POPULATION SURVEY AND SAMPLE STUDY
Sampling is that part of statistical
practice concerned with the selection of a subset of individuals from within a
population to yield some knowledge about the whole population, especially for
the purposes of making predictions based on statistical inference.
Researchers rarely survey the entire
population for two reasons the cost is too high, and the population is dynamic
in that the individuals making up the population may change over time. The
three main advantages of sampling are that the cost is lower, data collection
is faster, and since the data set is smaller it is possible to ensure
homogeneity and to improve the accuracy and quality of the data.
The sampling process comprises
several stages:
1. Defining the population of concern
2. Specifying a sampling frame, a set
of items or events possible to measure
3. Specifying a sampling method for
selecting items or events from the frame
4. Determining the sample size
5. Implementing the sampling plan
6. Sampling and data collecting
Population definition
Successful statistical practice is
based on focused problem definition. In sampling, this includes defining the
population from which our sample is drawn. A population can be defined as
including all people or items with the characteristic one wishes to understand.
Because there is very rarely enough time or money to gather information from
everyone or everything in a population, the goal becomes finding a
representative sample (or subset) of that population.
Sampling frame
In the most straightforward case,
such as the sentencing of a batch of material from production (acceptance
sampling by lots), it is possible to identify and measure every single item in
the population and to include any one of them in our sample. However, in the
more general case this is not possible. There is no way to identify all rats in
the set of all rats. Where voting is not compulsory, there is no way to
identify which people will actually vote at a forthcoming election (in advance
of the election). These imprecise populations are not amenable to sampling in
any of the ways below and to which we could apply statistical theory.
Probability and non-probability sampling
A probability sampling scheme is one
in which every unit in the population has a chance (greater than zero) of being
selected in the sample, and this probability can be accurately determined. The
combination of these traits makes it possible to produce unbiased estimates of
population totals, by weighting sampled units according to their probability of
selection.
Non probability sampling is any
sampling method where some elements of the population have no chance of
selection (these are sometimes referred to as 'out of
coverage'/'undercovered'), or where the probability of selection can't be
accurately determined. It involves the selection of elements based on
assumptions regarding the population of interest, which forms the criteria for
selection. Hence, because the selection of elements is nonrandom, non
probability sampling does not allow the estimation of sampling errors.
Sampling methods
Within any of the types of frame
identified above, a variety of sampling methods can be employed, individually
or in combination. Factors commonly influencing the choice between these
designs include:
Nature and quality of the frame
1. Availability of auxiliary
information about units on the frame
2. Accuracy requirements, and the
need to measure accuracy
3. Whether detailed analysis of the
sample is expected
4. Cost/operational concerns
5. Simple random sampling
In a simple random sample ('SRS') of
a given size, all such subsets of the frame are given an equal probability.
Each element of the frame thus has an equal probability of selection: the frame
is not subdivided or partitioned. Furthermore, any given pair of elements has
the same chance of selection as any other such pair (and similarly for triples,
and so on).
Simple random sampling is always an
EPS design, but not all EPS designs are simple random sampling.
Systematic sampling
Systematic sampling relies on
arranging the target population according to some ordering scheme and then
selecting elements at regular intervals through that ordered list. Systematic
sampling involves a random start and then proceeds with the selection of every
kth element from then onwards.
Stratified sampling
Where the population embraces a
number of distinct categories, the frame can be organized by these categories
into separate "strata." Each stratum is then sampled as an
independent sub-population, out of which individual elements can be randomly
selected. There are several potential benefits to stratified sampling.
First, divi
A stratified sampling approach is
most effective when three conditions are met
- Variability within strata are
minimized
- Variability between strata are
maximized
The variables upon which the
population is stratified are strongly correlated with the desired dependent
variable.
Advantages over other sampling methods
1. Focuses on important
subpopulations and ignores irrelevant ones.
2. Allows use of different sampling
techniques for different subpopulations.
3. Improves the accuracy/efficiency
of estimation.
4. Permits greater balancing of
statistical power of tests of differences between strata by sampling equal
numbers from strata varying widely in size.
Disadvantages
1. Requires selection of relevant
stratification variables which can be difficult.
2. Is not useful when there are no
homogeneous subgroups.
3. Can be expensive to implement.
Post stratification
Stratification is sometimes
introduced after the sampling phase in a process called "post
stratification". This approach is typically implemented due to a lack of
prior knowledge of an appropriate stratifying variable or when the experimenter
lacks the necessary information to create a stratifying variable during the
sampling phase. Although the method is susceptible to the pitfalls of post hoc
approaches, it can provide several benefits in the right situation.
Implementation usually follows a simple random sample. In addition to allowing
for stratification on an ancillary variable, poststratification can be used to
implement weighting, which can improve the precision of a sample's estimates.
Oversampling
Choice-based sampling is one of the
stratified sampling strategies. In choice-based sampling, the data are
stratified on the target and a sample is taken from each stratum so that the
rare target class will be more represented in the sample. The model is then
built on this biased sample. The effects of the input variables on the target
are often estimated with more precision with the choice-based sample even when
a smaller overall sample size is taken, compared to a random sample. The
results usually must be adjusted to correct for the oversampling.
Probability proportional to size sampling
In some cases the sample designer has
access to an "auxiliary variable" or "size measure",
believed to be correlated to the variable of interest, for each element in the
population. These data can be used to improve accuracy in sample design. One
option is to use the auxiliary variable as a basis for stratification, as
discussed above.
Another option is
probability-proportional-to-size ('PPS') sampling, in which the selection
probability for each element is set to be proportional to its size measure, up
to a maximum of 1. In a simple PPS design, these selection probabilities can
then be used as the basis for Poisson sampling.
The PPS approach can improve accuracy
for a given sample size by concentrating sample on large elements that have the
greatest impact on population estimates. PPS sampling is commonly used for
surveys of businesses, where element size varies greatly and auxiliary
information is often available - for instance, a survey attempting to measure
the number of guest-nights spent in hotels might use each hotel's number of
rooms as an auxiliary variable. In some cases, an older measurement of the
variable of interest can be used as an auxiliary variable when attempting to
produce more current estimates.
Cluster sampling
Sometimes it is cheaper to 'cluster'
the sample in some way e.g. by selecting respondents from certain areas only,
or certain time-periods only. (Nearly all samples are in some sense 'clustered'
in time - although this is rarely taken into account in the analysis.)
Cluster sampling is an example of
'two-stage sampling' or 'multistage sampling': in the first stage a sample of
areas is chosen; in the second stage a sample of respondentswithin those areas
is selected.
Multistage sampling
Multistage sampling is a complex form
of cluster sampling in which two or more levels of units are embedded one in
the other. The first stage consists of constructing the clusters that will be
used to sample from. In the second stage, a sample of primary units is randomly
selected from each cluster (rather than using all units contained in all
selected clusters). In following stages, in each of those selected clusters,
additional samples of units are selected, and so on. All ultimate units
(individuals, for instance) selected at the last step of this procedure are
then surveyed.
Matched random sampling
A method of assigning participants to
groups in which pairs of participants are first matched on some characteristic
and then individually assigned randomly to groups.
The procedure for matched random
sampling can be briefed with the following contexts,
Two samples in which the members are
clearly paired, or are matched explicitly by the researcher. For example, IQ
measurements or pairs of identical twins.
Those samples in which the same
attribute, or variable, is measured twice on each subject, under different
circumstances. Commonly called repeated measures. Examples include the times of
a group of athletes for 1500m before and after a week of special training; the
milk yields of cows before and after being fed a particular diet.
Quota sampling
In quota sampling, the population is
first segmented into mutually exclusive sub-groups, just as in stratified
sampling. Then judgment is used to select the subjects or units from each
segment based on a specified proportion. For example, an interviewer may be
told to sample 200 females and 300 males between the age of 45 and 60
Convenience sampling or Accidental Sampling
Convenience sampling (sometimes known
as grab or opportunity sampling) is a type of nonprobability sampling which
involves the sample being drawn from that part of the population which is close
to hand. That is, a sample population selected because it is readily available
and convenient.This type of sampling is most useful for pilot testing. Several important
considerations for researchers using convenience samples include:
Are there controls within the
research design or experiment which can serve to lessen the impact of a
non-random convenience sample, thereby ensuring the results will be more
representative of the population?
Is there good reason to believe that
a particular convenience sample would or should respond or behave differently
than a random sample from the same population?
Is the question being asked by the
research one that can adequately be answered using a convenience sample?
In social science research, snowball
sampling is a similar technique, where existing study subjects are used to
recruit more subjects into the sample.
Line-intercept sampling
Line-intercept sampling is a method
of sampling elements in a region whereby an element is sampled if a chosen line
segment, called a “transect”, intersects the element.
Panel sampling
Panel sampling is the method of first
selecting a group of participants through a random sampling method and then
asking that group for the same information again several times over a period of
time. Therefore, each participant is given the same survey or interview at two
or more time points; each period of data collection is called a
"wave". This sampling methodology is often chosen for large scale or
nation-wide studies in order to gauge changes in the population with regard to
any number of variables from chronic illness to job stress to weekly food
expenditures.
Event sampling methodology
Event sampling methodology (ESM) is a
new form of sampling method that allows researchers to study ongoing
experiences and events that vary across and within days in its
naturally-occurring environment. Because of the frequent sampling of events
inherent in ESM, it enables researchers to measure the typology of activity and
detect the temporal and dynamic fluctuations of work experiences. Popularity of
ESM as a new form of research design increased over the recent years because it
addresses the shortcomings of cross-sectional research, where once unable to,
researchers can now detect intra-individual variances across time. In ESM,
participants are asked to record their experiences and perceptions in a paper
or electronic diary.
There are three types of ESM:
Signal contingent – random beeping
notifies participants to record data. The advantage of this type of ESM is
minimization of recall bias.
Event contingent – records data when
certain events occur
Interval contingent – records data
according to the passing of a certain period of time
Sample size
Formulas, tables, and power function
charts are well known approaches to determine sample size.
Formulas
Where the frame and population are
identical, statistical theory yields exact recommendations on sample size.
However, where it is not straightforward to define a frame representative of
the population, it is more important to understand the cause system of which
the population are outcomes and to ensure that all sources of variation are
embraced in the frame.
Steps for using sample size tables
Postulate the effect size of
interest, α, and β.
Check sample size table
Select the table corresponding to the
selected α
Locate the row corresponding to the
desired power
Locate the column corresponding to
the estimated effect size.
The intersection of the column and
row is the minimum sample size required.
Sampling and data collection
Good data collection involves:
1. Following the defined sampling
process
2. Keeping the data in time order
3. Noting comments and other
contextual events
4. Recording non-responses
5. Most sampling books and papers
written by non-statisticians focus only in the data collection aspect, which is
just a small though important part of the sampling process.
Errors in sample surveys
Survey results are typically subject
to some error. Total errors can be classified into sampling errors and
non-sampling errors. The term "error" here includes systematic biases
as well as random errors.
Sampling errors and biases
Sampling errors and biases are
induced by the sample design. They include:
Selection bias: When the true
selection probabilities differ from those assumed in calculating the results.
Random sampling error: Random
variation in the results due to the elements in the sample being selected at
random.
Non-sampling error
Non-sampling errors are caused by
other problems in data collection and processing. They include:
Overcoverage: Inclusion of data from
outside of the population.
Undercoverage: Sampling frame does
not include elements in the population.
Measurement error: E.g. when
respondents misunderstand a question, or find it difficult to answer.
Processing error: Mistakes in data
coding.
Non-response: Failure to obtain
complete data from all selected individuals.
Survey weights
In many situations the sample
fraction may be varied by stratum and data will have to be weighted to
correctly represent the population. Thus for example, a simple random sample of
individuals in the United
Kingdom
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