This presentation is about sampling techniques along with types of sampling, sampling and non-sampling errors.

1. PROBABILITY SAMPLING
Presented by
Tejendra Singh
Id no. : 52674
Course : M.Sc.(Agricultural Statistics)
Advisor : Dr. Haseen Ahmad

2. CONTENTS
 Sampling
 Population
 Objectives of sampling
 Characteristics of good sample
 Probability Sampling
 Types of Probability Sampling
 Sampling Errors
 Non Sampling Errors
 Principle Steps in Sample Survey
 Conclusion

3. Sampling
Definition
 The process through which a sample is extracted from a
population is called as sampling.
Sample
 One or more sampling units are selected from the
population according to some specified procedure.
 A sample consists only of a portion of the population
units.
Sampling Unit
 An element or a group of elements on which
observations can be taken is called a sampling unit.

4. Population
Definition
 The collection of similar units i.e. collection of
similar objects or persons, plants, animals etc. is
referred to as a Population.
 Population may be living or non living & it may be
finite or infinite.

5. Objectives of Sampling
 To get a better representative of the population.
 To save resources i.e., time and money.
 To obtain the best possible estimates of the
population parameters.
Sampling Frame
 Sampling frame is the complete list of individuals in
the population having names, addresses and any
other identity details.

6. Characteristics of a good sample
Representative of the population.
Free from bias & errors.
No substitution & incompleteness.
Appropriate size.

7. Probability Sampling
 If each and every unit of a population have a
definite probability of being included in the
sample then the sampling is probability
sampling.
 Probability sampling is also referred to as
random sampling or representative sampling.

8. Types of Probability Sampling
Simple
Random
Sampling
SRSWOR
SRSWR
Stratified
Random
Sampling
Equal
allocation
Proportional
Allocation
Optimum
Allocation
Systematic
Sampling
Linear
Systematic
Sampling
Circular
Systematic
Sampling
Cluster
Sampling
Multistage
Sampling

9. Simple Random Sampling
 In simple random sampling, each member of the
population has the same probability of being included in
the sample.
 The larger the sample, more it represents the
population.
 It is a fair type of sampling without any bias.
 Simple random sampling is also called equal probability
sampling or random sampling.
Here pi= N
1

10. Methods of Selection of Sample in
Simple Random Sampling
Lottery Method Random number
table method

11. Procedure of selection by Random Number
Table:
 Identify ‘N’ units in the population with numbers
from 1 to N.
 Identify the number of digits in N. Suppose it is ‘k’.
 Select any ‘k’ consecutive columns from random
number table.
 Start at random from any place.
 Discard if unit selected is ‘0’ or greater than N.
 In this way select n units and units so obtained will
constitute the random sample.
 In case of SRSWR, all the random numbers are
accepted even if repeated more than once.
 In case of SRSWOR, if any random number is
repeated, then it is ignored and more numbers are
drawn.

12. Types of Simple Random Sampling
 Simple Random Sampling Without Replacement
 Simple Random Sampling With Replacement

13. Simple Random Sampling Without
Replacement (SRSWOR)
 In SRSWOR, the first member is chosen at random from
the population of size N, and once the first member has
been chosen, the second member is chosen at random
from the remaining N −1 members and so on, till there
are ‘n’ members in the sample.
 Here no unit of population may appear more than once
in a sample.
 If n units are selected by SRSWOR, the total number of
possible samples are ᴺСn.
 Each sample has a same probability of selection i.e.,
equal to
n
N
C
1

14. Simple Random Sample With
Replacement (SRSWR)
 SRSWR is a method of selection of n units out of
the N units one by one such that at each stage of
selection each unit has equal chance of being
selected, i.e., 1/ N
 When n units are selected with SRSWR, the total
number of possible samples are N
n
 The sampling units are chosen with replacement
in the sense that the chosen units are placed back
in the population.
 The Probability of drawing a sample is n
N
1

15. Advantages
 Easy method to use
 Sampling error can be easily measured.
Disadvantages
 Need complete list of units.
 Cost of collecting geographically spread
sampling units may be much in terms of time
and money.
 For a given precision it usually requires larger
sample size compared to stratified random
sampling.

16. Stratified Random Sampling
 In stratified random sampling entire heterogeneous
population divided into a number of homogeneous
groups.
 These groups are termed as strata, which differs from
one another but each of these groups homogeneous
within itself.
 These strata must be mutually exclusive and
exhaustive.
 Treat each stratum as separate population and draw a
sample by SRS from each stratum.

17. Problem of Allocation
Deciding the number of units to be taken from each
stratum is called the problem of allocation. This can be
done in three ways-
 Equal Allocation
 Optimum Allocation
 Proportional Allocation

18. Equal Allocation
 Choose the sample size ni to be the same for all the
strata.
 Draw samples of equal size from each stratum.
 Let n be the sample size and k be the number of
strata. Then, ni = n/k for all 1, 2,...,k.
Optimum Allocation
 In this allocation we select larger number of units
from a stratum whose size is larger and Variability is
larger.
ni ∝ Ni Si Or ni = C*Ni Si
 where C* is the constant of proportionality

19. Proportional Allocation
 We Select larger number of units from larger
stratum and smaller number of units from
smaller stratum.
 For fixed k, select ni such that it is proportional to
stratum size Ni , i.e., ni ∝ Ni Or ni = CNi
 where C is the constant of proportionality.

20. Advantages
 Can acquire information about whole population
and individual strata.
 Precision gets increased if variability within strata
is smaller than between strata.
 Full cross-section of population can be obtained
through stratified random sampling.
 Provides separate estimates for each stratum.
Disadvantages
 Sampling error is difficult to measure.
 Different strata can be difficult to identify.
 Loss of precision if size of individual strata is
small.

21. Systematic Sampling
 In this sampling we select 1st unit at random from the
population and remaining units of the samples are
selected automatically from the population at equal
interval.
 Two types of Systematic Sampling :
i. Linear Systematic Sampling
ii. Circular Systematic Sampling

22. Linear Systematic Sampling
 Let k = N/n be a positive integer. k is the multiple of
n.
 We select 1st unit of the sample from the 1st k units
and remaining (n-1) units of the sample at equal
interval of k.

23. Circular Systematic Sampling
In this method we select 1st unit of the sample at random
from N units of the population and then going round the
circle. Subtract N if the number selected is greater than N.
Example
Let N =14 and n= 5 Then, k =
nearest integer to 14/5=3. Let the
first number selected at random
from 1 to 14 be 7. Then, the
circular systematic sample consists
of units with serial numbers
7,10,13, 16-14=2, 19-14=5.
This procedure is illustrated.
diagrammatically in the figure

24. Advantages of Systematic Sampling
 It is easier to draw the systematic sample & it is easier
to execute it without any mistakes especially when the
drawing is done in the field.
 Suitable sampling frame can be identified easily.
 Sample evenly spread over entire reference population.
Disadvantage
 Sample may be biased if hidden periodicity in population
coincides with that of selection.
 Each element does not get equal chance.
 Ignorance of all element between two n element.

25. In terms of Intra class correlation
The systematic sampling is :
 More efficient than the corresponding equivalent
stratified sample when
 Less efficient than the corresponding equivalent
stratified sample when
 Equally efficient than the corresponding
equivalent stratified sample when ρwst = 0

26. Cluster Sampling
 In cluster sampling a given population is classified into a
number of subgroups, each group being considered as a
cluster.
 After classifying the population into a number of
clusters, a sample of cluster is selected according to
some sampling scheme (generally SRS) and each unit of
the selected cluster is surveyed.
 In cluster sampling cost of survey is reduced.

27. Example
 The list of all the agricultural farms in a village or a
district may not be easily available but the list of
village or districts are generally available. In this
case, every farm in sampling unit and every village
or district is the cluster.
 In a city, the list of all the individual persons staying
in the houses may be difficult to obtain or even
may be not available but a list of all the houses in
the city may be available. So every individual
person will be treated as sampling unit and every
house will be a cluster.

28. Difference between stratified and
cluster sampling
 In stratified sampling, the strata are constructed
such that they are
• within homogeneous and
• among heterogeneous.
 In cluster sampling, the clusters are constructed
such that they are
• within heterogeneous and
• among homogeneous.

29. Multistage Sampling
 Multistage sampling is the compromise
between SRS and cluster sampling.
 The entire population is classified into a
number of clusters .
 Select a sample of clusters.[first stage]
 From each of the selected cluster, select a
sample of specified number of elements.
[second stage]
 The procedure is generalized to three or more
stages.This is called Multistage Sampling .

31. Example
 In a crop survey - villages are the first stage
units, - fields within the villages are the second
stage units and - plots within the fields are the
third stage units.
 In another example, to obtain a sample of
fishes from a commercial fishery - first take a
sample of boats and - then take a sample of
fishes from each selected boat.
Advantage
 The principle advantage of two stage sampling
is that it is more flexible than the one stage
sampling.

32. SAMPLING ERRORS
 Sampling errors are restricted to sample surveys
only.
 They are measurable from the sample data in the
case of probability sampling.
 The sampling errors decrease as the sample size
increases.
 The data collected by complete enumeration in
census is free from sampling error.
 Sample size and variability within the population
are the factors affecting the sampling error.

33. NON SAMPLING ERRORS
 These are errors that arise during the
course of all data collection activities.
 Occurs in complete enumeration as well as
in sample surveys.
 Non-sampling error increases as the
sample size increases.

34. Sources of non-sampling errors
 Lack of proper specification of the domain of
study and scope of investigation.
 Incomplete coverage of the population or
sample.
 Defective methods of data collection
 Tabulation errors

35. Principle Steps in Sample Survey
 Defining the objectives of the sample survey
 Defining the population
 Determination of the data to be collected
 Degree of precision desired
 Deciding on the method of collection of data
 Getting a sample frame
 Designing the Survey
 Drawing the sample
 Training of personnel
 Analysis of the collected data

36. Thank You