2. Sampling Concept
1. Sample:
○ Many times it may happen that the study
of entire population is not possible since it
requires more time and money
○ Hence, to overcome this factor, we deal
with a small part or a fraction of the
population under study
○ This small part of the population is known
as “ Sample”
3. 2. Sampling:
○ This sample should be a representative of the
population with respect to the character under
study
○ This can be ensured by drawing the units from
the population at random in the sample with
equal probability
○ The procedure of selecting the sample from the
population under study is known as “Sampling”
4. Aims of sampling
(1)To get maximum information about the
population with limited time, cost and resources
(2)To get precise estimates
6. Steps in a sample survey
○ Points to be kept in mind before starting a
sample survey
(1) Aims and objectives of the survey must be clearly
explained to the respondents so that unnecessary data
may be avoided
(2) Population from which a sample is to be taken must be
clearly defined
(3)sampling units must together constitute the whole
population and they must be distinct and non-overlapping
7. Steps in a sample survey contd….
(4) Questions in the questionnaire or schedule should
be short, simple and comprehensive and be arranged in a
logical sequence according to object of the survey
(5) Cases of non-response should be handled carefully to draw
unbiased conclusions
(6)Construction of the frame must be clear and unambiguous.
Only good experience helps in constructing a good frame
8. Steps in a sample survey contd….
(7) If an appropriate design of experiment is selected,
the final estimates will be quite reliable. Hence,
selection of design must be properly made
(8) To achieve the aims of survey, the field work
should be properly and honestly done with careful
supervision of investigators
(9) After the data have been collected, the analysis is
to be made to get reliable estimates
9. Types of Error
(1)Sampling error:
○ The error arising due to drawing inferences about the
population on the basis of few observations is termed as
sampling error
○ This error does not appear in census i. e. census survey is
free from this error
10. ( 2 ) Non-sampling error:
● The error arising due to number of causes such as
defective methods of data collection and tabulation,
faulty definition, incomplete coverage of the population
or sample is known as non-sampling error
● This error is presented in both the surveys (sample as
well as census)
11. Random sample
○ A sample is said to be random if every unit in the
population has an equal chance of being selected for the
sample
○ If there are N units in the population, then the probability
of selection of any unit is 1/N in the first draw, 1/N-1 in
the second draw and so on in case of sampling is made
without replacement
○ The probability of selecting unit at any draw remains equal
to (1/N) if the sampling is made with replacement
12. Simple Random Sampling
○ A random sample is said to be simple if each unit of the
population has an equal and independent chance of being
included in the sample
○ The process of selecting simple random sample is called
simple random sampling (SRS)
○ If the selected unit for the sample is not replaced at the
successive draw, then it is called Simple Random Sampling
Without Replacement (SRSWOR), otherwise Simple
Random Sampling With Replacement (SRSWR)
○ This is the simplest method and is used when the whole
population is homogeneous
13. Stratified Sampling
○ When the population is heterogeneous, then SRS method
will fail.
○ In this situation the heterogeneous population is divided in
to different groups or classes, called strata and a sample is
drawn from each stratum at random
○ Such procedure of selecting the sample is known as
stratified sampling.
○ The purpose of stratification is to increase the efficiency of
sampling by dividing a non-homogeneous population in
such a way that there should be great homogeneity within
each stratum and great difference between the strata
○ In this method the estimates obtained are more precise
than SRS
14. Sampling with varying probabilities
○ When units vary in size and variable under study is
correlated with size, then SRSWOR may not be
appropriate as it does not take into account the
possible importance of the larger units in the
population
○ A sampling procedure in which the units are selected
with probabilities proportional to some measures of
their size is known as sampling with probability
proportional to size, which is briefly written as PPS
○ For example, villages with larger geographical area
are likely to have larger population and larger area
under food crops
○ In estimating production or food supply, the villages
are selected with probabilities proportional to their
populations or to their area
15. Cluster Sampling
○ The smallest units into which the population can be divided
are called the elements of the population
○ The groups of elements form the clusters, such clusters
form a population i.e. populations consist of number of
clusters and each cluster is a sampling unit
○ The procedure of selecting clusters for a sample is called
cluster sampling
16. Multistage Sampling
○ Sometimes sampling is done in stages in order to reduce
the cost of the survey and simultaneously to obtain precise
estimates
○ The procedure of first selecting a large sized sample and
then to select a smaller number of units to form a sample,
is called sub sampling or two stage sampling
○ The large sized units are called first stage units and
smaller sized units are second stage units ,since sampling
is done in two stages
○ Similarly, we can select even more smaller sample from
second stage units. This is called 3rd stage sampling
○ This procedure can be carried up to a number of stages,
which will be called multistage sampling
17. Systematic Sampling
○ Many a time we have to obtain the information from
registers or cards in serial order
○ Sometimes we may need the samples of houses in a city
or trees from a forest
○ In such case, a sampling plan known as systematic
sampling often works better than the SRS.
○ In this method, only the first number is selected at random
and rest of the units of a sample are selected according to
a pre-designed pattern
○ Such method of drawing samples is called systematic
sampling
18.
19. For example, there are 100,000
elements in the population and a
sample of 1,000 is desired. In this
case the sampling interval, i, is 100.
A random number between 1 and 100
is selected. If, for example, this
number is 23, the sample consists of
elements 23, 123, 223, 323, 423, 523,
and so on.
20. Purposive Sampling
○ This is the method of selecting samples in which the choice
of selection of sampling units depends entirely on the
judgment of the investigator
○ This method is also sometimes called judgment or non-
probability sampling
○ In this procedure, the investigator inspects the entire
population and selects a sample of typical units which
he considers close to the average of the population
21. Purposive Sampling contd…
○ This sampling method is mainly used for opinion surveys,
but can not be recommended for general use as it is
subject to the drawbacks of prejudice and bias of the
investigator
○ If the investigator is experienced and an expert, it is
possible that purposive sampling may yield useful results
○ However, it suffers from a serious defect that it is not
possible to compute the degree of precision of the
estimate from the sample values