biostatistics and research methodology, Sampling

SAMPLING
Shaikh Sabina Meraj
Assistant Professor
Aurangabad

CENSUS AND SAMPLE
◦ Suppose you wish to study the ‘impact of T.V. advertisements on children in Delhi, then you
have to collect relevant information from the children residing in Delhi who view T.V.
◦ Alternatively, we can say this is the population (statistical terminology) for your study.
◦ If you collect the data from all of them not leaving a single child, it known as Census method of
data collection. This means studying the whole population.
◦ Otherwise, if you select only some children from among them for gathering the desired
information for the study, because it is not feasible to gather the information from all the
children, then it is known as Sample for data collection.
◦ A population is a group of individual persons, objects, items or any other units from which
samples are taken for measurement.
◦ The numerical characteristics of a population are called parameters. They are fixed and usually
of unknown quantity. For example, the average () height of all Indian male adults is a
population parameter.

The following are the advantages of census:
1. In a census each and every respondent of the population is considered and various population
parameters are compiled for information.
2.The information obtained on the basis of census data is more reliable and accurate. It is an
adopted method of collecting data on exceptional matters like child labour, distribution by sex,
educational level of the people etc.
3.If we are conducting a survey for the first time we can have a census instead of sample survey.
The information based on this census method becomes a base for future studies. Similarly,
some of the studies of special importance like population data are obtained only through
census.

Sampling is the process of selecting observations (a sample) to
provide an adequate description and inferences of the
population.
◾ Sample
⦿It is a unit that is selected from
population
⦿Represents the whole population
⦿Purpose to draw the inference
◾ Why Sample???
◾ Sampling Frame
Listing of population from which a sample is chosen

Population
Sample
Sampling
Frame
Sampling
Process
What you
want to
talk about
What you
actually
observe
in the
data
Inference

biostatistics and research methodology, Sampling

◦ One of the decisions to be made by a researcher in conducting a survey is
whether to go for a census or a sample survey. We obtain a sample rather
than a complete enumeration (a census ) of the population for many reasons.
1. Cost: The cost of conducting surveys through census method would be
prohibitive and sampling helps in substantial cost reduction of surveys. Since
most often the financial resources available to conduct a survey are scarce, it
is imperative to go for a sample survey than census.
2.Size of the Population: If the size of the population is very large it is difficult
to conduct a census if not impossible. In such situations sample survey is the
only way to analyse the characteristics of a population.
3. Accuracy of Data: Although reliable information can be obtained through
census, sometime the accuracy of information may be lost because of a large
population. Sampling involves a small part of the population and a few trained
people can be involved to collect accurate data. On the other hand, a lot of
people are required to enumerate all the observations. Often it becomes
difficult to involve trained manpower in large numbers to collect the data
thereby compromising accuracy of data collected. In such a situation a sample
may be more accurate than a census. A sloppily conducted census can
provide less reliable information than a carefully obtained sample.

4. Accessibility of Population: There are some populations that are so
difficult to get access to that only a sample can be used, e.g., people in
prison, birds migrating from one place to another place etc. The
inaccessibility may be economic or time related. In a particular study,
population may be so costly to reach, like the population of planets, that only
a sample can be used.
5. Timeliness: Since we are covering a small portion of a large population
through sampling, it is possible to collect the data in far less time than
covering the entire population. Not only does it take less time to collect the
data through sampling but the data processing and analysis also takes less
time because fewer observations need to be covered. Suppose a company
wants to get a quick feedback from its consumers on assessing their
perceptions about a new improved detergent in comparison to an existing
version of the detergent. Here the time factor is very significant. In such
situations it is better to go for a sample survey rather than census because it
reduces a lot of time and product launch decision can be taken quickly.
6. Destructive Observations: Sometimes the very act of observing the
desired characteristics of a unit of the population destroys it for the intended
use. Good examples of this occur in quality control. For example, to test the
quality of a bulb, to determine whether it is defective, it must be destroyed.
To obtain a census of the quality of a lorry load of bulbs, you have to destroy
all of them. This is contrary to the purpose served by quality-control testing.

The disadvantages of sampling
1.Risk: Using a sample from a population and drawing inferences about
the entire population involves risk. In other words the risk results from
dealing with a part of a population. If the risk is not acceptable in
seeking a solution to a problem then a census must be conducted.
2.Lack of representativeness: Determining the representativeness of
the sample is the researcher’s greatest problem. By definition,
‘sample’means a representative part of an entire population. It is
necessary to obtain a sample that meets the requirement of
representativeness otherwise the sample will be biased. The inferences
drawn from nonreprentative samples will be misleading and potentially
dangerous.
3.Insufficient sample size: The other significant problem in sampling is
to determine the size of the sample. The size of the sample for a valid
sample depends on several factors such as extent of risk that the
researcher is willing to accept and the characteristics of the population
itself.

ESSENTIALS OF A GOOD SAMPLE
1.A sample must represent a true picture of the population from which it
is drawn.
2.A sample must be unbiased by the sampling procedure.
3. A sample must be taken at random so that every member of the
population of data has an equal chance of selection.
4.A sample must be sufficiently large but as economical as possible.
5. A sample must be accurate and complete. It should not leave any
information incomplete and should include all the respondents, units or
items included in the sample.
6.Adequate sample size must be taken considering the degree of
precision required in the results of inquiry.

METHODS OF SAMPLING
◦ Random Sampling Methods
◦ The random sampling method is also often called probability sampling.
◦ In random sampling all units or items in the population have a chance of being chosen in the
sample.
◦ In other words a random sample is a sample in which each element of the population has a
known and non-zero chance of being selected.
◦ Random sampling always produces the smallest possible sampling error.
◦ In the real sense, the size of the sampling error in a random sample is affected only by a
random chance.
◦ Because a random sample contains the least amount of sampling error, we may say that it is an
unbiased sample.
◦ The following are the important methods of random sampling:
1) Simple Random Sampling
2) Systematic Sampling
3) Stratified Random Sampling
4) Cluster Sampling

1. Simple Random Sampling:
◦ The most commonly used random sampling method is simple random
sampling method.
◦ A simple random sample is one in which each item in the total population
has an equal chance of being included in the sample.
◦ In addition, the selection of one item for inclusion in the sample should in no
way influence the selection of another item.
◦ Simple random sampling should be used with a homogeneous population,
that is, a population consisting of items that possess the same attributes that
the researcher is interested in.
◦ The characteristics of homogeneity may include such as age, sex, income,
social/religious/political affiliation, geographical region etc.
◦ A random sampling method should meet the following criteria.
1.Every member of the population must have an equal chance of inclusion in
the sample.
2.The selection of one member is not affected by the selection of previous
members.

◦ Advantages
1. The simple random sample requires less knowledge about the characteristics
of the population.
2. Since sample is selected at random giving each member of the population
equal chance of being selected the sample can be called as unbiased sample.
Bias due to human preferences and influences is eliminated.
3.Assessment of the accuracy of the results is possible by sample error
estimation.
4.It is a simple and practical sampling method provided population size is not
large.
◦ Limitations
1.If the population size is large, a great deal of time must be spent listing and
numbering the members of the population.
2.A simple random sample will not adequately represent many population
characteristics unless the sample is very large. That is, if the researcher is
interested in choosing a sample on the basis of the distribution in the
population of gender, age, social status, a simple random sample needs to be
very large to ensure all these distributions are representative of the

2. Systematic Sampling:
◦ In systematic sampling the sample units are selected from the
population at equal intervals in terms of time, space or order. The
selection of a sample using systematic sampling method is very simple.
From a population of ‘N’ units, a sample of ‘n’ units may be selected by
following the steps given below:
1.Arrange all the units in the population in an order by giving serial
numbers from1toN.
2.Determine the sampling interval by dividing the population by the
sample size. That is, K=N/n.
3.Select the first sample unit at random from the first sampling interval (1
to K).
4. Select the sub sequent sample units at equal regular intervals.

◦ Advantages
1.The main advantage of using systematic sample is that it is more expeditious to
collect a sample systematically since the time taken and work involved is less than in
simple random sampling. For example, it is frequently used in exit polls and store
consumers.
2.This method can be used even when no formal list of the population units is available.
For example, suppose if we are interested in knowing the opinion of consumers on
improving the services offered by a store we may simply choose every kth (say 6th)
consumer visiting a store provided that we know how many consumers are visiting the
store daily (say 1000 consumers visit and we want to have 100 consumers as sample
size).
◦ Limitations
1.If there is periodicity in the occurrence of elements of a population, the selection of
sample using systematic sample could give a highly un-representative sample. For
example, suppose the sales of a consumer store are arranged chronologically and
using systematic sampling we select sample for 1st of every month. The 1st day of a
month can not be a representative sample for the whole month. Thus in systematic
sampling there is a danger of order bias.
2. Every unit of the population does not have an equal chance of being selected and the

3. Stratified Random Sampling:
◦ Population is divided into two or more groups called strata
◦ Subsamples are randomly selected from each strata

3. Stratified Random Sampling:
◦ The stratified sampling method is used when the population is heterogeneous rather than
homogeneous.
◦ A heterogeneous population is composed of unlike elements such as male/female, rural/urban,
literate/illiterate, high income/low income groups, etc.
◦ In such cases, use of simple random sampling may not always provide a representative sample
of the population.
◦ In stratified sampling, we divide the population into relatively homogenous groups called strata.
◦ Then we select a sample using simple random sampling from each stratum.
◦ There are two approaches to decide the sample size from each stratum, namely, proportional
stratified sample and disproportional stratified sample.
◦ With either approach, the stratified sampling guarantees that every unit in the population has a
chance of being selected.
◦ We will now discuss these two approaches of selecting samples.

Proportional stratified sample
◦ If no of sampling units drawn from each stratum is in proportion to the corresponding stratum population
size, we say the sample is proportional stratified sample.
◦ For example, let us say we want to draw a stratified random sample from a heterogeneous
population (on some characteristics) consisting of rural/urban and male/female respondents.
◦ So we have to create 4 homogeneous sub groups called stratums as follows:
Urban Rural
Male Female Male Female

Disproportional Stratified Sample:
◦ In a disproportional stratified sample, sample size for each stratum is not allocated on
a proportional basis with the population size, but by analytical considerations of the
researcher such as stratum variance, stratum population, time and financial
constraints etc.
◦ For example, if the researcher is interested in finding differences among different
stratums, disproportional sampling should be used.
◦ Consider the example of income distribution of households.
◦ There is a small percentage of households within the high income brackets and a
large percentage of households within the low income brackets.
◦ The income among higher income group households has higher variance than the
variance among the lower income group households.
◦ To avoid under-representation of higher income groups in the sample, a
disproportional sample is taken.
◦ This indicates that as the variability within the stratum increases sample size must
increase to provide accurate estimates and vice-versa.

◦ Advantages
a) Since the sample are drawn from each of the stratums of the population,
stratified sampling is more representative and thus more accurately
reflects characteristics of the population from which they are chosen.
b) It is more precise and to a great extent avoids bias.
c) Since sample size can be less in this method, it saves a lot of
time, money and other resources for data collection.
◦ Limitations
a) Stratified sampling requires a detailed knowledge of the
distribution of attributes or characteristics of interest in the
population to determine the homogeneous groups that lie within it.
If we cannot accurately identify the homogeneous groups, it is
better to use simple random sample since improper stratification
can lead to serious errors.
b) Preparing a stratified list is a difficult task as the lists may not be
readily available.

4. Cluster Sampling
◦ The population is divided into subgroups (clusters) like families.
◦ A simple random sample is taken from each cluster.

4. Cluster Sampling
◦ In cluster sampling we divide the population into groups having heterogenous characteristics
called clusters and then select a sample of clusters using simple random sampling.
◦ We assume that each of the clusters is representative of the population as a whole. This
sampling is widely used for geographical studies of many issues.
◦ For example if we are interested in finding the consumers’ (residing in Delhi) attitudes towards
a new product of a company, the whole city of Delhi can be divided into 20 blocks.
◦ We assume that each of these blocks will represent the attitudes of consumers of Delhi as a
whole, we might use cluster sampling treating each block as a cluster.
◦ We will then select a sample of 2 or 3 clusters and obtain the information from consumers
covering all of them.
◦ The principles that are basic to the cluster sampling are as follows:
1.The differences or variability within a cluster should be as large as possible. As far as possible
the variability within each cluster should be the same as that of the population.
2.The variability between clusters should be as small as possible. Once the clusters are selected,
all the units in the selected clusters are covered for obtaining data.

◦ Advantages
1.The cluster sampling provides significant gains in data
collection costs, since traveling costs are smaller.
2.Since the researcher need not cover all the custers and only
a sample of clusters are covered, it becomes a more
practical method which facilitates fieldwork.
◦ Limitations
1.The cluster sampling method is less precise than sampling
of units from the whole population since the latter is expected
to provide a better cross-section of the population than the
former, due to the usual tendency of units in a cluster to be
homogeneous.
2.The sampling efficiency of cluster sampling is likely to
decrease with the decrease in cluster size or increase in
number of clusters.

5. Multistage Sampling:
◦ Carried out in stages
◦ Using smaller and smaller sampling units at each stage
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S e c o n d a r y
C l u s t e r s S i m p l e R a n d o m S a m p l i n g w i t h i n

5. Multistage Sampling:
◦ We have already covered two stage sampling. Multi stage sampling is a generalisation of two
stage sampling.
◦ As the name suggests, multi stage sampling is carried out in different stages.
◦ In each stage progressively smaller (population) geographic areas will be randomly selected.
◦ A political pollster interested in assembly elections in Uttar Pradesh may first divide the state
into different assembly units and a sample of assembly constituencies may be selected in the
first stage.
◦ In the second stage, each of the sampled assembly constituents are divided into a number of
segments and a second stage sampled assembly segments may be selected.
◦ In the third stage within each sampled assembly segment either all the house-holds or a sample
random of households would be interviewed.
◦ In this sampling method, it is possible to take as many stages as are necessary to achieve a
representative sample.
◦ Each stage results in a reduction of sample size.

◦ Advantages
1.Multistage sampling provides cost gains by reducing the
data collection on costs.
2.Multistage sampling is more flexible and allows us to use
different sampling procedures in different stages of
sampling.
3.If the population is spread over a very wide geographical
area, multistage sampling is the only sampling method
available in a number of practical situations.
◦Limitations
◦a) If the sampling units selected at different stages are
not representative multistage sampling becomes less
precise and efficient.

Non-Random Sampling Methods
◦ The non-random sampling methods are also often called non-probability
sampling methods.
◦ In a non-random sampling method the probability of any particular unit of the
population being chosen is unknown.
◦ Here the method of selection of sampling units is quite arbitrary as the
researchers rely heavily on personal judgment.
◦ Non-random sampling methods usually do not produce samples that are
representative of the general population from which they are drawn.
◦ The greatest error occurs when the researcher attempts to generalise the
results on the basis of a sample to the entire population.
◦ The various non-random sampling methods commonly used are:
1) Convenience Sampling;
2) Judgement Sampling
3) Quota Sampling.

1) Convenience Sampling:
◦ Convenience sampling refers to the method of obtaining a sample that
is most conveniently available to the researcher.
◦ For example, if we are interested in finding the overtime wage paid to
employees working in call centres, it may be convenient and
economical to sample employees of call centres in a near by area.
◦ Also, on various issues of public interest like budget, election, price rise
etc., the television channels often present on-the-street interviews with
people to reflect public opinion.
◦ It may be cautioned that the generalisation of results based on
convenience sampling beyond that particular sample may not be
appropriate. Convenience samples are best used for exploratory
research when additional research will be subsequently conducted with
a random sample. Convenience sampling is also useful in testing the
questionnaires designed on a pilot basis. Convenience sampling is
extensively used in marketing studies.

2) Judgement Sampling:
◦ Judgement sampling method is also known as purposive sampling.
◦ In this method of sampling the selection of sample is based on the researcher’s judgment about
some appropriate characteristic required of the sample units.
◦ For example, the calculation of consumer price index is based on a judgment sample of a
basket of consumer items, and other related commodities and services which are expected to
reflect a representative sample of items consumed by the people.
◦ The prices of these items are collected from selected cities which are viewed as typical cities
with demographic profiles matching the national profile.
◦ In business judgment sampling is often used to measure the performance of
salesmen/saleswomen.
◦ The salesmen/saleswomen are grouped into high, medium or low performers based on certain
specified qualities.
◦ Then the sales manager may actually classify the salesmen/saleswomen working under him/her
who in his/her opinion will fall in which group.
◦ Judgment sampling is also often used in forecasting election results.
◦ We may often wonder how a pollster can predict an election based on only 2% to 3% of votes
covered.
◦ It is needless to say the method is biased and does not have any scientific basis.

3) Quota Sampling:
◦ The quota sampling method is commonly used in marketing research studies.
◦ The samples are selected on the basis of some parameters such as age, sex, geographical
region, education, income, occupation etc, in order to make them as representative samples.
◦ The investigators, then, are assigned fixed quotas of the sample meeting these population
characteristics.
◦ The purpose of quota sampling is to ensure that various sub-groups of the population are
represented on pertinent sample characteristics to the extent that the investigator desires.
◦ The stratified random sampling also has this objective but should not be confused with quota
sampling.
◦ In the stratified sampling method the researcher selects a random sample from each group of
the population, where as, in quota sampling, the interviewer has a quota fixed for him/her to
achieve.
◦ For example, if a city has 10 market centres, a soft drink company may decide to interview 50
consumers from each of these 10 market centres to elicit information on their products.
◦ It is entirely left to the investigator whom he/she will interview at each of the market centres and
the time of interview.

◦ Advantage
◦ The sample confirms the selected characteristics of the population that the
researcher desires.
◦ The cost and time involved in collecting the data are also greatly reduced.
◦ Limitations
a) In quota sampling the respondents are selected according to the
convenience of the field investigator rather than on a random basis. This kind
of selection of sample may be biased.
b) If the number of parameters, on which basis the quotas are fixed, are larger
then it becomes difficult for the researcher to fix the quota for each sub-
group.
c) Thefieldworkershavethetendencytocoverthequotabygoingtothoseplaces
where the respondents may be willing to provide information and avoid those
with unwilling respondents

⦿The errors which arise due to the use of
sampling surveys are known as the sampling
errors.
Two types of sampling errors
⦿Biased Errors- Due to selection of sampling
techniques; size of the sample.
⦿Unbiased Errors / Random sampling errors-
Differences between the members of the
population included or not included.

⦿Specific problem selection.
⦿Systematic documentation of related research.
⦿Effective enumeration.
⦿Effective pre testing.
⦿Controlling methodological bias.
⦿Selection of appropriate sampling techniques.

⦿ Non-sampling errors refers to biases and
mistakes in selection of sample.
⦿CAUSES FOR NON-SAMPLING ERRORS
 Sampling operations
 Inadequate of response
 Misunderstanding the concept
 Lack of knowledge
 Concealment of the truth.
 Loaded questions
 Processing errors
 Sample size

biostatistics and research methodology, Sampling

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