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z
SAMPLING
TECHNIQUES
z
Goals for the Module
 Distinguish between various sampling techniques and
identify how to sample populations correctly using
acceptable statistical processes to further reliability of
research and minimize bias.
z
Data is Essential
 Data is essential for business research irrespective of whether
an investigation is quantitative or qualitative in nature. The data
can be obtained in a number of ways.
 Ideally the researcher would like to collect data from all
members of a population under investigation. This is known as a
census. But in most situations this is not feasible. Therefore a
sample of the population is drawn.
z
SAMPLING
 Sampling is the process of selecting units, like people,
organizations, or objects from a population of interest in order to
study and fairly generalize the results back to the population
from which the sample was taken.
 A sample should have the same characteristics as the
population it is representing. Here, the sample is a
representative of the population and this is a requirement for
statistical inference to be valid.
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Sampling design
 The sampling design process involves answering the following
questions:
 (1) Should a sample or a census be used?
 (2) If a sample, then which sampling approach is best?
 (3) How large a sample is necessary?
 In answering these questions, the researcher must always
consider ways to minimize error that might occur in the sampling
process.
z
The Sampling Process
 Representative samples are generally obtained by following a
set of well-defined procedures:
 1. Defining the target population
 2. Choosing the sampling frame
 3. Selecting the sampling method
 4. Determining the sample size
 5. Implementing the sampling plan
z
Defining the Target Population
 The research objectives and scope of the study are critical in
defining the target population.
 The target population is the complete group of objects or
elements relevant to the research project. They are relevant
because they possess the information the research project is
designed to collect.
 Other practical factors may influence the definition of the target
population. They include knowledge of the topic of interest,
access to elements (individuals, companies, etc.), availability of
elements, and time frame.
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Choosing the Sampling Frame
 A sampling frame is a comprehensive list of the elements from
which the sample is drawn.
 A sampling frame is a complete a list as possible of all the
elements in the population from which the sample is drawn.
 Ideally, a sampling frame is an accurate, complete listing of all
the elements in the population targeted by the research.
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Selecting the Sampling Method
 Selection of the sampling method to use in a study depends on
a number of related theoretical and practical issues.
 They include considering the nature of the study, the objectives
of the study, and the time and budget available.
 Traditional sampling methods can be divided into two broad
categories: probability and nonprobability.
z
Determining Sample Size
 Sampling From a Large Population
Researchers often need to estimate the characteristics of large
populations. To achieve this efficiently, it is necessary to determine the
appropriate sample size prior to data collection.
Determination of the sample size is complex because of the many
factors that need to be taken into account simultaneously. The
challenge is to obtain an acceptable balance among several of these
factors. These factors include the variability of elements in the target
population, type of sample required, time available, budget,required
estimation precision, and whether the findings are to be generalized
and, if so, with what degree of confidence.
z
Determining Sample Size
 Sampling From a Large Population
 Formulas based on statistical theory can be used to compute the
sample size.
 For pragmatic reasons, such as budget and time constraints,
alternative ad hoc methods are often used.
 Examples are sample sizes based on rules of thumb, previous
similar studies, one’s own experience, or simply what is affordable.
Irrespective of how the sample size is determined, it is essential
that it be of a sufficient size and quality to yield results that are seen
to be credible in terms of their accuracy and consistency.
z
Sample Size
 Sample size is an important consideration in both quantitative
and qualitative research.
 For example, to generalize to the population, a sufficiently large
sample is required. In contrast, when using a qualitative
approach to develop theory on organizational behavior, a small
number of cases may be sufficient.
z
Sample Size Criteria
 Level of Precision – it is also referred to as the sampling error
or margin of error. It is a range of values in which the true value
of the population parameter is estimated to be.
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Example
 Population: Accountants in Baguio City
 To determine whether they use the recommended accounting
system.
 Level of Precision: ±5%
 Survey Result: 75% in the sample have adopted the
recommended system
 It can be concluded that between 70% and 80% of accountants
in the population have adopted the recommended system
z
z
Sample Size Criteria
 Confidence Level – This is also called risk level. This represents
the proportion of all possible samples that can be expected to
contain the true population parameter.
 95% and 99% are used.
 Interpretation: 95% of the samples will have the true population
value within the range of precision specified
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Sample Size Criteria
 Degree of Variability - It refers to the distribution of attributes in
the population.
 The more heterogeneous (or spread out) the population is,
the larger the sample size required in order to achieve a
given level of precision.
 The more homogeneous (or less spread out) the
population is, the smaller the sample size.
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Determining the Sample Size
 Calculating the size of a Sample for Proportions
When the variable of interest in your study is a categorical
variable, that assumes a dichotomous response for the attribute of
interest.
Cochran’s formula: For Large population to yield representative for
proportions:
z
Cochran’s formula:
Where 𝑛0 is the sample size,
Z is the abscissa of the normal curve that cuts off an area 𝛼
at the tails ((1 − 𝛼 ) equals the desired confidence level),
𝑒 is the desired level of precision,
𝑝 is the estimated proportion of items in the population that
exhibits the attribute of interest,
𝑞 is the estimated proportion of items in the population that
does not exhibit the attribute of interest which is
determined by q = 1 − 𝑝
The values p and q are taken from previous surveys or from similar studies.
z
Values of Z for commonly used
Confidence Levels
z
 When the values of 𝑝 and 𝑞 are not known, indicating that we do
not know about the variability in the proportion, we assume both
to be equal to 0.5.
 Assuming p and q to be equal to 0.5 provides us with the
maximum variability in the proportion and hence, a
conservative estimate of the sample size.
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Example:
Suppose you wish to evaluate the implementation of a new
system in which employees of a big company that has
different branches are encouraged to adopt. Suppose the
population of employees is large and we have no information
as to the variability in the proportion of these employees that
will adopt the new system. With this, we assume p = 0.5 and
we desire to use a 95% confidence level and ± 3% precision.
z
 For a 95% confidence level, the corresponding Z value is 1.96.
The required sample size would be
 For this case, you would need a sample of 1,068 educators.
 Note: when the calculated sample size is not a whole
number, it should always be rounded up to the next higher
whole number.
 When the sample size is rounded-off to the nearest whole
number, then you exceed the maximum margin of error (level of
precision) of your estimate in some cases.
z
Finite Population Correction for Proportions
 If the population is small, then we can slightly reduce the sample
size.
where n is the sample size while N is the population size
z
Example:
Suppose that in the previous example, there is information that only
3,000 educators were affected by the implementation of a new
system. The necessary sample size for the study, based on the
information about the affected population, will now be:
z
The Yamane’s formula
 If the researcher is not familiar with the behavior of the population, the Yaro
Yamen’s formula (1980), or Taro Yamane (1967) is used (nwaogazie, 2009;
ogbadu, 2009; ibikunle et al., 2012; okpiliya et al., 2012). This formula was also
referred to as the Slovin’s formula (pagoso, 1992) by kulkol magnus mcleod aka
kulkol slovin in 1843 as claimed by some. This is a simplified formula for
computing sample sizes for proportions by Yamane (1967). Yamane’s
formula assumes a 95% confidence level and a p value of 0.5
where 𝒏 is the sample size, 𝑵 is the population size, and 𝒆 is the level of
precision.
z
Example
z
Calculating the size of a Sample for the Mean
 Used when the variable assumes a polytomous response or if
the variable is quantitative
 When the variable of interest is polytomous or is quantitative,
one way of computing for the sample size is to combine the
responses into two categories and use the formula for
proportions.
 The other way, which applies to quantitative variables only, is to
use the formula for the sample size for the mean which is given
by
z
Calculating the size of a Sample for the Mean
 The other way, which applies to quantitative variables only, is to use
the formula for the sample size for the mean which is given by
where 𝒏𝒐 is the sample size,
𝒁 is the abscissa of the normal curve that cuts off an area 𝛼
at the tails,
𝒆 is the desired level of precision (in the same unit of
measure as the variance)
𝝈𝟐
is the variance of the attribute in the population.
z
Other Strategies
 Using a census for small populations. Use the entire
population as the sample. This would eliminate sampling
error and it would provide data for all items or individuals in
the population.
 Use the sample size of a similar study. Reviewing these
studies in your discipline or area of research can provide
guidance as to the typical sample sizes which are used.
z
Sampling techniques
 Random Samples. A random sample is a sample drawn in
such a way that each member of the population has equal
chance of being selected in the sample.
 Non-random Samples. In a non-random sample, some
members of the population may not have any chance of
being selected in the sample. Nonrandom sampling uses
some criteria for choosing the sample.
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The results obtained from a sample survey
may contain two types of errors:
 Sampling errors: The sampling error is also called the
chance error.
 The sampling error is the difference between the result
obtained from a sample survey and the result that would
have been obtained if the whole population had been
included in the survey.
 The actual process of sampling causes sampling errors
z
 Non-sampling errors. Non-sampling errors are also called
the systematic errors.
 Factors not related to the sampling process cause non-
sampling errors. These are errors that occur in the
collection, recording, and tabulation of data.
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Types of Errors
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Random Sampling Methods
 Probability sampling is typically used in quantitative
research.
 Simple random sampling (SRS) - most basic and well-
known type of random sampling technique.
A selection process ensures that every sample of size n has
an equal chance of being selected.
z
Systematic sampling - consists of randomly selecting one unit
and choosing additional elements at equal intervals until the
desired sample size is achieved.
z
 Stratified random sampling. This involves dividing the potential
samples into two or more mutually exclusive groups based on
strata/categories of interest in the research so that each
population item belongs to only one stratum.
z
Example
 Suppose a certain company has five departments
composed of the following number of employees.
Determine the number of employees to be part of the
sample when the researcher needs 363 respondents.
z
 Cluster Random Sampling. In cluster random sampling, you
randomly select clusters instead of individual samples in the
first stage of sampling.
 A cluster is any group of persons or experimental units having
similar characteristics. Cluster sampling is useful when the
members of the population under consideration are scattered
geographically.
z
 Multi-stage sampling. This method uses several stages or
phases in getting random samples from the general population.
this is useful in conducting nationwide surveys or any survey
involving a very large population.
 Multistage sampling is rarely used because of the complexity
of its strategy and it incurs a lot of time, effort, and expense. For
instance in a national survey, one can start by randomly
selecting a few regions from the various regions, then from each
of the regions select at random several provinces, and from the
selected provinces, randomly select some municipalities. The
gathering of data will be done in these municipalities.
z
Non-Probability Sampling
Nonprobability sampling is typically used in qualitative research.
In non-probability sampling, the selection of units is solely
determined by rules or guidelines set by the researcher/
investigator. Furthermore, in non-probability sampling, not all
members of the population are given equal chances to be
selected; certain elements in the population are deliberately left
out for some reasons. These types therefore, are prone to bias.
This is a sampling method that does not involve random selection
of samples. With non-probability samples, the population may or
may not be represented well, and it will often be difficult to know
how well the population has been represented.
z
 Accidental or Haphazard or Convenience sampling
 Convenience sampling is often used when it is really impossible
to select a random sample. Under this method, a group of
subjects is selected at will and at the researcher’s convenience.
 Purposive Sampling
sampling is based on certain criteria laid down by the researcher.
People who satisfy the criteria are interviewed.
z
Subcategories of Purposive sampling
 Modal instance sampling
When we do modal instance sampling, we are sampling the most
frequent case. The problem with modal instance sampling is
identifying the “modal” case. Modal instance sampling is only
sensible for informal sampling contexts.
 Expert sampling
Involves the assembling of a sample of persons with known or
demonstrable experience and expertise in some area.
Two reasons we might do expert sampling:
1. It would be the best way to elicit the views of persons who have
specific expertise.
2. To provide evidence for the validity of another sampling
approach you’ve chosen.
z
 Quota sampling
Select items non-randomly according to some fixed quota.
 Snowball sampling
Begin by identifying someone who meets the criteria for
inclusion in your study. You then ask them to recommend
others who they may know who also meet the criteria.
 Snowball sampling is especially useful when populations are
inaccessible or hard to find.

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Sampling Theory.pdf

  • 2. z Goals for the Module  Distinguish between various sampling techniques and identify how to sample populations correctly using acceptable statistical processes to further reliability of research and minimize bias.
  • 3. z Data is Essential  Data is essential for business research irrespective of whether an investigation is quantitative or qualitative in nature. The data can be obtained in a number of ways.  Ideally the researcher would like to collect data from all members of a population under investigation. This is known as a census. But in most situations this is not feasible. Therefore a sample of the population is drawn.
  • 4. z SAMPLING  Sampling is the process of selecting units, like people, organizations, or objects from a population of interest in order to study and fairly generalize the results back to the population from which the sample was taken.  A sample should have the same characteristics as the population it is representing. Here, the sample is a representative of the population and this is a requirement for statistical inference to be valid.
  • 5. z Sampling design  The sampling design process involves answering the following questions:  (1) Should a sample or a census be used?  (2) If a sample, then which sampling approach is best?  (3) How large a sample is necessary?  In answering these questions, the researcher must always consider ways to minimize error that might occur in the sampling process.
  • 6. z The Sampling Process  Representative samples are generally obtained by following a set of well-defined procedures:  1. Defining the target population  2. Choosing the sampling frame  3. Selecting the sampling method  4. Determining the sample size  5. Implementing the sampling plan
  • 7. z Defining the Target Population  The research objectives and scope of the study are critical in defining the target population.  The target population is the complete group of objects or elements relevant to the research project. They are relevant because they possess the information the research project is designed to collect.  Other practical factors may influence the definition of the target population. They include knowledge of the topic of interest, access to elements (individuals, companies, etc.), availability of elements, and time frame.
  • 8. z Choosing the Sampling Frame  A sampling frame is a comprehensive list of the elements from which the sample is drawn.  A sampling frame is a complete a list as possible of all the elements in the population from which the sample is drawn.  Ideally, a sampling frame is an accurate, complete listing of all the elements in the population targeted by the research.
  • 9. z Selecting the Sampling Method  Selection of the sampling method to use in a study depends on a number of related theoretical and practical issues.  They include considering the nature of the study, the objectives of the study, and the time and budget available.  Traditional sampling methods can be divided into two broad categories: probability and nonprobability.
  • 10. z Determining Sample Size  Sampling From a Large Population Researchers often need to estimate the characteristics of large populations. To achieve this efficiently, it is necessary to determine the appropriate sample size prior to data collection. Determination of the sample size is complex because of the many factors that need to be taken into account simultaneously. The challenge is to obtain an acceptable balance among several of these factors. These factors include the variability of elements in the target population, type of sample required, time available, budget,required estimation precision, and whether the findings are to be generalized and, if so, with what degree of confidence.
  • 11. z Determining Sample Size  Sampling From a Large Population  Formulas based on statistical theory can be used to compute the sample size.  For pragmatic reasons, such as budget and time constraints, alternative ad hoc methods are often used.  Examples are sample sizes based on rules of thumb, previous similar studies, one’s own experience, or simply what is affordable. Irrespective of how the sample size is determined, it is essential that it be of a sufficient size and quality to yield results that are seen to be credible in terms of their accuracy and consistency.
  • 12. z Sample Size  Sample size is an important consideration in both quantitative and qualitative research.  For example, to generalize to the population, a sufficiently large sample is required. In contrast, when using a qualitative approach to develop theory on organizational behavior, a small number of cases may be sufficient.
  • 13. z Sample Size Criteria  Level of Precision – it is also referred to as the sampling error or margin of error. It is a range of values in which the true value of the population parameter is estimated to be.
  • 14. z Example  Population: Accountants in Baguio City  To determine whether they use the recommended accounting system.  Level of Precision: ±5%  Survey Result: 75% in the sample have adopted the recommended system  It can be concluded that between 70% and 80% of accountants in the population have adopted the recommended system
  • 15. z
  • 16. z Sample Size Criteria  Confidence Level – This is also called risk level. This represents the proportion of all possible samples that can be expected to contain the true population parameter.  95% and 99% are used.  Interpretation: 95% of the samples will have the true population value within the range of precision specified
  • 17. z Sample Size Criteria  Degree of Variability - It refers to the distribution of attributes in the population.  The more heterogeneous (or spread out) the population is, the larger the sample size required in order to achieve a given level of precision.  The more homogeneous (or less spread out) the population is, the smaller the sample size.
  • 18. z Determining the Sample Size  Calculating the size of a Sample for Proportions When the variable of interest in your study is a categorical variable, that assumes a dichotomous response for the attribute of interest. Cochran’s formula: For Large population to yield representative for proportions:
  • 19. z Cochran’s formula: Where 𝑛0 is the sample size, Z is the abscissa of the normal curve that cuts off an area 𝛼 at the tails ((1 − 𝛼 ) equals the desired confidence level), 𝑒 is the desired level of precision, 𝑝 is the estimated proportion of items in the population that exhibits the attribute of interest, 𝑞 is the estimated proportion of items in the population that does not exhibit the attribute of interest which is determined by q = 1 − 𝑝 The values p and q are taken from previous surveys or from similar studies.
  • 20. z Values of Z for commonly used Confidence Levels
  • 21. z  When the values of 𝑝 and 𝑞 are not known, indicating that we do not know about the variability in the proportion, we assume both to be equal to 0.5.  Assuming p and q to be equal to 0.5 provides us with the maximum variability in the proportion and hence, a conservative estimate of the sample size.
  • 22. z Example: Suppose you wish to evaluate the implementation of a new system in which employees of a big company that has different branches are encouraged to adopt. Suppose the population of employees is large and we have no information as to the variability in the proportion of these employees that will adopt the new system. With this, we assume p = 0.5 and we desire to use a 95% confidence level and ± 3% precision.
  • 23. z  For a 95% confidence level, the corresponding Z value is 1.96. The required sample size would be  For this case, you would need a sample of 1,068 educators.  Note: when the calculated sample size is not a whole number, it should always be rounded up to the next higher whole number.  When the sample size is rounded-off to the nearest whole number, then you exceed the maximum margin of error (level of precision) of your estimate in some cases.
  • 24. z Finite Population Correction for Proportions  If the population is small, then we can slightly reduce the sample size. where n is the sample size while N is the population size
  • 25. z Example: Suppose that in the previous example, there is information that only 3,000 educators were affected by the implementation of a new system. The necessary sample size for the study, based on the information about the affected population, will now be:
  • 26. z The Yamane’s formula  If the researcher is not familiar with the behavior of the population, the Yaro Yamen’s formula (1980), or Taro Yamane (1967) is used (nwaogazie, 2009; ogbadu, 2009; ibikunle et al., 2012; okpiliya et al., 2012). This formula was also referred to as the Slovin’s formula (pagoso, 1992) by kulkol magnus mcleod aka kulkol slovin in 1843 as claimed by some. This is a simplified formula for computing sample sizes for proportions by Yamane (1967). Yamane’s formula assumes a 95% confidence level and a p value of 0.5 where 𝒏 is the sample size, 𝑵 is the population size, and 𝒆 is the level of precision.
  • 28. z Calculating the size of a Sample for the Mean  Used when the variable assumes a polytomous response or if the variable is quantitative  When the variable of interest is polytomous or is quantitative, one way of computing for the sample size is to combine the responses into two categories and use the formula for proportions.  The other way, which applies to quantitative variables only, is to use the formula for the sample size for the mean which is given by
  • 29. z Calculating the size of a Sample for the Mean  The other way, which applies to quantitative variables only, is to use the formula for the sample size for the mean which is given by where 𝒏𝒐 is the sample size, 𝒁 is the abscissa of the normal curve that cuts off an area 𝛼 at the tails, 𝒆 is the desired level of precision (in the same unit of measure as the variance) 𝝈𝟐 is the variance of the attribute in the population.
  • 30. z Other Strategies  Using a census for small populations. Use the entire population as the sample. This would eliminate sampling error and it would provide data for all items or individuals in the population.  Use the sample size of a similar study. Reviewing these studies in your discipline or area of research can provide guidance as to the typical sample sizes which are used.
  • 31. z Sampling techniques  Random Samples. A random sample is a sample drawn in such a way that each member of the population has equal chance of being selected in the sample.  Non-random Samples. In a non-random sample, some members of the population may not have any chance of being selected in the sample. Nonrandom sampling uses some criteria for choosing the sample.
  • 32. z The results obtained from a sample survey may contain two types of errors:  Sampling errors: The sampling error is also called the chance error.  The sampling error is the difference between the result obtained from a sample survey and the result that would have been obtained if the whole population had been included in the survey.  The actual process of sampling causes sampling errors
  • 33. z  Non-sampling errors. Non-sampling errors are also called the systematic errors.  Factors not related to the sampling process cause non- sampling errors. These are errors that occur in the collection, recording, and tabulation of data.
  • 35. z Random Sampling Methods  Probability sampling is typically used in quantitative research.  Simple random sampling (SRS) - most basic and well- known type of random sampling technique. A selection process ensures that every sample of size n has an equal chance of being selected.
  • 36. z Systematic sampling - consists of randomly selecting one unit and choosing additional elements at equal intervals until the desired sample size is achieved.
  • 37. z  Stratified random sampling. This involves dividing the potential samples into two or more mutually exclusive groups based on strata/categories of interest in the research so that each population item belongs to only one stratum.
  • 38. z Example  Suppose a certain company has five departments composed of the following number of employees. Determine the number of employees to be part of the sample when the researcher needs 363 respondents.
  • 39. z  Cluster Random Sampling. In cluster random sampling, you randomly select clusters instead of individual samples in the first stage of sampling.  A cluster is any group of persons or experimental units having similar characteristics. Cluster sampling is useful when the members of the population under consideration are scattered geographically.
  • 40. z  Multi-stage sampling. This method uses several stages or phases in getting random samples from the general population. this is useful in conducting nationwide surveys or any survey involving a very large population.  Multistage sampling is rarely used because of the complexity of its strategy and it incurs a lot of time, effort, and expense. For instance in a national survey, one can start by randomly selecting a few regions from the various regions, then from each of the regions select at random several provinces, and from the selected provinces, randomly select some municipalities. The gathering of data will be done in these municipalities.
  • 41. z Non-Probability Sampling Nonprobability sampling is typically used in qualitative research. In non-probability sampling, the selection of units is solely determined by rules or guidelines set by the researcher/ investigator. Furthermore, in non-probability sampling, not all members of the population are given equal chances to be selected; certain elements in the population are deliberately left out for some reasons. These types therefore, are prone to bias. This is a sampling method that does not involve random selection of samples. With non-probability samples, the population may or may not be represented well, and it will often be difficult to know how well the population has been represented.
  • 42. z  Accidental or Haphazard or Convenience sampling  Convenience sampling is often used when it is really impossible to select a random sample. Under this method, a group of subjects is selected at will and at the researcher’s convenience.  Purposive Sampling sampling is based on certain criteria laid down by the researcher. People who satisfy the criteria are interviewed.
  • 43. z Subcategories of Purposive sampling  Modal instance sampling When we do modal instance sampling, we are sampling the most frequent case. The problem with modal instance sampling is identifying the “modal” case. Modal instance sampling is only sensible for informal sampling contexts.  Expert sampling Involves the assembling of a sample of persons with known or demonstrable experience and expertise in some area. Two reasons we might do expert sampling: 1. It would be the best way to elicit the views of persons who have specific expertise. 2. To provide evidence for the validity of another sampling approach you’ve chosen.
  • 44. z  Quota sampling Select items non-randomly according to some fixed quota.  Snowball sampling Begin by identifying someone who meets the criteria for inclusion in your study. You then ask them to recommend others who they may know who also meet the criteria.  Snowball sampling is especially useful when populations are inaccessible or hard to find.