Chapter 13 - Sampling
Introduction
Experimental designs and surveys are useful and powerful in finding answers to research
questions through data collection and analyses. The process of selecting the right
individuals, objects, or events as representatives for the entire population is known as
sampling. Study of a sample instead of an entire population reduces time, cost and other
human resources. It can also be more reliable.
Population, Element, Sample, Sampling Unit, and Subject
Population
The population refers to the entire group of people, events, or things of interest that the
researcher wishes to investigate.
Element
An element is a single member of the population.
Sample
A sample is a subset of the population, researchers should be able to draw conclusions that
are generalizable to the population of interest after studying a sample.
Sampling Unit
The sampling unit is the element or set of elements that are available for selection in some
stage of the sampling process.
Subject
A subject is a single member of the sample.
Sample Data and Population Values
When we sample, the sampling units provide us with responses. We examine the responses
that we get for our entire samples, we make use of statistics. The reason we sample is that
we are interested in the characteristics of the population we sample from. If we study the
entire population and calculate the mean or standard deviation, we don't refer to this as a
statistic, instead, we call it a parameter.
Parameters
The characteristics of the population such as mean, standard deviation, and variance are
referred to as its parameters. The sample statistics such as sample mean, standard
deviation, and variation in the sample are used as estimates of the population parameters.
Representativeness of Sample
It is possible to choose the sample in such a way that it is representative of the population.
There is always a slight probability, however, that sample values might fall outside the
population parameters.
Normality of Distribution
From the central limit theorem, we know that the sampling distribution of the sample mean is
normally distributed. As the sample size ‘n’ increases, the means of the random samples
taken from practically any population approach a normal distribution with mean and standard
deviation. If we take a sufficiently large number of samples and choose them with care, we
will have a sampling distribution of the means that have normality. When the properties of
the population are not overrepresented or underrepresented in the sample, we have a
, representative sample. The more representative of the population the sample is, the more
generalizable are the findings of the research.
The Sampling Process
Sampling is the process of selecting a sufficient number of the right elements from the
population. The major steps include:
1. Define the population.
a. Sampling begins with precisely defining the target population. It must be
defined in terms of elements, geographical boundaries, and time.
2. Determine the sample frame.
a. The sampling frame is a physical representation of all the elements in the
population from which the sample is drawn.
3. Determine the sampling design.
a. There are two major types of sampling design; probability and nonprobability
sampling. In probability sampling, the elements in the population have some
known, nonzero chance or probability of being selected as sample subjects.
In nonprobability sampling, the elements do not have a known or
predetermined chance of being selected as subjects. The choice of the
sampling procedure is a very important one, being in mind the following points
in the determination of choice:
i. What is the relevant target of focus to the study
ii. What exactly are the parameters we are interested in investigating?
iii. What kind of sampling frame is available?
iv. What costs are attached to the sampling design?
v. How much time is available to collect the data from the sample?
4. Determine the appropriate sample size.
a. We can summarize the factors affecting decisions on sample size as:
i. The research objective.
ii. The extent of precision desired (the confidence interval)
iii. The acceptable risk in predicting that level of precision (confidence
level)
iv. The amount of variability in the population itself
v. The cost and time constraints.
vi. The size of the population itself
5. Execute the sampling process.
Probability Sampling
When elements in the population have a known, nonzero chance of being chosen as
subjects in the sample, we resort to a probability sampling design. Probability sampling can
either be unrestricted or restricted in nature.
Unrestricted or simple random sampling
In the unrestricted probability sampling design, more commonly known as simple random
sampling, every element in the population has a known and equal chance of being selected
Introduction
Experimental designs and surveys are useful and powerful in finding answers to research
questions through data collection and analyses. The process of selecting the right
individuals, objects, or events as representatives for the entire population is known as
sampling. Study of a sample instead of an entire population reduces time, cost and other
human resources. It can also be more reliable.
Population, Element, Sample, Sampling Unit, and Subject
Population
The population refers to the entire group of people, events, or things of interest that the
researcher wishes to investigate.
Element
An element is a single member of the population.
Sample
A sample is a subset of the population, researchers should be able to draw conclusions that
are generalizable to the population of interest after studying a sample.
Sampling Unit
The sampling unit is the element or set of elements that are available for selection in some
stage of the sampling process.
Subject
A subject is a single member of the sample.
Sample Data and Population Values
When we sample, the sampling units provide us with responses. We examine the responses
that we get for our entire samples, we make use of statistics. The reason we sample is that
we are interested in the characteristics of the population we sample from. If we study the
entire population and calculate the mean or standard deviation, we don't refer to this as a
statistic, instead, we call it a parameter.
Parameters
The characteristics of the population such as mean, standard deviation, and variance are
referred to as its parameters. The sample statistics such as sample mean, standard
deviation, and variation in the sample are used as estimates of the population parameters.
Representativeness of Sample
It is possible to choose the sample in such a way that it is representative of the population.
There is always a slight probability, however, that sample values might fall outside the
population parameters.
Normality of Distribution
From the central limit theorem, we know that the sampling distribution of the sample mean is
normally distributed. As the sample size ‘n’ increases, the means of the random samples
taken from practically any population approach a normal distribution with mean and standard
deviation. If we take a sufficiently large number of samples and choose them with care, we
will have a sampling distribution of the means that have normality. When the properties of
the population are not overrepresented or underrepresented in the sample, we have a
, representative sample. The more representative of the population the sample is, the more
generalizable are the findings of the research.
The Sampling Process
Sampling is the process of selecting a sufficient number of the right elements from the
population. The major steps include:
1. Define the population.
a. Sampling begins with precisely defining the target population. It must be
defined in terms of elements, geographical boundaries, and time.
2. Determine the sample frame.
a. The sampling frame is a physical representation of all the elements in the
population from which the sample is drawn.
3. Determine the sampling design.
a. There are two major types of sampling design; probability and nonprobability
sampling. In probability sampling, the elements in the population have some
known, nonzero chance or probability of being selected as sample subjects.
In nonprobability sampling, the elements do not have a known or
predetermined chance of being selected as subjects. The choice of the
sampling procedure is a very important one, being in mind the following points
in the determination of choice:
i. What is the relevant target of focus to the study
ii. What exactly are the parameters we are interested in investigating?
iii. What kind of sampling frame is available?
iv. What costs are attached to the sampling design?
v. How much time is available to collect the data from the sample?
4. Determine the appropriate sample size.
a. We can summarize the factors affecting decisions on sample size as:
i. The research objective.
ii. The extent of precision desired (the confidence interval)
iii. The acceptable risk in predicting that level of precision (confidence
level)
iv. The amount of variability in the population itself
v. The cost and time constraints.
vi. The size of the population itself
5. Execute the sampling process.
Probability Sampling
When elements in the population have a known, nonzero chance of being chosen as
subjects in the sample, we resort to a probability sampling design. Probability sampling can
either be unrestricted or restricted in nature.
Unrestricted or simple random sampling
In the unrestricted probability sampling design, more commonly known as simple random
sampling, every element in the population has a known and equal chance of being selected
