Understanding Sampling in Survey Research

 
EMR 6500:
Survey Research
 
Dr. Chris L. S. Coryn
Lyssa N. Wilson
Spring 2015
 
 
Agenda
 
Elements of the sampling problem
Some basic concepts of statistics
Case Study #1
 
Elements of the Sampling
Problem
 
Technical Terms (Again)
 
An 
element 
is an object on which a
measurement is taken
A 
population 
is a collection of elements
to which an inference is made
A 
sample
 is a collection of sampling
units drawn from a frame or frames
Sampling units
 are nonoverlapping
collections of elements from the
population that cover the entire
population
A 
frame
 is a list of sampling units
 
How to Select the Sample: The
Design of the Survey Sample
 
How to Select the Sample
 
The objective of sampling is to
estimate population parameters such
as the mean, proportion, or total
The quantity of information is
controlled by the number of units
included in a sample and the method
used to select a sample
 
How to Select the Sample
 
The primary questions addressed by
sampling theory are:
What sampling procedure should be
used?
What number of sampling units should
be included in a sample?
The answer to both depends on how
much information one is willing to
buy
 
How to Select the Sample
 
If    is the population parameter of
interest and    is an estimator of
then a bound on the error of
estimation, 
B
, should be specified
that represents the difference in
absolute value between    and
 
How to Select the Sample
 
A probability,        , specifies the
fraction of times in repeated samples
the the error of estimation is less
than 
B
 
How to Select a Sample
 
Typically 
B
 is set to       and,
therefore,         will be approximately
.95
Once a bound, 
B
, has been specified,
along with its associated probability,
        , different sampling designs can
be compared to determine which is
most efficient for a particular
purpose
 
Probability Sampling
 
Statistical estimation requires
randomness in sampling designs so
that properties of statistical
estimators can be assessed
probabilistically
Sampling designs based on planned
randomness are probability samples
 
Simple Random Sampling
 
The basic probability sampling
design, simple random sampling,
consists of selecting a group of 
n
sampling units in such a way that all
samples of size 
n
 have the same
probability of selection
 
Stratified Random Sampling
 
A stratified random sample is one
obtained by separating the
population elements into discrete,
nonoverlapping groups, called strata,
and then selecting a simple random
sample from each stratum
 
Stratified Random Sampling
 
The principle reasons for using stratified
random sampling rather than simple random
sampling are:
1.
Stratification may produce a smaller bound on the
error of estimation than would be produced by a
simple random sample of the same size (this is
particularly true if measurements within strata
are homogenous)
2.
The cost per observation may be reduced by
stratification of the population elements into
convenient groupings
3.
Estimate of population parameters may be
desired for subgroups of the population (these
subgroups should then be identifiable strata)
 
Cluster Sampling
 
Cluster sampling is a less costly
alternative to simple or stratified
random sampling if the cost of
obtaining a frame that lists all
population elements is very high or if
the cost of obtaining observations
increases as the distance separating
elements increases
 
Cluster Sampling
 
Cluster sampling is an effective
design for obtaining a specified
amount of information under the
following conditions:
1.
A good frame listing all population
elements is not available or is very
costly to obtain, but a frame listing
clusters is easily obtained
2.
The cost of obtaining observations
increases as the distances separating
the elements increases
 
Cluster Sampling
 
Clusters typically consist of herds,
households, or other units of clustering
(e.g., an orange tree forms a cluster of
oranges for investigating insect infestations)
A farm herd contains a cluster of livestock
for estimating proportions of diseased
animals
Elements within a cluster are often
physically close together and hence tend to
have similar characteristics and the
measurement on one element within a
cluster may be correlated with the
measurement on another
 
Systematic Sampling
 
Systematic sampling involves
random selection of one element
from the first 
k
 elements and then
selecting every 
k
th
 element
thereafter
 
Systematic Sampling
 
Systematic sampling is a useful alternative
to simple random sampling for the following
reasons:
1.
Systematic sampling is easier to perform in
the field and hence is less subject to selection
errors by field-workers than are either simple
random samples or stratified random
samples, especially if a good frame is not
available
2.
Systematic sampling can provide greater
information per unit cost than simple random
sampling can provide for certain populations
with certain patterns in the arrangement of
elements
 
Multi-Stage Sampling
 
Sampling conducted in stages, often
taking into account the hierarchical
(nested) structure of a population
Primary sampling units (PSUs) are sampled
first (e.g., cities)
Secondary sampling units (SSUs) are
sampled next (e.g., city blocks)
Ultimate sampling units (actual elements)
are sampled last (e.g., households)
Especially useful when no frame can be
established for a single-stage sample
 
Multi-Stage Sampling
 
For a fixed sample size of elements,
a multi-stage sampling design is
almost always less efficient than a
simple random sample (though often
more feasible)
Variance estimation methods for
complex sample designs must be
used to obtain correct standard
errors
 
Multiple-Frame Sampling
 
Quota Sampling
 
A nonprobability sampling method
(although randomness is sometimes
part of the design) in which a
prespecified number of surveys is
obtained from specific subgroups of a
target population (e.g., Republicans,
Democrats)
Introduces unknown sampling biases
into survey estimates
 
Chain-Referral Sampling
 
Snowball sampling methods for sampling in
rare/hard-to-reach populations
One or more persons having the trait of
interest serve as seeds and identify others
Persons with many connections are likely to
be included, whereas isolated persons may
not be included at all
Information about network connections in
the sample can be used to weight sample
units (respondent-driven sampling, which is
premised on Markov-chain theory)
 
Recruitment Network
 
Equilibrium
 
Planning a Survey
 
Planning A Survey
 
1.
Statement of objectives
2.
Target population
3.
The frame
4.
Sample design
5.
Method of measurement
6.
Measurement instrument
7.
Selection and training of fieldworkers
8.
The pretest (pilot)
9.
Organization of fieldwork
10.
Organization of data management
11.
Data analysis
 
Some Basic Concepts of
Statistics
 
Finite Population Correction
 
Most statistical theory is premised on an
underlying infinite population
Sampling theory and practice is founded on
the assumption of sampling from a finite
population
In the general framework of finite
population sampling, sample sizes of size 
n
are taken from a population of size 
N
In the finite population case, the variance
estimate of a statistical estimator must be
adjusted due to the fact that not all data
from a finite population are observed, using
the finite population correction (fpc)
 
Finite Population Correction
 
For simple random samples (without
replacement) the fpc is expressed as
or
 
Where 
f
 is the sampling fraction or
rate
 
 
 
 
Finite Population Correction
 
The fpc is, therefore, the fraction of a
finite population that is not sampled
Because the fpc is literally a factor in
the calculation of an estimate of
variance for an estimated finite
population parameter, the estimated
variance is reduced to zero if 
n
 = 
N
 
Finite Population Correction
 
When 
n
 is small relative to 
N
, the fpc is
close to unity
In samples of very large populations 
f
is very small and the fpc may be
ignored
Ignore if 1-
n
/
N
>.95
Although the fpc is applicable for
estimation, it often is not necessary for
many inferential uses such as statistical
significance testing (e.g., comparison
between sampled subgroups).
 
Estimate of Population Mean
 
 
Estimate of Population
Proportion
 
where
 
Estimate of Population Total
 
Case Study #1
 
Case Study Activity
 
In small groups, address the
following questions in relation to
Case Study #1 relying only on the
material that was discussed thus far
in the semester
1.
Has the surveyor committed any
serious error(s)?
2.
If so, what type and why? If not, why?
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This content covers essential concepts of survey research, statistics, and sampling methods. It delves into elements of the sampling problem, technical terms, and how to select a sample for surveys. The discussions revolve around population parameters, sampling procedures, and the control of information quantity in a sample. Key questions addressed include the selection of sampling units and the error of estimation in survey research.


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  1. EMR 6500: Survey Research Dr. Chris L. S. Coryn Lyssa N. Wilson Spring 2015

  2. Agenda Elements of the sampling problem Some basic concepts of statistics Case Study #1

  3. Elements of the Sampling Problem

  4. Technical Terms (Again) An element is an object on which a measurement is taken A population is a collection of elements to which an inference is made A sample is a collection of sampling units drawn from a frame or frames Sampling units are nonoverlapping collections of elements from the population that cover the entire population A frame is a list of sampling units

  5. How to Select the Sample: The Design of the Survey Sample

  6. How to Select the Sample The objective of sampling is to estimate population parameters such as the mean, proportion, or total The quantity of information is controlled by the number of units included in a sample and the method used to select a sample

  7. How to Select the Sample The primary questions addressed by sampling theory are: What sampling procedure should be used? What number of sampling units should be included in a sample? The answer to both depends on how much information one is willing to buy

  8. How to Select the Sample Q If is the population parameter of interest and is an estimator of then a bound on the error of estimation, B, should be specified that represents the difference in absolute value between and Q Q Q Q Error of estimation= Q- Q <B

  9. How to Select the Sample 1-a ( ) A probability, , specifies the fraction of times in repeated samples the the error of estimation is less than B [ ]=1-a P Error of estimation<B

  10. How to Select a Sample 2s Q Typically B is set to and, therefore, will be approximately .95 Once a bound, B, has been specified, along with its associated probability, , different sampling designs can be compared to determine which is most efficient for a particular purpose 1-a ( ) 1-a ( )

  11. Probability Sampling Statistical estimation requires randomness in sampling designs so that properties of statistical estimators can be assessed probabilistically Sampling designs based on planned randomness are probability samples

  12. Simple Random Sampling The basic probability sampling design, simple random sampling, consists of selecting a group of n sampling units in such a way that all samples of size n have the same probability of selection

  13. Stratified Random Sampling A stratified random sample is one obtained by separating the population elements into discrete, nonoverlapping groups, called strata, and then selecting a simple random sample from each stratum

  14. Stratified Random Sampling The principle reasons for using stratified random sampling rather than simple random sampling are: 1. Stratification may produce a smaller bound on the error of estimation than would be produced by a simple random sample of the same size (this is particularly true if measurements within strata are homogenous) 2. The cost per observation may be reduced by stratification of the population elements into convenient groupings 3. Estimate of population parameters may be desired for subgroups of the population (these subgroups should then be identifiable strata)

  15. Cluster Sampling Cluster sampling is a less costly alternative to simple or stratified random sampling if the cost of obtaining a frame that lists all population elements is very high or if the cost of obtaining observations increases as the distance separating elements increases

  16. Cluster Sampling Cluster sampling is an effective design for obtaining a specified amount of information under the following conditions: 1. A good frame listing all population elements is not available or is very costly to obtain, but a frame listing clusters is easily obtained 2. The cost of obtaining observations increases as the distances separating the elements increases

  17. Cluster Sampling Clusters typically consist of herds, households, or other units of clustering (e.g., an orange tree forms a cluster of oranges for investigating insect infestations) A farm herd contains a cluster of livestock for estimating proportions of diseased animals Elements within a cluster are often physically close together and hence tend to have similar characteristics and the measurement on one element within a cluster may be correlated with the measurement on another

  18. Each element of the population is in exactly one stratum Each element of the population is in exactly one cluster Take a simple random sample of clusters; observe all elements within clusters in the sample Take a simple random sample from every stratum Variance of the estimate depends on the variability within strata Variance of the estimate depends primarily on the variability between clusters For greatest precision, individual elements within each cluster should be heterogeneous, and cluster means should be similar to one another For greatest precision, individual elements within each stratum should have similar values, but stratum means should differ from each other as much as possible

  19. Systematic Sampling Systematic sampling involves random selection of one element from the first k elements and then selecting every kthelement thereafter

  20. Systematic Sampling Systematic sampling is a useful alternative to simple random sampling for the following reasons: 1. Systematic sampling is easier to perform in the field and hence is less subject to selection errors by field-workers than are either simple random samples or stratified random samples, especially if a good frame is not available 2. Systematic sampling can provide greater information per unit cost than simple random sampling can provide for certain populations with certain patterns in the arrangement of elements

  21. Multi-Stage Sampling Sampling conducted in stages, often taking into account the hierarchical (nested) structure of a population Primary sampling units (PSUs) are sampled first (e.g., cities) Secondary sampling units (SSUs) are sampled next (e.g., city blocks) Ultimate sampling units (actual elements) are sampled last (e.g., households) Especially useful when no frame can be established for a single-stage sample

  22. Multi-Stage Sampling For a fixed sample size of elements, a multi-stage sampling design is almost always less efficient than a simple random sample (though often more feasible) Variance estimation methods for complex sample designs must be used to obtain correct standard errors

  23. Multiple-Frame Sampling

  24. Quota Sampling A nonprobability sampling method (although randomness is sometimes part of the design) in which a prespecified number of surveys is obtained from specific subgroups of a target population (e.g., Republicans, Democrats) Introduces unknown sampling biases into survey estimates

  25. Chain-Referral Sampling Snowball sampling methods for sampling in rare/hard-to-reach populations One or more persons having the trait of interest serve as seeds and identify others Persons with many connections are likely to be included, whereas isolated persons may not be included at all Information about network connections in the sample can be used to weight sample units (respondent-driven sampling, which is premised on Markov-chain theory)

  26. Recruitment Network + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

  27. Equilibrium 100% 90% 80% 70% Percentage of Population 60% 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 6 7 8 9 10 Recruitment Wave

  28. Planning a Survey

  29. Planning A Survey 1. Statement of objectives 2. Target population 3. The frame 4. Sample design 5. Method of measurement 6. Measurement instrument 7. Selection and training of fieldworkers 8. The pretest (pilot) 9. Organization of fieldwork 10.Organization of data management 11.Data analysis

  30. Some Basic Concepts of Statistics

  31. Finite Population Correction Most statistical theory is premised on an underlying infinite population Sampling theory and practice is founded on the assumption of sampling from a finite population In the general framework of finite population sampling, sample sizes of size n are taken from a population of size N In the finite population case, the variance estimate of a statistical estimator must be adjusted due to the fact that not all data from a finite population are observed, using the finite population correction (fpc)

  32. Finite Population Correction For simple random samples (without replacement) the fpc is expressed as or N n 1 or - 1 f Where f is the sampling fraction or rate f = n N

  33. Finite Population Correction The fpc is, therefore, the fraction of a finite population that is not sampled Because the fpc is literally a factor in the calculation of an estimate of variance for an estimated finite population parameter, the estimated variance is reduced to zero if n = N

  34. Finite Population Correction When n is small relative to N, the fpc is close to unity In samples of very large populations f is very small and the fpc may be ignored Ignore if 1-n/N>.95 Although the fpc is applicable for estimation, it often is not necessary for many inferential uses such as statistical significance testing (e.g., comparison between sampled subgroups).

  35. Estimate of Population Mean n yi m = y = i=1 n s2 V(y)= 1-n N n s2 1-n V y ( )=2 2 N n

  36. Estimate of Population Proportion n yi p= y = i=1 n p q n-1 V( p)= 1-n q=1- p where N p q n-1 1-n V p ( )=2 2 N

  37. Estimate of Population Total n N yi t = Ny = i=1 n s2 )= N21-n ( V( t)= V Ny N n s2 )=2 N21-n V Ny ( 2 N n

  38. Case Study #1

  39. Case Study Activity In small groups, address the following questions in relation to Case Study #1 relying only on the material that was discussed thus far in the semester 1. Has the surveyor committed any serious error(s)? 2. If so, what type and why? If not, why?

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