Unit 4c
SAMPLING Design
• Sampling is the process or technique of
selecting a suitable sample for the purpose of
determining parameters or characteristics of
the whole population
• To carry out a study, one might bear in mind
what size the sample should be, and whether
the size is statistically justified and lastly,
what method of sampling is to be used
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The concept of sampling in qualitative
research
• In qualitative research the issue of sampling
has little significance as the main aim of most
qualitative inquiries is either to explore or
describe the diversity in a situation,
phenomenon or issue.
• Qualitative research does not make an
attempt to either quantify or determine the
extent of this diversity
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Contd.
• The class, families living the city or electorates
from which you select a few students,
families, electors to question in order to find
answers to your research questions are called
the population or study population, and are
usually denoted by the letter (N).
• The small group of students, families or electors from whom
you collect the required information to estimate the average
age of the class, average income or the election outcome is
called the sample.
• The number of students, families or electors from whom you
obtain the required information is called the sample size and
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is usually denoted by the letter (n).
• The way you select students, families or
electors is called the sampling design or
strategy.
• Each student, family or elector that becomes
the basis for selecting your sample is called
the sampling unit or sampling element
• A list identifying each student, family or
elector in the study population is called the
sampling frame.
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• Your findings based on the information
obtained from your respondents (sample) are
called sample statistics.
• From sample statistics we make so estimate of
the answers to our research questions in the
study population.
• The estimates arrived at from sample statistics
are called population parameters or the
population mean.
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Principles of sampling
• Principle one-In a majority of cases of
sampling there will be a difference between
the sample statistics and the True population
mean, which is attributable to the selection
of random elements in the sample.
• Principle two-the greater the sample size, the
more accurate will be the estimate of the
true population mean
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• Principle three -The greater the deference in
the variable under study in a population for a
given sample size, the greater will be the
difference between the sample statistics and
the true population mean
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Factors affecting the inferences
drawn from a sample
• The size of the sample -As a rule, the larger
the sample size, the more accurate will be the
findings
• The extent of variation in the sampling
population-As a rule, the higher the variation
with respect to the characteristics under study
in the study population, the greater will be the
uncertainty for a given sample size.
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• How ‘representative’ is one’s sample may be a
common question. Researchers always try to
draw a representative sample to draw any
conclusion about the ‘real world’
• This is a part of the researcher’s responsibility
• There are two basic sampling techniques:
probability and non-probability sampling.
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• A probability sample is defined as a sample in
which every element of the population has an
equal chance of being selected.
• if sample units are selected on the basis of
personal judgment, the sample method is a non
probability sample
• A sampling frame is the list of elements from
which the sample may be drawn
• sampling frame might be a list of all members of
an institute or workers in a company
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• The sampling unit is a single element or group
of elements subject to selection in the sample
• flights can be selected as sampling units. The
term primary sampling units (PSUs) designates
units selected in the first stage of sampling. If
successive stages of sampling are conducted,
sampling units are called secondary sampling
units, or tertiary sampling units (if three stages
are necessary).
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REPRESENTATIVE SAMPLING PLANS
• Simple Random Sample A random sample is
defined as follows:
• Selections are made from a specified and
defined population (i.e., the frame is known).
• Each unit is selected with known and non-zero
probability, so that every unit in the population
has an equal (known) chance of selection.
• The method of selection is specified, objective
and replicable
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Stratified Random Sampling
• the population is observed to be
heterogeneous in nature
• in order to apply simple random techniques to
such a heterogeneous population, we have to
group them as homogeneouslyas possible,
where each group is termed a ‘stratum’ (in
plural ‘strata’).
• Then samples are drawn equally or proportionately
from each stratum and, therefore, the procedure is
called stratified random sampling
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• The procedure for selecting a stratified Sample
• Step 1 Identify all elements or sampling units in the
sampling population.
• Step 2 Decide upon the different strata (k) into which you
want to stratify the population.
• Step 3 Place each element into the appropriate stratum.
• Step 4 Number every element in each stratum separately.
• Step 5 Decide the total sample size (n)
• Step 6 Decide whether you want to select proportionate or
disproportionate stratified sampling and follow the steps
below
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Contd.
• Systematic (Quasi-random) Sampling
• In systematic random sampling, we range the
population from which selections are to be
made in a list or series, choose a random
staring point and then count through the list
selecting every n-th unit
• Systematic sampling has been classified under
the `mixed' sampling category because it has
the characteristics of both random and nonrandom sampling designs
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Cluster (Multistage) Sampling
• In cluster sampling we have to have a number of
clusters which are characterized by heterogeneity in
between and homogeneity within.
• Cluster sampling is used for a variety of purposes
particularly for large sample surveys or a nation-wide
survey
• If we consider two stages to conduct the survey, then it
is called two-stage cluster sampling. If someone
considers more than two stages to collect the data, then
it is called multistage sampling.
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Sequential (Multiphase) Sampling
• This is a sampling scheme where the researcher is
allowed to draw sample on more than one occasions.
• It may be economically more convenient to collect
information by a sample and then use this information
as a basis for selecting a sub-sample for further study.
This procedure is called double sampling, multiphase
sampling or sequential sampling. This is a technique
frequently used to draw samples in industries for
ensuring the quality of their products
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Non-probability Sampling Methods
• In non-probability sampling, the probability of
selecting population elements is unknown
• Convenience Sampling
• Non-probability samples that are unrestricted are
called convenience samples
• They are the least reliable design but, normally,
the cheapest and easiest to conduct. Interviewers
have the sole freedom to choose whomever they
find, thus the name convenience
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Purposive Sampling
• Judgement sampling and
• Quota sampling.
• Snowball (Network or Chain) Sampling
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SAMPLE SIZE DETERMINATION
• Sample size is associated with time and cost
• A more relevant issue is how to judge whether the
sample size is adequate in relation to the goals of
the study. Strictly speaking, exact tests to check
whether sample size is adequate for the analysis
• required can be carried out by using statistical
methods such as significance tests, but, in many
studies, readers who do not have the required
statistical skills can use a more common-sense
approach to the problem
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• a sample which has to be able to produce
results that are statistically significant,
statistically robust or statistically justified,
but, more importantly, representative of the
whole population
• determination of sample sizes for mean and
proportion can be calculated under the
normality conditions where standard error
plays an important role
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Contd.
• The formula for determining sample size in the case of testing
hypothesis of population means can be
• expressed as:n=zα/2(sd)2
d2
• where n = sample size,
• Z = Standardised normal value, usually taken as 1.96 for a 95
per cent confidence interval,
• α = Level of significance,
• SD = Standard deviation (assumed to be known from prior
survey or can be guessed or other published
• studies can inform on this),
• d = Precision range (the required confidence interval)
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• Assume that a researcher wants the estimate
to be within ±£25 of the true population value
and he/she wishes to be 95 per cent confident
it will contain the true population mean. Also
assume that early studies have demonstrated
the standard deviation to be around £100.
What would be the required sample size?
• given Z = 1.96, SD = 100, d = 25
• n=64
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KEY STATISTICAL CONCEPTS
• Statistical Estimates
• It is relatively straightforward to gather
information about small, subsets of
populations (for example,employees of a
particular small- or medium-sized company
• Population or Universe
• The population consists of any well-defined
set of elements
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• The characteristics of a population such as its
population mean (μ), and population standard
deviation (σ) are population parameters.
• The characteristics of the sample such as
sample mean and sample variance are called
sample statistics
• Why Sample?
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•
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•
•
•
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Cost
Relevance and Flexibility
Speed
Practicality and Feasibility
Higher Data Quality
Public Acceptability
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Variance and Bias
• The results of sample surveys are not
completely precise, but suffer from random
sampling variability.
• This means that the same sampling method
applied repeatedly to the same population will
not produce identical results each time.
• Bias is different from random variation
• A biased method
will systematically
misrepresent the population, no matter how
large the sample
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The main sources of bias are
•
•
•
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Imperfect Coverage
Sampling Bias
Non-response Bias
Response and Other Data Collection and
Processing Biases
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Methods of drawing a random
sample
• The fishbowl draw-if your total population is
small, an easy procedure is to number each
element using separate slips of paper for each
element, put all the slips into a box, and then
pick them out one by one without looking,
until the number of slips selected equals the
sample size you decided upon. This method is
used in some lotteries.
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• Computer program-there is a number of
programs that can help you to select a random
sample
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