:2

then, the statistics

/q- + t

e'

andb. t!

nr'

given an

indication

of the

shape

of

^the

distribution.

fif

measures the tendency of the

tails

of

the distribution

to

be larger

in

one

direction (negative/positive) than the other (negative/positive)

while b2

measures the peakedness

of the

distribution.

A

normal distribution is a smooth symmetric function otten referred to as "bell-shaped" and for this distribution the value of

rffand

b2 are zero and 3, respectively. Any departure of {U1 from zero

is an

indication

of

skewness while

departure of b2 from 3 indicates the departure

from

normality

in

terms

of

kurtosis. For samples less than 200 observations Geary

( 1936, 1947) has suggested

an

alternative statistic which may be used detecting changes

in kurtosis with accuracy than that of b2. This statistic is

Mean deviation

a=-

Standard deviation

For the normal population this ratio has the value 0.7979; the ratio

will

be higher for

platykurtic and lower for

leptokurtic distribution.

For different sample size the values

of {

^b1

and 'a' are available in the Biometrika Tables for Statistician (Pearson and Hartely, t958).

2. Shapiro-Wilk W-tesr of normality For a random sample x1, x2...xn, of size n Shapiro W-Statistic is defined as

) -'v'

'

'' i-t'aryrl'

flr l't --

f,{r.-fl.

A

ve smusucs o of variation (CV) fbr selected characters of rice

characrcr Mean stan(hlu

deviation

Minimum _Maxinrum Sample size

varietal trial

Total vield I l.l7 5.12 3.98 2E.3'i 194

PYT vield I t.88 5.83 4.il 28.37 30

STY vield I t.73 5.93 5.00 27.0O 87

RYT vield t0.34 3.82 3.98 25.00 77

Fertilizer trial

Cmin vield 10.24 4.73 2.43 3 r.00 56

Panicle/m2 9.25' 2.77 5.(x) t8.00 t4

Tiller no/m2 I 1.45 5.68 3.00 3 r.00 39

Straw yield r3.60 5.47 7.00 33.00 34

Plant heisht 6.23 4.40 2.00 10.00 25

Table I . Descriptive statistics of'coefficient

Table2. Test of normality of the distribution of original CV and CV rransformed ro logarithmic scale.

*

significant at 57o level.

**

significant at lvo level, ns Not significant.

Type of Trtal Character Test criterion Original CV CV trunsformed to

logarithmic scale

Varietaltrial Cmin yield (Total)

\r

^{I . I 9597x,* 0.27198ns}

a 0.79039ns 0.80056ns

w 0.862 l5x,'r, 0.9.5410ns

Crain yield (PYT)

\[

0.87072,t,,i, -0.34070ns

a 0.76912ns 0.66919{,{,

w 0.86430{,'r, L l4840ns

Cmin yield (SYT) .,f,"- ^{0.97072r* 0. I 9627ns}

a o.82ll5ns 0.81508ns

w 0.9 t550,i 0.94260ns

Grain yield (RYT)

,,/]il

^1.23933*,e O.0d294ns

a 0.7.5520x 0.7t303ns

w 0.891t0,x 0.93040ns

Fetilizer tdal Grain yield

1r

^{L59 t50{,* -0.04294ns}

a 0.74313,x,', 0.78289ns

w 0.97380ns 0.9491Ons

Panicle/m2

,tr

^{1.00805,r* 0,0l6l2ns}

a 4.76772ns 0.79099ns

w 0.92930r 0.97E90ns

Straw yield

,ffi

2.05041,r,t 0.75605*

a 0.67594** 0.79179ns

w 0.77E60'r,,n 0.92750ns

Tiller no./m2 _h. I.4l8M'r* -0.06888ns

a 0.74089* 0.49939 ns

w 0.89170'i* 0.9uu40ns

Plant height _l.. 1.t3250'r,,r, 0.7E027ns

a 0.72636* 0.78027ns

w 0.77650{,4 0.05000ns

a

_J-

where yl < .. < Yn, the

^ordered

observations

of

the random sample. Shapiro

and Wilk (1965)

describes

the

detailed computational procedure

of

W-statistic and values of ai coefficients for different sample sizes are also available in their paper.

Results and

discussion

The descriptive statistics of ^the CV for

selected rice characters are shown in Table l. ^In all cases the range of CV was large. For grain yield, the range of CV was found to be higher in t'ertilizer trials (2-3lVo) than in varietal trials (4-29Vo). A similar trend in CV values of yield data trom t'ertilizer and verietal trial was also reported by Gomez and Gomez (1984). They observed lowest

CV for

plant height which was also true from our observation where plant height ranged ftom 2 to lOVo. The range of CV fbr panicle number,

tiller

number and straw yield was fbund to be 5 to 18, 3 to

3l

and 7 to 337o, respectively.

The observed value and significant level

of

the tcst statistics

^E

'a' and

W of

the

original CV and CV transformed

to Iogarithmic scale for the selected characters ol rice are shown

in

Table

2. ln all

^cases

of

varietal and fertilizer trial the values of

fil1

was positive and highly significant for original CV, indicating positively skewed distribution

of

original

CV.

On the other hand, results obtained by applying the same statistic on CV transfbrmed to logarithmic scale showed that

the distribution of CV for the

selected biometric characters of rice except for straw yield in t'ertilizer trial could well be considered to be symmetric.

The value of 'a' statistic revealed that the

distribution

of

original

CV

departed from normality in terms of kurtosis only in case of grain yield data from BYT. In ^case of fertilizer trial original CV

of

all characters except for

panicle/m"

)

departed from normality in terms of kurtosis. On the other hand, by applying ^'a' statistic on transfbrmed CV, only grain yield fiom PYT was fbund to depart from normality in terms of kurtosis.

Shapiro-Wilk W-test

declared the distribution

of

original CV

of all

characters under study to be non-norrnal except for grain yield data of fertilizer trial. But the distribution of CV appeared to be normal in all cases from the same test on

CV

values transformed to logarithmic scale. These results indicated log- normal distribution to be a good representation

of the distribution of CV.

References

Geary,

R.C.

1936. The

ratio of

the mean deviation to the standard deviation as a test

of

normality. Biometrika. 27:310- 332.

Geary,

R. C.

1947. Testing

for

normality.

B i ometrik a. 34:2A9 -242.

Gomez,

K. A. and A.A. Gomez.

1984.

Statistical Procedure

for

Agricultural

Research. 2nd ed.

(lst

ed. 1976). John

Wiley

&

Sons. USA.

Kandaswamy,

A.

1988. Commercial Crops in India. Indian J.

Agril.

Econ. 43:444- 445.

Mitra,

T.K.

1989. Growth and Instability

of

Agricultural Prices

in

West Bengal.

'

_{Indian J. Agril.} Econ. 44:67-71.

Pearson,

E. S.

and

H. O. Hartely.

1962.

Biometrika Tables

for

Statisticians,

Vol. l, 2nd ed.

^{( I}

st ed.

^1956).

Cambridge University Press. London.

Shapiro, S.S.

and M.B. Wilk.

1965. An analysis of Variance test fbr Normality

(Complete Samples).

Biometrika,

52:591-61

l.

Singh,

I.J.

1989. Agricultural Instability and Farm Poverty in India. Indian J. Agril.

Econ. 44: l-16.

x