This document defines key concepts related to sampling, including populations, samples, sampling methods, and estimating sample size. It discusses different types of populations and how samples are used to represent populations. Various probability and non-probability sampling methods are described, such as simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Factors that influence sample size like desired precision and population size are also covered. The relationship between samples and populations is explained through parameters and statistics.

1. Sample and Sampling
Definition of a population, sample; characteristics of a good sample,
sampling methods-simple random sampling, stratified random
sampling, systematic sampling, cluster sampling, multistage
sampling, sampling error.

2. Population
• Population is the group of elements have common characteristics
• Finite population: the elements of population/elements are
countable.
• E.g. number of farmers having commercial fish growers in
Bhandara
• Infinite population: the elements of population/elements are
not countable.
• E.g. number of bacteria present in field of rice infected with
bacterial leaf spot
• Element is a unit of a population

3. Sample
• Statisticians use the word sample to describe a portion
chosen from the population.
• Sampling is simply the process of drawing part of population
as a sample
• A finite subset of statistical individuals defined in a
population is called a sample. The number of units in a
sample is called the sample size.
• For adopting any sampling procedure it is essential to have a
list identifying each sampling unit by a number. Such a list
or map is called sampling frame.
• Sampling error is the difference in between average value of
the population parameter and average value of statistics.
• e.g. 𝜇 = 0.5 ha, 𝑥 = 0.47 ha, SE = 0.03 ha
• SE can be minimized by increasing sample size

4. The relationship between sample size
and sample error:

5. Approaches to determining the sample size
1. Census for small populations and national survey
2. Imitating a sample size of similar studies
3. Using published tables
4. Applying formulas to calculate a sample size
5. Sample size estimation through software

6. Census for small populations
o Use the entire population as the sample.
o Cost considerations make this impossible for large
populations.
o A census is attractive for small populations size like
200 or less
o Achieve a desirable level of precision.

7. Imitating a sample size of similar studies
o Use the same sample size as those of studies similar
to the one we plan.

8. Using published tables
o Published tables which provide the sample size for a given
set of criteria.
Population Size of Sample Size (n) for Precision (e) of:
±5% ±7% ±10%
100 81 67 51
125 96 78 56
150 110 86 61
175 122 94 64
200 134 101 67
225 144 107 70
250 154 112 72
300 172 121 76
350 187 129 78
400 201 135 81
450 212 140 82

9. Using published tables
Population Size of Sample Size (n) for Precision (e) of:
±3% ±5% ±7% ±10%
500 a 222 145 83
600 a 240 152 86
700 a 255 158 88
800 a 267 163 89
900 a 277 166 90
1000 a 286 169 91
2000 714 333 185 95
3000 811 353 191 97
4000 870 364 194 98
5000 909 370 196 98
a = Assumption of normal population is poor (Yamane,
1967). The entire population should be sampled.

10. Applying formulas to calculate a
sample size
• Sample size when estimating a mean
• n = 𝑧2 𝜎2
𝑒2
(for infinite population)
• n =
𝑧2 . 𝑁 . 𝜎2
𝑝
𝑁 − 1 𝑒2 + 𝑧2 𝜎𝑝
2
(for finite population)
Where,
Z = 1.96 (at 95 % confidence level)
σ = population standard deviation ∗
e = sampling error (acceptable error, precision)
N = population size

11. Sample size estimation through
software
Sample Size Calculator by Raosoft, Inc.htm
o Arbitrary sample size approaches rely on erroneous rules of
thumb (e.g. “n must be at least 5% of the population”).
o Arbitrary sample sizes are simple and easy to apply, but they
are neither efficient nor economical. (e.g. Using the “5
percent rule,” if the universe is 12 million, n = 600,000 – a
very large and costly result)
Arbitrary “percentage rule of thumb”
sample size

12. Parameters and statistics
• We can describe samples and populations by using
measures such as the mean, median, mode and standard
deviation.
• When these terms describe the characteristics of a
population, they are called parameters. When they
describe the characteristics of a sample, they are called
statistics.
• A parameter is a characteristic of a population and a
statistic is a characteristic of a sample. Since samples are
subsets of population statistics provide estimates of the

13. Principles of sampling
• Principle of statistical regularity. A moderately large
number of units chosen at random from a large group are
almost sure on the average to possess the characteristics of
the large group.
• Principle of Inertia of large numbers. Other things
being equal, as the sample size increases, the results tend to
be more accurate and reliable.
• Principle of Validity. This states that the sampling
methods provide valid estimates about the population units.
• Principle of Optimisation. This principle takes into
account the desirability of obtaining a sampling design
which gives optimum results. This minimizes the risk or
loss of the sampling design.

14. Advantages of sampling
• There are many advantages of sampling methods over census
method. They are as follows:
o Sampling saves time and labour.
o It results in reduction of cost in terms of money and man-
days.
o Sampling ends up with greater accuracy of results.
o It has greater scope and adaptability.
o If the population is too large, or hypothetical or
destroyable sampling is the only method to be used.

15. Limitations of sampling
• Sampling is to be done by qualified and experienced
persons. Otherwise, the information will be unbelievable.
• Sample method may give the extreme values sometimes
instead of the mixed values.
• There is the possibility of sampling errors. Census survey is
free from sampling error.

16. Types of sampling
• The technique of selecting a sample is of fundamental
importance in sampling theory and it depends upon the
nature of investigation.
• The sampling procedures which are commonly used may be
classified as
• Probability sampling (N =200, n = 40, equal
probability=40/200)
• Non-probability sampling (N =200 (30 Female HH, 170
Male HH head), n = 40 (15 female HH head), unequal
probability, Female HH head = 15/30; Male HH head =
25/170)
• Mixed sampling.

17. Type of sampling
• Each and every element of
the sampling frame has same
probability being as sample
• Scientific method when the
population is homogeneous
Probability
sampling
• Sampling methods in which
every element dose not
possess probability of being as
sample
Non- probability
sampling

18. Probability sampling
• An element drawn as sample is
replaced in the frame list before
making another drawn at the time
sampling
• Each elements have equal probability
• Considered as a most scientific
Simple random
sampling with
replacement
• An element drawn as sample is not
replaced in the frame list before
making another drawn at the time
sampling
• Each elements have not equal
probability
Simple random
sampling without
replacement

19. Probability sampling
Restricted random sampling
• Systematic sampling
• Stratified sampling
• Cluster sampling
• Multistage sampling

20. Systematic sampling
• Formed by selecting one unit at random and then
selecting additional units at evenly spaced intervals until
the sample has been formed
• The first item is selected at random generally by lottery
method. Subsequent items are selected by taking every kth
item from the list
k= N/n
k=sampling interval, N=population, n=sample size
• It is applicable when the distribution of population is
homogenous
• Systematic sampling is best when the periodic fluctuation
is absent

21. Merits and limitations of systematic
sampling
• Merits:
• This method is simple and convenient.
• Time and work is reduced much.
• If proper care is taken result will be accurate.
• It can be used in infinite population.
• Limitations:
• Systematic sampling may not represent the
whole population.
• There is a chance of personal bias of the
investigators.

22. Stratified sampling
• The most scientific method when the population is
heterogeneous
• Should stratify population according to certain
characteristics
• Also called probability proportional to size sampling
• In each stratum, size of sample is depends on the size
of stratum

23. Merits of stratified sampling:
• It is more representative.
• It ensures greater accuracy.
• It is easy to administer as the universe is sub-divided.
• Greater geographical concentration reduces time and
expenses.
• When the original population is badly skewed, this
method is appropriate.
• For non-homogeneous population, it may field good
results.

24. Limitation of stratified sampling:
• To divide the population into homogeneous strata, it
requires more money, time and statistical experience
which is a difficult one.
• Improper stratification leads to bias, if the different
strata overlap such a sample will not be a
representative one.

25. Cluster sampling
• The techniques is applicable when the elements
under population are scatter over a large
geographical area
• In this techniques, clusters are selected randomly
to achieve required size of sampling

26. Multistage sampling
• Here the sampling units are selected in different stages
• E.g.
• A sample of 100 farmers was selected from Chitwan
among the different district lying at the terai part of
central region of Nepal
• 100 farmers belongs to 2 purposively selected VDC of
Chitwan namely Saradanagar and Pithuwa
• That belongs to the 2,4 and 1, 8 wards of Saradanagar
and Pithuwa, respectively

27. Non probability sampling
• Accidental sampling: covers the element which
happened on the way forward
• Purposive sampling: techniques implies the
selection of elements based on researchers’ interest
and objective
• Quota sampling: reservation is provided to
different stratum and if random sampling is applied
to select elements from the stratum then it becomes
stratified random sampling

28. Sampling errors and non-sampling
errors
• The two types of errors in a sample survey are sampling
errors and non - sampling errors.
• Sampling errors. There may be in most cases
difference between statistics and parameters. The
discrepancy between a parameter and its estimate due to
sampling process is known as sampling error.
• Non-sampling errors. In all surveys some errors may
occur during collection of actual information. These
errors are called Non-sampling errors.

29. Thank you