Sample and sampling

Sample and Sampling
• Definition: It is the process of selection of a part of a
population from the population to represent the whole
population.
• The main objective of sampling is to get information
regarding the population from which the sample is obtained.
• The sampling enables to draw inferences about the whole
population.
1

Important terms related to Sampling
• Sampling unit: Every item or every individual in a population is referred as
sampling unit.
• Sample: It is the part selected from the population or a group of individuals
selected from population. It is enables to learn about the whole population by
observing a few individuals.
• Population: It is the totality or aggregate of individuals with specified
characteristics. Population may be finite or infinite.
• E.g. Finite population: Number of plants in a quadrat is finite, number of
students in the class.
• Infinite population: Number of phytoplanktons in a pond, number of stars in
the sky, number of viruses in human body.
2

Size of sample
1. It denotes the number of sampling units, that are selected from
population. Sample size is based on decided on the time, resources
available, reliability, and expected outcomes.
2. Before deciding the size of sample following aspects are to be
considered:
i) Larger the population size, bigger should be the sample size.
ii) If population has homogenous units, small size sample serves the
purpose however, if the population has heterogeneous units, the
large size sample is essential. 3

Size of sample
iii) The nature and purpose of study is also important in
determination of the size of sample. Small sample is suitable for
continuous and intensive study.
iv) The factors like availability of finance, time and trained
persons is important in sample size.
v) For random sampling, the large number of samples gives better
accuracy in results.
vi) As a rule of thumb 1/10 part of the whole population is
taken as sample size.
4

Choice of sampling methods
• It is difficult to say that a particular sampling method would always be
better than the other ones. Each method has its own merits and demerits.
• The choice of selection of a particular method depends on the number of
factors like the nature of the problem, the size of the sample, the size of
population, availability of finance, time and trained persons etc.
• If the size of sample is small in relation to the size of population, then
judgment sampling would yield better results. For large- size sample,
random sampling would be more appropriate.
• When sample units are heterogeneous, the stratified sampling may give
better results than simple random sampling.
5

Advantages of sampling
1.The study of whole population requires much time, physical labour
and finance. By sampling, one can reduce this, as only a few
selected items are studied.
2.In the studies where individuals are short-lived, the sampling is the
only appropriate method.
3.Sampling is the most appropriate for the study of infinite population.
4.It is easy to handle a sample unit than to handle a whole population
that consists of many units.
6

Limitations of sampling technique
1.If sampling is not done properly, then results may be false, inaccurate
and misleading.
2.Personal bias regarding the choice of sampling size and sampling
method leads to wrongs conclusions.
3.Although there are some shortcomings in sampling techniques, yet it
is a very useful method for biostatistical investigations.
7

Types of sampling methods
• The purpose of sampling and the nature of the population will determine
choice of the sampling type. However, selection of sample should be done in
such a way that the sample taken should be a true representative of population.
• Sampling methods must have less sampling error i.e. the sample must have
characteristics as close as possible to the value that the researcher might have
obtained, if he had studied the whole population.
• There are two main types of sampling methods:
1. Random Sampling (probability sampling)
2. Non-Random Sampling (non-probability)
8

Random sampling with replicates
• Replication is the repetition of equivalent measurements.
• Replication is an essential element of a good field design.
• Generally replicated measurements will be more representative if they are
independent of each other and interspersed across the community.
• Replication is the repetition of an experimental condition to estimate the variability
associated with the phenomenon.
Need of random sampling:
• It provides equal opportunity for an item to get selected from the population.
• If data is not randomized, then the data collected from this design is likely to provide
an inaccurate representation of the entire study area.
• However, random sampling without replicates saves time and money in sampling but
it is not the true representative.
9

Methodology of achieving randomness
• Consider some alternatives. A bad approach is to throw randomization out the
window and subjectively select your sampling locations to ensure interspersion.
• Another bad approach is to make your random selection, but discard it if it has poor
interspersion.
• The problem here is that subjective bias can creep into the process when you decide
whether to discard a scheme.
• A good version of this approach would be to decide ahead of time on an objective
way to cull out sample arrangements with unacceptably poor interspersion.
• In the example above, a good rule might be to accept only those arrangements with
quadrats in all four quarters of the study area.
10

Randomness
• Measurements are usually subject to variation and
uncertainty.
• The experiments are replicated to identify the
sources of variation, to estimate the true effects of
treatments, to strengthen the reliability and validity
of experiment and to add to the existing knowledge
of the topic.
11

Randomness
12
Less randomness
More randomness

Random sampling
• This is also called probability sampling method.
• In this method all the items in the population have an equal chance
of being selected.
• Random sample is not a haphazard choice but is a careful selection
to ensure that every item has an equal chance of inclusion.
• Random sampling is widely used in medical, agricultural and
biological sciences.
• Major types of random sampling are lottery method, random
number method, systematic sampling, stratified sampling, etc.
13

Simple Random sampling
• It is the type of random sampling.
• This is the most common method in which a random sample
is chosen in such a way that all the items have an equal
chance of appearing in the sample.
• It ensures the randomness
• There are two major methods of simple random sampling
• i) Lottery method or
• Ii) Random number method
14

Lottery method
• This is the most popular and the simplest method.
• In this method all the items of the population are numbered
on separate paper slips of identical size, shape and colour.
• These paper slips are folded and mixed in a box and blind
selection is made.
• In this, the selection of each item depends on chance.
• This is also called unrestricted random sampling because
samples are selected without any restriction. 15

Lottery method
Merits:
• It is very simple to perform and easy to understand.
• This is the most common method is biological and
agricultural sciences.
Demerits:
• The limitation of this method is that it is used only
for finite populations. It not suitable for infinite
population.
16

Random number method
• It is a popular and the most practical method of random
sampling.
• In this Table of random numbers are used in place of
paper slips and blind selection.
• Random number table (5 digit) of Snedecor and
Cochran (1988) are used either horizontally or vertically
for selection of sample and it is without bias.
• There are several random number tables viz. Tippets
table, Fisher and Yates table, Rao and Mitra table and
Snedecor and Cochran table.
17

Random number method
• One can use the table of random numbers
from any position either horizontally or
vertically e.g. if we want to select 10 pods
from 200 pods, then each pod is assigned
a number from 00001 to 00200.
• One can start at any line and column from
the table. The numbers, which fall in that
line and column are taken and accordingly
10 samples are selected.
18
Part of random number table

Simple random sampling
• Merits of simple random sampling:
1. It is a more scientific method because there are less chances of personal bias.
2. One can measure sampling error.
3. The theory of probability is applicable, as sample is random.
• Demerits of simple random sampling:
1. It requires a complete list of all the items of the population. Many a times an
update lists are not available.
2. This method is not useful when the units of population are spread over a large
area.
19

Systematic sampling
• Selection of random samples is very tedious when samples to be selected are
very large population.
• Systematic sampling method is practiced when population is large, scattered
and not homogenous.
• In this method the items are arranged in numerical or geographical or
alphabetical or any other order.
• Eg. Samples of trees from a forest or houses in a city. In such cases a systematic
sampling is applied. Population
20

Systematic sampling
• Systematic procedure follows to choose a sample by taking every Kth
individual, where K refers the sample interval calculated by the
formula:
• K= Total population/Sample size desired.
• Ex. 20% sample to be taken from 1000 individual of a population,
• K= 1,000/20% of 1,000= 5
• So the first sample will be 5th individual
• Second sample will be 10th individual and third sample will be 15th
individual.
21

Systematic sampling
Merits of systematic sampling:
1. This method is simple and convenient.
2. It is inexpensive as it saves time and labour.
3. To maintain the randomness and to minimize tedious selection, systematic sampling
is used.
4. The sample is evenly distributed over the whole population and hence all
contiguous parts of the population are represented in the sample.
Demerits:
1. The major demerit of this is that it may not represent the whole population.
2. There is no single reliable formula available for estimating the standard error of
sample.
22

Stratified sampling
• This method gives better results as compared to other methods when
population is heterogeneous with respect to variable under study.
• In this method of sampling, the population is divided into relatively
homogenous groups, called strata or sub-populations.
• A random sample is drawn out from each stratum to produce an
overall sample.
23

Stratified sampling
• Drawing out of sample is proportional or non-proportional.
• In the former, items are taken from each stratum in the
proportion of the units of the stratum to the total population.
• In non-proportional sampling, equal numbers of units are taken
from each stratum irrespective of its size.
• E.g. Agronomists may stratify a plot of land based on its known
fertility level and then take a sample of plants from each
different stratum to measure their yield.
24

Stratified sampling
Merits:
1. It is more representative as every group is represented in a sample.
2. This method is more appropriate when the original population is badly skewed.
3. In a non-homogeneous population, this method gives more reliable results.
Demerits:
1. There is always a problem of deciding the criterion for stratification.
2. Prior knowledge of the population is required for better stratification, but this is not
always possible.
3. Many a times the points of demarcation of the strata are not clear-cut and the strata
overlaps.
4. If proper stratification is not done, then the sampling will be biased.
25

Non-random sampling
• The samples selected by these methods do not permit all the items in
the population to have an equal chance of being selected.
• Non-random (non- probability) sampling method is rarely used
because the sample estimates are subject to greater variability than the
probability sampling.
• The most common types of non-random sampling techniques are
• Judgment sampling,
• Quota sampling and
• Convenience sampling
26

Judgment sampling
• In this method the choice of the sample items depends exclusively on the
judgment of the investigator.
• The investigator selects only those items of the population in the sample
which he thinks are the representative of the whole population.
• In this, the method of selection is based on predetermined criteria. e.g. if a
sample of 10 plants of wheat bearing reproductive tillers is to be taken
from a plot of 100 plants for analyzing the yield of the plants, the
experimenter would select only 10 plants with a greater number of tillers
which he thinks are the representative of the whole population.
•
27

Judgment sampling
Merits:
1.It is a simple method.
2.It is useful when the size of the sample of the population is small.
3.It is very useful when sampling needed to be done under time
constraint.
Demerits:
1.The sample may not be a representative one due to individual bias.
2.The estimates are not accurate.
3.The results obtained can not be compared with other sampling
studies. 28

Convenience sampling
• As the name implies this technique is simply convenient to the
researcher in terms of time, money and administration.
• It also known as Chunk sampling.
• This method is occasionally used in special circumstances.
• Generally this method is not used in making inferences of the whole
population.
• This method is usually used for pilot studies before a final sampling
plan is decided upon.
• For example you can pick out 100 people to be surveyed simply from
telephone directory.
29

Convenience sampling
Merits:
1.It is a convenient method for researcher in terms of money,
time and administration.
2.The selection of sample is easy.
Demerits:
1.This method is biased.
2.The results obtained are unsatisfactory as they can not be
representative of the whole population.
30

Quota sampling
• This is most used in non-random categories.
• In this method sample quotas are fixed for characteristic of population.
• The selection of sample item in each quota depends on personal judgment.
• This method is a combination of judgment sampling and convenient
sampling.
• E.g. an animal scientist recognizing that variability in the daily milk
production is due to the age differences in cows. So he will fix quota for
cows from the different age groups. For instance 30% of cows between 4-6
years and remaining 70% of cows between 6-8 years old.
31

Quota sampling
Merit:
• It requires less money and time.
Demerits:
1.It is based on personal bias.
2.The samples may not be representative of the whole
population.
32

Sample and sampling

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