SOME IMPORTANT TERMS IN SAMPLING
Population
By population we mean the aggregate
or totality of objects or individuals regarding which inferences are to be made
in a sampling study. A population is any group of individuals that have one or
more characteristics in common that are of interest of the researcher.
Sample
A sample is a small proposition of a
population selected for observation and analysis. By observing the
characteristics of the sample, one can make certain inferences about the
characteristics of the population from which it is drawn.
Sampling
It is the
process of selection of sample from the population. For this purpose, the
population is divided into a number of parts called sampling units.
Parameter
A parameter is the population value
representing any trait or characteristics of the population as a whole.
Statistics
A statistics is the sample value
representing any trait or characteristic of the members of the sampling.
Sampling
Error
Sampling error is simply the
difference between the value of parameter and that of corresponding statistic
or the difference between population value and sample value.
Sampling
Distribution
The sampling distribution is the
relative frequency distribution of an infinity of determinants of the value of
this statistic.
Sampling
Bias
If the mean of the sampling
distribution of a statistic coincides with or equals that of the corresponding
parameter it is said to be unbiased. If, on the other hand, the mean of its
sampling distribution does not coincide with the parameter, it is said to be
biased.
Standard
Error
The standard error of any statistic
is the standard deviation of its sampling distribution.
·
When the population is very large it can be
satisfactorily corrected by sampling.
·
It saves a lot of money, time, energy etc.
· Especially when the units of the area are homogeneous
sampling technique is merely useful.
·
When the data’s are unlimited the use of this method
is readily useful.
Characteristics
of a good sampling:
1. True representative:
A good
sample is a true representative of the population corresponding to its
properties.
2. Free from bias:
A good
sample is free from bias. It does not permit prejudicious, preconceptions and
imagination to influence its choice.
3. Objective:
A good
sample is an objective one. It prefers to objectivity in selection procedure or
absence of subjective elements from the situation.
4. Accurate:
A good
sample maintains accuracy. It gives accurate estimates or statistics and does
not involve errors.
5. Comprehensive:
A good
sample is comprehensive in nature. A comprehensive sample is controlled by
specific purpose of the investigator.
6. Economical:
A
good sample is economical in terms of energy, time at any point of view.
7. Approachable:
The
subjects of good sample are easily approachable. The research tools can be
easily administrated on them and the data can be easily collected.
8. Good size:
The size of
good sample is such that it yields an accurate result. The probability of
errors can be estimated.
9.
Feasible:
A good sample makes the research work more feasible.
METHODS OF SAMPLING
Bloomers and Lindquist have said, in general
sampling schemes may be classified into two they are:
a)
Probability Sampling
b)
Non-probability Sampling
a)
Probability Sampling:
·
In probability sampling every
individual of the population has equal chance of selecting.
·
Probability sample may be
representative of the population.
·
The observations (Data) of the
probability sample are used for the inferential purpose.
·
Inferential or parametric
statistics are used for probability sample.
·
There is a risk for drawing
conclusions from probability sample.
b)
Non-Probability Sampling:
·
There is no probability of
selecting any individual.
·
The observations of non-probability
sample are not used for generalization purpose.
·
Non-parametric or non-inferential
statics are used in non-probability sample.
·
There is no risk for drawing
conclusions from non-probability sample.
Probability
Sampling Techniques
1.
Simple Random Sampling
A
simple random sample is one in which each element of the population has an
equal and independent chance of being included in the sample. It is defined as
a sampling technique where every item in the population has an even chance and
likelihood of being selected in the sample. Here the selection of items
entirely depends on luck or probability, and therefore this sampling technique
is also sometimes known as a method of chances. Randomization is done by using a
number of techniques as: Tossing a coin, Throwing a dice, Lottery method etc.
For example to select a sample of 200 students from a population of 10,000
students using simple random sampling, the researcher has to number all the
10,000 students as 1,2,3,….10,000. Then using random number table or a computer
generated random numbers, a list of 200 students are prepared and invited to be
the sample for the research study.
Advantages
• It is free from subjectivity and free from
personal error.
• It provides appropriate data for the purpose
of research.
• The observations of the sample can be used for
inferential purpose.
Dis-advantages
•
The inferential accuracy of the finding
depends upon the size of the sample. So the greater the sample size, the greater is the
accuracy of results.
•
The representativeness of a sample cannot
be ensured by this method.
•
Inappropriate for heterogeneous sample.
2.
Systematic Sampling
Systematic
random sampling is a type of probability sampling technique. With the
systematic random sample, there is an equal chance (probability) of selecting
each unit from within the population when creating the sample. The systematic
sample is a variation on the simple random sample. Rather than referring to
random number tables to select the cases, the researcher selects units directly
from the sample frame. This method selects the individuals of the population in
any systematic way. It involves selecting every Kth item (K=
Sampling Interval). Which can be determined by K=No. of items in the population
/ No. of items in the sample. For example: Imagine that a researcher wants to study
about the career goals of students at a University, and if the university has
roughly 10,000 students. These 10,000 students form the population (N). In
order to select a sample of 400 students from this population of 10,000
students, using systematic random sampling, the
researcher could select every 25th student to get a sample of 400 where 25 is the
sampling interval ie. (10000/400).
Advantages
• This is a simple method of selecting a large
number of samples.
• This method improves the possibility for the sampling
units to be more evenly spread over the population.
• This method reduces the potential for human
bias in the selection of cases to be included in the sample. So it provides a
highly representative sample
Dis-advantages
• There
is a chance of selecting the homogeneous group if the list of the population
has some kind of standardized arrangement (order/pattern). In that case
systematic sampling could pick out similar cases rather than completely random
ones.
• Attaining
a complete list of the population can be a difficult task for the researcher in
certain cases.
3.
Stratified Sampling
Unlike the simple random sampling and the systematic
random sampling, sometimes if the researcher is interested in particular strata
or groups within the population such as male vs. female, rural vs urban etc., In
that case, stratified random sampling method is the most useful method. In this
method the population is divided into strata on the basis of some
characteristics such as gender, locality, medium of instruction etc., and from
each of these smaller homogeneous groups (Strata) samples are selected randomly.
This stratification of the population should be relevant to the particular
research study. Stratified random sampling can be classified as proportionate
sampling and disproportionate sampling.
·
Proportionate sampling: In this technique,
the samples are selected from each stratum as they stand in the universe ie. in
the way they are distributed in the population.
·
Dis-proportionate sampling: In this
technique an equal number of samples are taken from each stratum regardless of
the size of strata in proportion to the universe or population.
For example if a researcher wants to
select a sample of 100 from a population of 10,000 students he may choose the
100 as 50 male and 50 female.
Advantages
• It yields a
sample that is a good representative of the population.
• It is an
objective method of sampling.
Dis-advantages
• It is
difficult for the researcher to decide the relevant criterion for
stratification. Also a complete list of population is needed for doing this
method of sampling.
• Bias
may occur due to improper stratification
4.
Cluster sampling
Cluster
sampling is typically used in market research. It’s used when a researcher
can’t get information about the population as a whole, but they can get
information about the clusters. In cluster sampling, the researcher divides the
population into separate groups, called clusters. Then, a simple random sample
of clusters are selected from the population. Example: Imagine an organization wants
to survey the performance of smartphones across a country. They can divide the
entire country’s population into cities (clusters) and select n cities among
them and include all the members of the city.
Thus in cluster sampling the total
population is divided into a number of relatively small subdivisions called
clusters then from these clusters respondents or cases are randomly selected
for inclusion in the overall sample. Suppose we want to estimate the proportion
of machine parts in an inventory which are defective. Also assume that there
are 20000 machine parts in the inventory at a given point of time, stored in
400 cases of 50 each. Now using a cluster sampling, we would consider the 400
cases as clusters and randomly select ‘n’ cases and examine all the machine
parts in each randomly selected case.
Advantages
• It is an
easy method and economical method.
• It is
practical and highly applicable in education.
Dis-advantages
• Produces larger sampling error
• May be biased in certain cases.
• Generalizations may lack precision.
5.
Multistage sampling
Multistage
sampling divides large populations into stages to make the sampling process
more practical. It is a complex form of cluster sampling, sometimes, also known
as multistage cluster sampling. In this method, significant clusters of the
selected groups are split into sub-groups at various stages to make it simpler
for primary data collection. In this method first the researcher samples
inclusive groups from the population and then select subgroups from the
inclusive groups. At the third stage individual cases are selected from the
selected subgroups. At every level sampling is done at random. Suppose is a
researcher wants to investigate the working efficiency of nationalized banks in
India. The researcher using multi-stage sampling divides the population into
states and take a simple random sample of states. For the next stage, the
researcher takes a simple random sample of banks from within those states. Then
he may randomly select certain districts and interview all banks in the chosen
districts.
Advantages
• It is a good representation of the
population.
• It is an objective procedure of sampling.
Dis-advantages
• It is a difficult and complex method of
sampling.
• It involves error in the primary and
secondary stages of sampling.
Non-Probability Techniques
• There is no idea of population in
non-probability sampling.
• There is no probability of selecting any
individual
• Non probability sample has a free
distribution.
• Observations are not used for
generalization purpose.
• Non Parametric or Non –Inferential
statistics are used.
Non-Probability
based Sampling Techniques
1.
Incidental or Accidental Sampling
The term incident
or accidental applied to those samples that are taken because they are most
frequently available, i.e., this refers to group which are used as samples of a
population because they are readily available or the researcher is unable to
employ more acceptable sampling methods. It is applicable when such groups used
as samples are easily available eg., Children in a school, members of a club It
may be quite acceptable for certain action research projects which do not
require generalizations. It is generally used in exploratory studies where much
accuracy is not needed.
Advantages
·
It
is very easy method of sampling.
·
It
reduces the time, money and energy, i.e., it is an economical method.
Dis-advantages
·
It
is not a representative of the population.
·
It
is not free from error.
2. Judgement Sampling
This involves the selection of a
group from the population on the basis of available information thought it is
to be representative of the total population. In this method the investigator
selects a particular group and leaves the rest of the members of the group. The
researcher himself judges that this is a good representative sample.
Advantages
·
Knowledge
of the investigator can be best used in this technique of sampling.
·
This
technique of sampling is also economical.
Dis-advantages
·
It
is not free from error.
·
It
includes uncontrolled variation.
3. Quota Sampling
This is a combined form of both
judgement sampling and probability sampling. The population is classified into
several categories. On the basis of judgement or assumption or the previous
knowledge, the proportion of population falling into each category is decided.
Quota sampling is very arbitrary and likely to figure in municipal surveys.
Advantages
·
It
is an easy sampling technique.
·
It
is most frequently used in social surveys.
Dis-advantages
·
It
is not a representative sample.
·
It
is not free from error.
·
It
has the influence of regional, geographical and social factors.
4. Convenience sampling
It is also known as careless, unsystematic or opportunistic
sampling. In this type the researcher select certain units, which are
convenient to him. No preplanning is necessary for the selection of items. This
method may be used for pilot studies. It is also used when the Universe is not
clear, Sampling unit is not clear and complete source list is not available.
5. Snowball Sampling
Snowball
sampling or chain-referral sampling is defined as a non-probability sampling
technique in which the samples have traits that are rare to find. This is a
sampling technique, in which existing subjects provide referrals to recruit
samples required for a research study. Snowball sampling method is purely based
on referrals and that is how a researcher is able to generate a sample.
Therefore this method is also called the chain-referral sampling method. The
snowball sampling method is extensively used where a population is unknown and
rare and it is tough to choose subjects to assemble them as samples for
research.
Advantages
·
The chain referral process allows the
researcher to reach populations that are difficult to sample when using other
sampling methods.
·
The process is cheap, simple and
cost-efficient.
·
This sampling technique needs little
planning and fewer workforce compared to other sampling techniques.
Disadvantages
of Snowball Sampling
·
The researcher has little control over the
sampling method. The subjects that the researcher can obtain rely mainly on the
previous subjects that were observed.
·
Representativeness of the sample is not
guaranteed. The researcher has no idea of the true distribution of the
population and of the sample.
·
Sampling bias is also a fear of
researchers when using this sampling technique. Initial subjects tend to
nominate people that they know well. Because of this, it is possible that the
sample that the researcher will obtain is only a small subgroup of the entire
population with similar characteristics.
Sampling error
Sampling
error is incurred when the statistical characteristics of a population are
estimated from a subset, or sample, of that population. Since the sample does
not include all members of the population, statistics on the sample, such as
means and quantiles, generally differ from the characteristics of the entire
population, which are known as parameters. Since sampling is typically done to
determine the characteristics of a whole population, the difference between the
sample and population values is considered a sampling error.
Population
Specification Error: This error occurs when the researcher does not understand
who he/she should survey. If the researcher is not aware of the population
clearly then he is likely to draw a faulty sample which may lead to sampling
error.
Sample
frame Error - A frame error occurs when the wrong sub-population is used to
select a sample. Sometimes the researcher may choose his/her sample from a
biased frame which may cause sampling error.
Selection
Error - This occurs when respondents self-select their participation in the
study – only those that are interested respond. Selection error can be
controlled by going extra lengths to get participation.
Non-Response
- Non-response errors occur when respondents are different than those who do
not respond. This may occur because either the potential respondent was not
contacted or they refused to respond. The extent of this non-response error can
be checked through follow-up surveys using alternate modes.
These
errors occur because of variation in the number or representativeness of the
sample that responds. Sampling errors can be controlled by (1) careful sample
designs, (2) large samples, and (3) multiple contacts to assure representative
response.
Sample Size
The
sample size is a term used for defining the number of subjects included in a
sample size. By sample size, we understand a group of subjects that are
selected from the general population and is considered a representative of the
real population for that specific study. Sample size in the context of
educational research refers to the number of participants in an experiment or
study.
For
example, if we want to predict how the population in a specific age group will
react to a new product, we can first test it on a sample size that is
representative of the targeted population.
The
sample size is a subset, an extract, several persons extracted from that
population. The population is considered infinite; in practice, we cannot study
an endless number of cases.
The
size of the sample should be large enough to be an accurate representation of
the population and large enough to achieve statistically significant results.
For
descriptive research (ex: aviators), a number of 20% of the respective
population is sufficient. The larger the population, the smaller the
percentage. Ex: 20% of 1000 people = 200 people; 10% of 5000 people = 500 people.
For small populations (under 100 persons), the sample size is approximately
equal to the population.
