IMS   Sponsored Mini-meeting on

“Statistics in Social Science and Agricultural Research”

December 20-21, 2003

Santiniketan, India

Venue : Conference Hall, Hotel Unique Palace , Santiniketan 

   

ABSTRACTS

Sada Nand Dwivedi
All India Institute of Medical Sciences
New Delhi, 110029,India. 

A number of micro as well as macro level analyses are reported on various public health issues as an attempt to understand its regional epidemiology. But, most of the analyses dealing with identification of associated factors, especially in developing countries like India, do not make efforts to consider hierarchical structure of data. They simply disaggregate higher-level variables at lower level and carry out analysis through traditional methods that need assumption of independence of records. However, disaggregation under traditional methods of data analysis distorts this assumption and it results into underestimation of standard error of estimates providing significance of some of irrelevant covariates. Similarly, aggregation of lower level variables at higher level also provides distorted results under traditional methods. To overcome this problem, modelsusing multilevel analysis may be appropriate that take hierarchical structure into account. This procedure makes it possible to incorporate variables from all levels at their own level to get correct analysis and proper interpretation of the data on current contraceptive use. Unobserved community effects are also taken into account. It also provides the relative importance of characteristics related to various levels, which provides important clues strengthening ensuing public health programs. This presentation will discuss about the multilevel analysis. For this, for example, the data of a most populous Indian State "Uttar Pradesh (UP)", covered under National Family Health Survey (NFHS) conducted during 1998-1999, will be used. The sample design adopted for the NFHS is a systematic, two-stage-stratified sample of households. The NFHS in UP is a state representative survey of ever- married women age 15-49. The main objective of the survey was to collect reliable and up-to -date information on family planning, fertility, mortality, and maternal and child health providing state-level estimates. Its important objective was to provide high quality data to academicians and researchers for undertaking analytical research. For analysis, currently married women who were neither pregnant nor continuing with post-partum amenorrhea (PPA) will be considered. A two-level logistic regression analysis may be carried out for which women's level (level 1) and PSU(Primary Sampling Unit) level (level 2) variables may be considered. Women whose records were complete in relation to all variables considered in analysis may only be included in the analysis. Women with incomplete records may however be negligible. In view of poor contraceptive adoption and majority of couples going for sterilization in Uttar Pradesh and also taking into account the results from a series of exploratory models, to have meaningful observations, the current contraceptive use (including sterilization, modern methods etc) may be considered as dependent variable. 

 

 

POST-PARTUM AMENORRHOEA AND LACTATION: A STATISTICAL STUDY
H. J. Vaman
Department of Statistics, Bangalore University
Bangalore 560 056 ,India.

The contraceptive effect of breastfeeding in terms of delaying the next pregnancy following a child birth, as reflected by the post-partum amenorrhoea, is well known to the social scientists.  However, studies that deal with its statistical modelling considering different levels of lactation and analysis thereby are sparse. The present work reports a distinct new approach to such a study of the phenomenon employing a semi-Markov model. Besides developing the model, this paper discusses relevant statistical inference and applies it to a real life data from a longitudinal study at a Rural PHC near Bangalore. 

 
 

CHOICE OF ESTIMATORS FOR THE POPULATION MEAN OF SOME CHARACTERISTICSBASED ON MULTIVARIATE DATA
Anirban Singha
&
Ajit Kumar Das
Bidhan Chandra Krishi Viswavidyalaya,India
T.P. Tripathi
Indian Institute of Statistics, Kolkata,India 

In many situations one may have data set for several variables y , z₁, …, z_m where y is the principal variable and z₁ , z₂ ,… , z_m are m auxiliary variables supplying information about y. In case the population means  z₁, z₂,… ,z_m   of z variables are known, one may define the weighted ratio, regression estimators etc for estimating the population means  Y of  the principal variable y . The discussion of such estimators have been made by Olkin (1952), Des Raj(1965) and Tripathi (1987) including several others.The problem arises when the population means of auxiliary variables are unknown and one has the data set ( yi , z_1i ,…, z_mi ) i =1, 2,…, n. Tripathi and Chaubey (1992) obtained an estimator better than the sample mean  y=(1/n)åy_i , based on the data set , where only one auxiliary variable z is there. Singha etal. (2000) have defined and studied the properties of several estimators of Y  for the situation m=1 as in case of Tripathi and Chaubey. In this paper  the above mentioned situation of several auxiliary variables for estimating Y  without the knowledge of   z_j,   j =1, 2,…,m  is considered . For this purpose we look at the nature of the data and taking the help of nature of the correlation co-efficient between y and z_j , and through the scatter plot of the data guess the approximate relationship
                           ( a ) between y and z_j , j =1,…, m   and
                           ( b ) between y and transformed variable x_j = g_j (z_j) , j =1 , …,m 

This approximate relationship is then utilized for defining estimators for Y . Some new estimators for Y  in addition to the customary estimator (sample mean) Y  are defined and  the empirical study of these estimators is carried on to obtain their relative efficiencies over y. Some of these are found to be of high relative efficiency. 

 
 

CUSTOMER SATISFACTION: AN OVERVIEW FROM THE BANKING SECTOR IN INDIA

R. K. das, A. K. Das & S. R. Pal
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India 

Measurement of customer satisfaction is a difficult job especially when it is concerned with services offered to the customers like the banking service, railways service, aviation service, telecommunication service, etc. Following a purposive sampling scheme such a measurement of customer satisfaction is being carried out particularly from the banking sector in India, although confined within Calcutta (Kolkata) and its greater part. The responses are collected from the customers of two nationalized banks (State Bank of India and United Bank of India)and two foreign banks (Hong Kong Sanghai Banking Corporations and Australia -New Zealand Grindleys)following a well-constructed questionnaire, we have studied the level of customer satisfaction from the services commonly offered by those banks such as the Fixed Deposit Service, Savings Deposit Service, Current Account Service, Withdrawal of Cash Service, Visit to the Manager for Loan purpose, Visit to the Manager regarding any specific banking problems, Draft Making, and tried to prepare a rank of those banks. In this paper, a new criteria for measuring customer satisfaction (U%) is defined and the collected data is fitted to the Weibull distribution. Also, Kolmogorov-Smirnov non-parametric test procedure is given for the goodness-of-fit to a specified distribution. It is observed that if the U% is positive as well as the data is fitted well to the Weibull distribution, then the service is satisfactory. 

 
 

A STOCHASTIC MODEL TO STUDY INTER-ARRIVAL TIME FOR DRY AND WET YEARS OF MONSOON   RAINFALL

Banjul Bhattacharya and Swaraj Kumar Mukhopadhyay
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India 

An important feature of the climatic conditions is dependent upon monsoon rainfall of a region which does not remain constant over the years; it may exceed or fall short of the average causing flood or draught in extreme conditions. Due to this randomness of the monsoon phenomenon a prior knowledge about the pattern of rainfall is of great attraction for planning and management  of water resource system as well as agricultural production process. The inter-arrival time between the occurrence of successive dry and wet years in two observatory centers of Sub-Himalayan meteorological region of west Bengal viz., Jalpaiguri and Malda have been considered in this study.102 years (1901-2002) monsoon rainfall data (from June-September) have been used to determine the monsoon rainfall anomalies. A suitable Rainfall Index is introduced here to take account the year to year variability of monsoon rainfall during study period. The Rainfall Index (RI) is obtained as follows: 

                         RI= [(X-m)/s ] 

The positive value of the index indicates the wet years whereas the negative value stands for dry years. Historical rainfall time series data have been used to determine the sequences of dry and wet years separately for the two stations .The time interval between the successive dry and wet years have been measured in the study. In general the probability distribution of the inter-arrival time follows Poisson distribution .In the present study the mean of the Poisson distribution is not a constant but is a random variable. The Poisson distribution with this type of mean follows Gamma distribution. By analogy, the mean value of the Poisson distribution, which obeys the Gamma probability law, is a negative binomial distribution. Kendall and Stuart support this analogy. From the historical time series the sequences of inter-arrival of wet years as well as of dry years have been formed for two meteorological stations separately. Means and variances of four sequences have been obtained by using the method of moments. In a similar way these are estimated for combined dry and wet series of the two places separately. All the sequences of inter-arrival time follow negative binomial distribution (in cases of combined series also). The goodness of fit test has been tested by Chi-square test. Lastly, an attempt has been made to determine the return period of the wet years using  above frequency distribution of combined sequence for inter-arrival time of wet years. 

 
 

SMALL AREA ESTIMATION 

Partha Lahiri, University of Maryland at College Park,USA

 
 

TIME SERIES MODELING AND FORECASTING OF WHEAT PRODUCTION IN WEST BENGAL

Swaraj Kumar Mukhopadhyay and Banjul Bhattacharya
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India

Forecasting has a very important role in the management of agriculture. Univariate time series modeling by Box-Jenkins method have been useful in describing and forecasting the wheat production. Many sophisticated statistical prediction models for univariate time  series  have been developed so far of whichAutoregressive Integrated Moving Average (ARIMA) process has been widely  used in attempting  to forecast the wheat production. Modeling  by this method is based on time domain and frequency domain Approach. The time series is non stationary in both mean and variance .The autocorrelations remain closed  to one throughout, declining very gradually to zero. The spectral analysis has low frequency range and this is consistent with high positive autocorrelation. Differencing , a special type of filtering has been successfully utilized here to  remove the trend and non stationarity in mean. Also transformation by logarithm of the time series is necessary for obtaining the non-stationarity in variance. The same is considered to obtain the normality and to avoid the robustness of the series. The procedure for model identification ,estimation of parameters, diagnostic  checking and finally forecasting has been adopted to fit the ARIMA(2,2,1)model for wheat production of West Bengal. All the coefficients of the model are tested by using t-value and the model is justified by AIC. Minimization of the criterion and verifying the resulting residuals are considered as white noise by using autoregressive determination criterion. Moreover, Ljung-Box(LB) statistic suggests the residuals of the time series are white noise. The spectral density function does not identify any hidden periodicity from the residuals of the fitted model. The 7-step ahead  forecasting have been computed and also estimates the confidence limit for the validation period. The forecast comparison  has been carried out in terms of MAPE, which is a very small value. This measures the forecast accuracy. Thus the model is fitted accurately and it is considered as a forecasting model. 

 
 

USE OF ARIMA MODEL ON RICE  PRODUCTION IN BIRBHUM DISTRICT

Manas Kumar Sanyal and Swaraj Kumar Mukhopadhyay
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India 

In any locality ,the choice of a crop depends on past and present decisions by individuals, communities or Government and their agencies. These decisions are usually  based on experience, tradition ,personal preferences , resources etc.. The past and present rice production in the district of Birbhum are discussed on the basis of time series data on production of rice in the district. Time domain and frequency domain approaches have been utilized here to study the non-stationarity of the time series. Univariate time series modeling by BOX –Jenkins method has been useful in describing and forecasting the production of rice in the district of Birbhum. By this process the time series of production of rice in the district has been identified as ARIMA process. After fitting the model ,estimation of parameters, diagnosis checking and forecasting up to 2007 have been  made in this study. The forecast comparison has been carried out in terms of MAPE, which is a very small value. This measures the forecast accuracy. This model is fitted accurately and it is considered as a forecasting model. 

 
 

PREDICTION IN PRODUCTION OF PULSES TO MEET THE NUTRITIONAL REQUIREMENT OF HUMAN BEINGS

P.K.Sahu,
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India 

The availability of pulses ,termed as ‘poor man’s meat’, is decreasing day by day due to ever increasing pressure of population ,especially in a country like India. In India per capita availability of pulses has declined to 30gm. In 2001 from 61gm.in 1951 against FAO’s recommendation of  80gm. Per day per capita. The present study aims at analyzing the growth and trends in production of pulses in West Bengal, India and the whole world for three periods viz. the pre-green revolution period, the green revolution period and the post green revolution period. Taking data for the period 1961-2001,attempts have been made to forecast the availability of pulses in near future using “fitting of conventional trend”,  “B-J method”, and mixed B-J method  of  forecasting technique. The study reveals different growths and trends in different time periods and different places (West Bengal, India and the whole world).The study also expresses serious concern over the future production vis-à-vis availability of pulses and urge for immediate action for its improvement. 

A STABILITY STUDY OF  EOQ MODEL UNDER COMPLETE INSPECTION

R.M.Panda
Dept. Agril. Statistics, Faculty of Agriculture,
Bidhan Chandra Krishi Viswavidyalaya,
Mohanpur, Nadia, W.B. - 741 252,India 

The standard  EOQ model has been extended to the situation where lots whenever received are first completely inspected before they are used  to meet demands .On the basis of such inspection items conforming to specification  requirements are accepted and thereby stocked to meet  future demand  is completely known. The best order size is found to be the solution of an equation, which depends on the probability distribution of proportion of good items. It has been empirically shown the best order size is found to be stable within the family of beta distribution. 

 
 

Maximum Likelihood methods for the analysis of Medical and Social Science Research data with Quantal Responses

K.R.Sundaram
Professor & Head
Department of Biostatistics
All India Institute of Medical Sciences
Ansari Nagar  ,New Delhi-110029 ,India

Many  of the variables in medical and social science  research  are of quantal response type such as yes/no. Though the variable will be quantitative,  the responses to the different values of the quantitative variable may be qualitative in nature. For example, different doses of a drug are given to different comparable groups of subjects (animals, humans, tissues etc.) to study the average dose at which 50 % of the subjects show a particular response, say, death or improvement  or free from the disease etc.  Since different subjects are given different doses of the drug, it is not known whether the response could be different if a  different dose is given to these subjects. The ideal method of analysis in such data is to find the percentage of subjects receiving a particular dose giving the defined response and repeating this for all the considered doses. This will generate a sigmoid type of curve for the various doses from the lowest to the highest. From this distribution the average dose (median) at which the defined response occurs  is computed by applying Maximum likelihood (ML) method after transforming the percentages at different doses to Probits or Logits or Angles, depending upon the distribution. The ML  method will allow us to compute the corresponding Confidence limits also.  This method is widely used  not only in Pharmacology, but, also in social   sciences .For example  ML method can be used to estimate the average age at which a phenomenon occurs in children, The phenomenon could be the appearance of various stages of puberty, axillary hair, voice change, upper lip hair, menarche in girls etc. The method can be extended to many other situations where data may be tabulated in similar way and direct method of estimation is not possible or not reliable. In this paper, ML method for estimation of median dose at which a defined response occurs  and  median age at which a phenomenon occurs in the subjects  is discussed with examples in medical and social science research . Some simple methods also are discussed for the same where proper computer facilities or softwares are not available  and at the same time without loss of precision in the estimate. Relevant references of such analysis on the research data  pertaining to medical and social  sciences  are also  given. 

 
 

On A Comparison of Randomized Response Technique and Group Response Technique for Eliciting Sensitive Information
 Yogendra P. Chaubey,
Concordia University, Montreal , Canada

Here, a new technique called the group response technique (GRT)  (based on batch sampling) as an alternative to the randomized response technique (RRT)  to elicit information about a sensitive question is considered.  Results of an empirical study to assess the reliability and validity for the two techniques will be reported. 

 
 

Professor P V Sukhatme- A tribute

B K Kale
Professor of Statistics (Retd)
Department of Statistics, University of Pune, Pune 411007,India 

Late Professor P V Sukhatme is well known for his contribution to Sampling and Agricultural Statistics. After his retirement from FAO as Chief Statistical Advisor he continued his pioneering research in nutrition and health for almost 25 years at Maharashtra  Association of Cultivation of Sciences. We review here the life of Professor P V Sukhatme and his impact on Statistics, Science and Society. 

 
 

STATISTICAL METHODS FOR COMPARATIVE STUDIES IN SOCIAL SCIENCES: MEASURES OF INEQUALITY

Dr. T S K MOOTHATHU
Department of statistics
University of Kerala
Trivandrum – 695 581, India 

Summary: Statistical methods are at the very heart and soul of comparative studies in Social Science. They not only provide qualitative methods for making economic, political, psychological or social comparisons among groups but often provide precision & clarity in our approach to such comparative studies. During the last century several comparative studies had their focus on cross sectional or longitudinal comparisons of ‘inequality’ in the distributions of wealth, income, household consumption, etc. a knowledge of the following three major categories indices of ‘inequality’ are essential for such comparisons. Positive indices of ‘inequality’ (e.g., Lorenz curve, Gini index, Piesch index, Mehran index), entropy indices of ‘inequality’ (e.g., Theil indices, Hirschman index, generalized entropy index) and normative indices of ‘inequality’ (e.g., Dalton index, Atkinson’s inequality index). The focus of the present paper is on major advances on them, which provide necessary statistical tools and methodology for quantitative group comparisons in Social Science Research. 

 
 

SOCIAL AND OCCUPATIONAL MOBILITY – A REVIEW

Asis Kumar Chattopadhyay, Department of Statistics
Calcutta University , India 

The best way of quantifying human populations is by classifying their members on the basis of some personal attribute. One may classify families according to where they reside or workers by their occupations. Thus  to study the dynamics of social processes, it is natural to start by looking at the movement of people between categories. Since such moves are largely
unpredictable at the individual level it is necessary for a model to describe mechanism of movement in probabilistic terms. The earliest paper in which social mobility was viewed as stochastic processes appears to be that of Prais (1955). Since then their has been grown
up a large literature. A distinction has to be made between intergenerational mobility and intragenerational mobility. The former refers to changes of social class from one generation to another. Here the generation provides a natural discrete time unit. This phenomenon is usually called social mobility. Intragenerational mobility refers to changes of classes
which take place during an individual's life span. This type of movement is called occupational or labour mobility since it is usually more directly concerned with occupations. A characteristic feature of occupational mobility is that there is no natural time interval between changes of state. Moves can take place at any time and therefore such process are more appropriately modeled in continuous time. Many deterministic and stochastic models have been developed to study social and occupational mobility situations in the different parts of the world. Several empirical studies of mobility have been published. 

 
 

Use of Statistics by Plant Pathologists in India

N.C.Mondal,Sandipan Garai and Tapan Bhattacharya 

Department of Plant Protection, Institute of Agriculture, 

Visva-Bharati, Santiniketan,India 

This paper attempts to identify the kind and quality of Statistics used by the plant pathologists in their research. Future scopes of the use of more sophisticated statistical methods under the exact plant pathological requirement have also been emphasized. 

 
 

STATISTICS IN CLAY MINERALOGY

Chandrika Varadachari * and Kunal Ghosh° 

*Raman Centre for Applied and Interdisciplinary Sciences,16A Jheel Road, 

Calcutta 700 075,India

°Department of Agricultural Chemistry & Soil Science, University of Calcutta 35 BC Road, Calcutta 700 019,India 

Clay minerals have complex chemical compositions that are diffuse and ill-defined. Consequently, chemical differences between various types of clay minerals are not clearly understood. Statistical analysis provides an appropriate tool for determining the chemical factors, which differ significantly between mineral groups and subgroups.
Statistics provides an answer to whether the clay minerals are chemically distinct from each other and, if so, in which chemical parameters. Thus, linear discriminant analysis shows that in spite of overlap in individual chemical parameters, the minerals differ significantly in their chemical nature at the group and subgroup levels when several parameters are considered together. We can see that at the group level, the minerals can be distinguished by only two factors, viz., total layer charge and K contents. At the subgroup level, four other chemical parameters when considered together provide a clear difference between the minerals. A method for statistical classification of clay minerals on the basis of their chemical composition has been derived. Statistics is also applied for derivation of various parameters for a fuzzy mathematical description of clay mineral compositions. Here, statistical methods are used to derive ‘ideal’ compositional parameters as well as the ‘scale’ for membership values. Statistical methods may be used in place of fuzzy mathematical methods that are now used to derive fuzzy phase diagrams of clay minerals. 

 
 

CROP FORECASTING USING TIME-SERIES DATA

Sugata Sen Roy & Sourav Chakraborty

University of Calcutta,India

Generally time-series models are used to predict the production of a particular crop on the basis of past productions. However, since the area under the crop varies from year to year, a better prediction may be obtained by multiplying the average yield-rate by the area under the crop in that year. These two again can be predicted on the basis of autoregressive models of appropriate orders. In this presentation we have looked into the prediction of certain major crops in West Bengal based on the last 11 years data. In the course of the study we have, however, found certain observations which are markedly different from the rest. Although these outliers can substantially distort the parameter estimates, they cannot be excluded because of the structure of the models. Here we have suggested five different techniques for substituting these observations and estimating the parameters on the basis of the ‘estimated’ observations.

 
 

STOCHASTIC MODELING OF UNEMPLOYMENT IN A REGION

K.SRINIVASA RAO,Department of Statistics, Andhra University

 

ARCH PROCESSES AND THEIR APPLICATIONS IN STOCK RETURN DATA

A.K.Basu, S Sen Roy and Sankha Bhattacharya

Department of Statistics,Calcutta University,India

 
 

STOCHASTIC MODELING FOR AGES AT MARRIAGE AND STERILIZATION

Prof.M.Vivekananda Murty ,Head, Department of Statistics and

Hon. Director, Population Research Centre,Andhra University, Visakhapatnam,India

 
 

A LINGUO-STATISTICAL STUDY OF PROSE –LITERATURE IN ORUNODOI ERA OF MODERN ASSAMESE LANGUAGE 

N R Majumder

This paper deals with a statistical investigation on the morphological and syntactical features of the prose-literature created during the Orunodio era of modern Asamese language. Morphological characters such as word-length in phonemic syllables, proportion of words belong to different parts of speech, proportion of words belong to various etymological classes, and syntactical character such as sentence-length in words in use have been statistically estimated separately for texts of creative and constructive literature. The factors responsible for text differences have been pointed out to conceive an idea about the stylo-variation exist in those texts of different kind of literature. Style-statistics of an author for this creative and constructive types of literature and more specifically for his dramatical, biographical and historical writings have also been estimated to depict his style during Orunodoi period. 

 
 

PARTICIPATROY RURAL APPRIASAL –A COMPLEMENTARY METHODOLOGY IN SOCIAL SCIENCE RESEARCH

V.G. GIRISH* & S. B. MUKHOPADHYAY**

Several traditional approaches/methods of social research aimed at development of people areavailable. Such conventional, especially the survey methods through lengthy questionnaire/ schedule, are primarily extraction by ‘outside’ researchers, top down in mode, time consuming and cost intensive. These methods provide limited scope of participation of local people.Participatory Rural Appraisal (PRA) is a way of enabling communities to define, evaluate and influence their economic, environmental, health and educational status. PRA is a methodology for interacting with the villagers, understanding them and learning from them. Because of its participatory nature, it is a useful methodology to focus attention on people, their relationship with socio-economic and ecological factors. Different tools/methods in PRA deals with space,time,flow and decision analyses.The participatory methods can be put into four different classes, for group andteam dynamics, for sampling, for interviewing and dialogue and for visualization and diagramming. Some of the important principles of PRA are: offsetting biases of rural development tourism,(spatial, project, person-gender, elite, seasonal, professional, courtesy etc). Triangulation- using methods, sources and disciplines, and a range of information and cross checking to get closer to the truth through successive approximation. Optimal ignorance and appropriate imprecision avoiding unnecessary detail , accuracy and over collection of data which is not really needed for the purpose. We are tend to make absolute measurements, but often trends, scores or ranking are all that are required. PRA methods are complementary to other research methods not supplementary, a mid way between formal and non structured methods of situation analysis and hence more realistic approach for a short time frame. Thus provides an alternative frame work of data collection and analysis.

*Research Scholar, ** Head, Dept. of Agril. Extension, Agril. Economics and Agril. Statistics, Institute of Agriculture,Visva-Bharati, Sriniketan,India

 
 

APPLICATION OF STATISTICS IN GENETIC ANALYAIS OF QUALITATIVE AND QUANTITATIVE CHHARACTERS

P.C.Koley,

Department of CIHAB,Institute of agriculture,Visva-Bharati,India

To studythe genetics of characters,both qualitative and quantitative, which are of economic importance is a very well known problem.Genetic analysis of qualititative characters is mainly related to the detection of number of gene(s) that controls the phenotypic expression of the characters and linkage among genes.In both the cases chi-square test can reliably be employed provided some precautions are taken.Genetic analysis of quantitative characters is accomplished by applying biometrical genetical procedures that use analysis ofgeneration means ,the firstdegree statistics and second degree statistics.The information obtained from such genetic analysis can effectively be utilizedfor the purposeplant breeding .

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