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

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 , z_{1},
…, z_{m} where y is the principal variable and z_{1} ,
z_{2} ,… , z_{m} are m auxiliary variables supplying information
about y. In case the population means z_{1}, z_{2},…
,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 **

Various government
agencies are in need of producing reliable small-area statistics. A small-
area (or small domain) generally refers to a subgroup of a large target
population.Thesubgroup
may refer to a small geographical region (e.g., state, county, municipality,
etc.), aparticular demographic group
(e.g., black female in the age group 18-24) or a demographic group within
a small geographic region. Small-area statistics are needed in regional
planningand fund allocation in many
government programs and thus the importance of producingreliable
small-area statistics cannot be over-emphasized.Clearly, a design-based
estimatorwhich uses only the sample
survey data for a particular small-area of interest is unreliable due to
the small sample size for the small-area.In
order to improve on design-based estimators,several
indirect and model-based methods have been proposed in the literature.
These improved estimation procedures essentially use implicit or explicit
models which borrow strengthfrom
related resources such as administrative and census records and previous
survey data.In this context, we
review the empirical best linear unbiased prediction approach with applications
in agriculture and social sciences.

__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**

The
uncertainty associated with the human behaviour compel analytically oriented
social and behavioural scientists to appeal stochastic models based on
probability theory and stochastic process. The knowledge on behaviour of
the stochastic process associated with social phenomenon is highly desirable
in understanding and analyzing the real life situations, especially when
the system is complex. For example consider the unemployment situation
in a region. It is more realistic to consider the growth of unemployment
as stochastic rather than deterministic. The external factors, which influence
the growth of unemployment like, economic conditions, industrialization,
educational facilities, wage structure etc., are too varied and random.
The modeling and analysis of unemployment duration of individuals in a
region is needed in order to analyse the conditions there in and to develop
suitable programmes in rural and industrial development in order to utilize
the manpower resources more optimally. In this paper, we develop a stochastic
model for number of unemployed persons of a region in an employment exchange
and analyse for both transient and equilibrium states with the assumptions
that the enrollment in the employment exchange is Poisson and recruitment
process in that region is also Markovian. The characteristics of the model
are derived and analysed through obtaining the explicit expressions for
the mean number of unemployed persons, variance of the number of unemployed,
the distribution of unemployment period, the force of absorption (rate
of employment), the joint probability distribution of number of persons
recruited and number of persons waiting for job, the distribution of number
of persons recruited during the time T, etc,. The sensitivity of the model
with respect to the parameters is also discussed. These models are useful
in analysing the situations arising in developing countries like, India
in order to assess the economic development of the nation.

Nowadays
time series models are very useful in the area of finance. A variety of
time series models are available in literature. In the current work we
have discussed the ARCH Model of Engle (1982) and the developments thereafter.
Applications of such models are also considered in Stock Return Data.

**STOCHASTIC
MODELING FOR**** ****AGES AT MARRIAGE
AND STERILIZATION**

Stochastic
Models provide the basic framework for the analysis of several real life
phenomenon. One such area is fertility studies in Demography. Hence modeling
of fertility parametersprovide insight
for understanding the phenomenon of population growth. Many studies revealed
that the age at marriage and age at sterilization are the important prerequisite
for understanding the fertility pattern of any region. As the ages at marriage
and sterilisation in a region are influenced by different socio-economic,
educational, religious and cultural factors, which are random in nature,
they can be treated as random variables. Accordingly, suitable probability
distributions are identified for both the age at marriage and age at sterilisation,
through utilizing the data collected in Andhra Pradesh (1998-99) under
RHS-RCH survey. Since the two variables age at sterilization and age at
marriage are inter linked, the study of their joint relation on fertility
is more relevant and hence a suitable joint distribution of these two variables
is developed through Morgenstern’s form of bivariate distributions and
analysed. This joint distribution is used to derive regression surfaces
through conditional expectations and found that they are non-linear. These
regression surfaces are very useful for obtaining the characteristics of
the model and play a greater role in evaluation and implementation of sterilization
programmes. The data analysis is carried for the three regions of Andhra
Pradesh namely Andhra, Rayalaseema and Telangana, as these three regions
are different in nature due to the differences in social, economic, demographic
and cultural factors existing. These regional variations are further compared
with Andhra Pradesh as a whole. This study is very useful in understanding
different characteristics of the age pattern of acceptance of family planning
in Andhra Pradesh as a whole as well as in the three regions Andhra, Rayalaseema
and Telangana, which provide insight for proper planning and implementation
of family welfare activities in AndhraPradesh.

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

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 .