# Survey sampling Sampling Theory Concepts by wmo26898

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```									                     ADMS 3352 3.0 Sampling Technique and Survey Studies

Survey sampling
Many of our behaviours and action are based on samples (could be of size one),
for incidence, our like or dislike of a foreign dish. Would such a sample be
representative of the whole population? How many should we try /samples to
be drawn?

Sample design determines the precision of estimates. It consists of both a sample
selection plan and an estimation procedure.

Population:
The entire set of persons, objects, or events, which the researcher intends
to study.
Must specify the inclusion and exclusion criteria that define a pop’s
characteristics

Sample: A subset of the pop, serves as the ref group for drawing inference about pop
e.g. for quality control: a sample of items from the entire inventory
In a survey: a sample of households

Sampling: involves the selection of the sample from the population
A good sample reflects the relevant characteristics and variations of the
population
No guarantee that a sample represents the pop
Probability sampling procedures minimize bias and error in choosing a
representative sample

Sampling Theory Concepts

population

Target Population:
The universe of interest, or reference population e.g. all learning disabled

Accessible/experimental Population
A population very close to the target population and can be assessed e.g.
learning-disabled in a given city’s school system
Validity of the accessible pop is not readily testable, require good
judgement and expertise

Elements of a Population
Individual units of a population
When elements are persons, they are referred to as subjects

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ADMS 3352 3.0 Sampling Technique and Survey Studies

Sampling Criteria
Characteristics essential for membership in the target population

Representativeness
An objective plan of selection, minimize bias
Drop out
Non-response

Sampling Error
Discrepancy between the true population parameter and the sample statistic.

•   Random Variation
Differences are due to chance, not human bias

•   Systematic Variation
Sampling bias occurs when individuals selected for a sample over-
represent or under-represent the population attributes that are related
to the phenomenon under study, e.g. random sampling at the corner of
a street (unconscious bias: haphazard sample)

Randomization
• Obtain samples to represent the population
• Permits valid generalization of the findings of an investigation to
the population (external validity : population validity) or
other situations/settings (external validity : ecological validity)
• Random sample affords the greatest possible confidence in the sample’s
validity because in the long run, it will produce samples that most
accurately reflect the population’s characteristics

Sampling Frame
A listing of all members in the target (accessible) pop
Subjects are selected from the sampling frame using a sampling plan
Accessible population is usually defined according to available listing(s)

Sampling Plans
Define the process / strategies of making a sample selection

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ADMS 3352 3.0 Sampling Technique and Survey Studies

Sampling techniques

Probability sampling methods
Samples are created through a process of random selection
Every element has a chance to be selected
The sample is considered representative of the population
Provides a mechanism to estimate sampling distribution and error

Nonprobability sampling methods
Degree of sampling error cannot be estimated

Probability (Random) Sampling Methods / Schemes

•   Simple random sampling
Sampling without replacement
Each selection is independent
Each possible sample of a specified size of the population has equal chance of
being selected
The accessible pop is organized as a finite, pre-numbered list
Blind draw, use of dice, random numbers

•   Systematic sampling
1. Divide the total number of elements in the accessible pop by the number
of elements to be selected: sampling interval (n)
2. Determine a starting point on the list at random
3. Now pick every nth element on the list from this starting point
Considered equivalent to random sampling, as long as no recurring
pattern or particular order exists in the listing

•   Stratified random sampling
Identify relevant population characteristics, then
Partition members of a population into homogeneous non-overlapping strata
(subsets) based on the identified characteristics
Random or systematic samples are then drawn from each stratum
Proportional stratified samples could be drawn to reflect pop composition
Stratification increases the precision of estimates only when the stratification
variable is closely related to the variables of experimental / study interest

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ADMS 3352 3.0 Sampling Technique and Survey Studies

•   Disproportional sampling
Select random samples of adequate size from each category (for comparison)
This may lead to over-representation of the characteristics of one group
(stratum) in the pop
Control this error by calculating proportional weights for strata

•   Cluster sampling
If it is impractical or impossible to obtain a complete listing of a large
dispersed pop, then use cluster / multi-stage sampling
For example, a random selection of province; within selected province,
random selection of hospitals; within each selected hospital, a random
selection of therapists
Advantages: convenience and efficiency (time-wise)
Price paid: increased sampling error because of the number of samples
drawn, each subjected to error

Examples used in survey:
Area probability sampling (sampled geographically-> districts->households)
Random-digit dialing (sample area-code->telephone exchanges);
bias: can only reach those with phones; timing of calls

Nonprobability (Nonrandom) Sampling Methods
q Generalization of data collected from nonrandom samples must be made
with caution

q   Keppel suggests that researchers can distinguish between
o statistical (require random sampling and based on the validity of
representativeness) and
o nonstatistical generalization (justified on the basis of knowledge of
the research topic, the logic of the study, and consistency in
replicated outcomes).

•   Convenience (Accidental) sampling
Chosen on the basis of availability
Potential bias of self-selection
Not possible to assess the attributes that are present in those who offer
themselves
Unclear how these attributes affect the ability to generalize the study
/experimental outcomes

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ADMS 3352 3.0 Sampling Technique and Survey Studies

•   Quota sampling
A convenience sample with added feature:
maintain a balance of specific characteristics
For example: maintain a certain proportion of each gender

•   Purposive sampling
Researcher handpicks subjects OR use of groups of elements as sampling unit
on the basis of specific criteria
Generalization of results is limited to those who have these characteristics

Snowball / Network sampling
1. When subjects with specific characteristics are hard to locate, a few
subjects are identified
2. Interview /test the few subjects
3. These subjects further id others who have the requisite characteristics
4. A chain referral / snowballing / network referral until an adequate
sample is obtained
5. Researcher must verify the eligibility of each respondent to ensure a
representative group

Sample Surveys
Ø Descriptive:
For example, study the proportion of pop watching a certain TV program
Ø Analytical: for example, compare groups and employ stat techniques in
order to estimate pop parameters

Factors influencing Sample Sizes
•   Sampling technique
•   Estimation procedure
•   Measurement sensitivity: precision
•   Effect size: the extent of the presence of a phenomenon
•   Number of variables
•   Data analysis techniques
(Chi-square test on association between categorical variables have weak
power)
•   Significance level

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ADMS 3352 3.0 Sampling Technique and Survey Studies

Conducting a Survey
(from the perspective of sampling for estimation with specified precision)

1.  Make a clear statement of objectives
2.  Define the population to be sampled
3.  List the relevant data to be collected
4.  Specify the required precision of estimates
5.  Determine well-defined sampling units
(The list of sampling units is called a frame)
6. Determine the sampling scheme – method of selecting the sample
7. Plan ahead how to handle non-response
8. Collect data
9. Summarize the data
a. Take into consideration if there was large non-response
b. If sample size is large, may apply central limit theorems
c. If sample size is small, may wish to apply distribution free
techniques
10. Proceed with sample estimation procedure (if appropriate)
11. Identify mistakes in the present survey for the benefit of future work.

Reference:

Govindarajulu, Zakkula (1999), Elements of Sampling Theory and Methods,
Prentice-Hall, New Jersey.

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