SAMPLING DEFINITIONS
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Population:
The group of people, items or units
under investigation
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Census:
Obtained by collecting information
about each member of a population
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Sample
Obtained by collecting information
only about some members of a "population"
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Sampling
Frame:
The list of people from which the sample is
taken. It should be comprehensive, complete and up-to-date.
TYPES OF SAMPLING
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A probability sample is one in which
each member of the population has an known chance of being selected.
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In a non-probability sample, some people
have a greater, but unknown, chance than others of selection.
TYPES OF SAMPLING
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Probability Sampling
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Non-Probability Sampling
Non-Probability - Advantages
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Cheaper
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Used when sampling frame
is not available
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Useful when population
is so widely dispersed that cluster sampling would not be efficient
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Often used in
exploratory studies, e.g. for hypothesis generation
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For research interested
in obtaining an idea of the range of responses on ideas that people have
Purposive Sampling
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A purposive sample is
one which is selected by the researcher subjectively. The researcher attempts to
obtain sample that appears to him/her to be representative of the population and
will usually try to ensure that a range from one extreme to the other is
included.
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Often used in political
polling - districts chosen because their pattern has in the past provided good
idea of outcomes for whole electorate.
Snowball Sampling
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With this approach, you
initially contact a few potential respondents and then ask them whether they
know of anybody with the same characteristics that you are looking for in your
research. For example, if you wanted to interview a sample of vegetarians /
cyclists / people with a particular disability / people who support a particular
political party etc., your initial contacts may well have knowledge
(through e.g. support group) of others.
Convenience Sample
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A convenience sample is
used when you simply ask people you meet whether they will answer your
questions. The sample comprises subjects who are simply available in a
convenient way to the researcher. There is no randomness and the likelihood of
bias is high. You can't draw any meaningful conclusions from the results you
obtain. However, this method can legitimately be used provided its limitations
are clearly understood and stated.
Self-selection Sample
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Self-selection is when respondents themselves
decide that they would like to take part in your survey.
Quota Sampling
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Often used in market
research. Interviewers are given quota of particular types of people to
interview and the final sample should be representative of population.
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Disadvantage -
Interviewers choose who they like (within above criteria) and may therefore
select those who are easiest to interview, so bias can result. Also, impossible
to estimate accuracy (because not random sample)
Stages of Quota Sampling
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Decide on
characteristic(s) of which sample is to be representative, e.g. age, sex, race
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Find out distribution of
this variable in population and set quota accordingly. (If 20% of population is
between 20 and 30, and sample is to be 1,000 then 200 respondents must be
between 20 and 30).
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Complex quotas can be
developed so that several characteristics are used simultaneously.
Definitions
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Element: the unit about
which information is collected and provides the basis of analysis (analogous to
units of analysis)
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Population: the
theoretically specified aggregation of elements in a study
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Study population: the
aggregation of elements from which the sample is actually selected
Probability Sampling
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Basic principle: sample
will representative of the population from which it is selected
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Key to probability
sampling is random selection
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Random selection: each
element has an equal chance of selection independent of any other event in the
selection process
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If all members of sample
have equal chance of being selected – EPSEM – equal probability of selection
method
Probability Theory
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Allows researchers to
calculate the population parameters
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Parameter:
the summary description of a given variable in a population
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Generalize:
we estimate the population parameters from the sample observations. Probability
theory allows us to estimate how accurate those estimates are to the true
population parameter. How “off” we are is called the “margin of error.”
An important note - there will always be some sampling error.
Sampling Error
1. Random Error
Difference between the sample results and the true results because of chance
variation. This error cannot be avoided, only reduced by increasing the sample
size. It is possible to estimate the range of random error at a particular level
of confidence.
2. Systematic Error
Systematic error occurs when sample results consistently vary in one
direction from the true values for that population. Systematic error is made up
of sample design error and measurement error.
Sample Design Error.
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Frame Error.
The sampling frame is the list of population
elements or members from which sample is selected.
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specification error
Results from an incorrect definition of the
universe or population from which the sample is to be selected
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Selection error
Selection error involves a systematic bias
in the manner in which respondents are selected for participation in the survey.
Random Error
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Based on sampling distributions and the Central
Limit Theorem
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Can be calculated with 3 pieces of information
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The population parameter
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The sample size
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The standard error
Simple Random Sample
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Each person has same chance as any other of being
selected
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Standard against which other methods are sometimes
evaluated
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Suitable where population is relatively small and
where sampling frame is complete and up-to-date
Procedure for SRS:
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Obtain a complete sampling frame
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Give each case a unique number, starting at one
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Decide on the required sample size
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Select that many numbers from a table of random
numbers or using computer
Table of random numbers
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Decide on a pattern of
movement through table and stick to it, e.g. numbers from every second column
and every row. If a number comes up twice or a number is selected which is
larger than population number, discard it.
92941 04999 77422 25992
27372 94157
43252 48135 34237 46293 46178 50110
78907 37586 50940 88094 28209 67334
82843 43383 32561 62108 46076 91276
Possible questionnaire-based surveys.
Which of them do you feel would have
simple random sampling as an appropriate sampling method?
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A survey of shoppers in
a clothes shop on a Saturday morning
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A study of employees in
an organization
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A survey of teenage
prostitutes
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Survey of a theatre
audience following a play
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School-children's
attitudes to branded clothing
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Feedback from hotel
clients on perceptions of their last visit to that hotel
Systematic sampling
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Similar to SRS; instead
of selecting random numbers from tables, you move through sample frame picking
every nth name.
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Procedure
1. Calculate SAMPLING FRACTION
by dividing population size by required sample size. E.g. for a population of
500 and a sample of 100, the sampling fraction is 1/5 i.e. you will select one
person out of every five in the population.
2. Random number needs to be used only to
decide on starting point. With the sampling fraction of 1/5, the starting point
must be within the first 5 people in your list
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Disadvantage:
Effect of periodicity (bias caused by particular characteristics arising
in the sampling frame at regular units). An example of this would occur if you
used a sampling frame of adult residents in an area composed of predominantly
couples or young families. If this list was arranged: Husband / Wife / Husband /
Wife etc. and if every tenth person was to be interviewed, there would be an
increased chance of males being selected.
Stratified Sampling
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All people in sampling frame are divided into
"strata" (groups or categories). Within each stratum, a simple random sample or
systematic sample is selected.
Example of stratified sampling
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If we want to ensure
that a sample of 5 students from a population of 50 contains both male and
female students in same proportions as in the full population, we first divide
that population into male and female.
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There are 20 male
and 30 female students in the population. To work out the number of males and
females in the sample…
No. of males in sample = (5 / 50) x 20 = 2.0 No. of females in sample = (5 / 50)
x 30 = 3.0
We choose 2 males and 3 females for the sample, which are then
selected using
simple random
or
systematic sample
methods.
Exercise
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A company
employs 200 part-time staff and 800 full-time staff, and you want to do 20
interviews. If you were to take a random sample, you might find that all
of the names you selected were part-time staff. For this reason you have decided
to do a stratified sample. Work out how many part-time and how many full-time
employees you should interview so as to accurately reflect the proportions of
the two groups in the whole workforce.
Multi-stage cluster sampling
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As the name implies,
this involves drawing several different samples. It does so in such a way that
cost of final interviewing is minimized.
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Basic procedure:
First draw sample of areas. Initially large areas selected then progressively
smaller areas within larger area are sampled. Eventually end up with sample of
households (or other units such as schools) and use method of selecting
individuals from these selected households.
Example of Multi-Stage Cluster Sampling
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You have been
asked to undertake a study across the whole of American universities to
determine student drug use.
What are the possible sampling frames for this study?
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You have been
asked to interview 2,000 people in total. Consider what would happen if you
undertook a simple random survey. Of these 2,000 you might have to interview
students in hundreds of colleges all over the country. It would be more
efficient to undertake a Multi-stage Cluster Sample.