Sampling

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SAMPLING

• Presented by
• Ulliyadhi Satria R.
• Kharis Subkhan
• Fuad Abdul Majid
• M. Arif Al Hakim
• SEMARANG STATE UNIVERSITY
• 2016

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Sampling in Educational Research

• The quality of a piece of research stands or
  falls not only by the appropriateness of
  methodology and instrumentation but also by the
  suitability of the sampling strategy that has
  been adopted.
• Researchers must take sampling decisions early in
  the overall planning of a piece of research.
• The researchers often need to be able to obtain
  data from a smaller group of the total population
  in certain way as a representative of the total
  population under study.

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An example of the importance of sampling in
conducting research in educational field
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The big questions are..

• How will she decide that selection?
• How will she select which students to interview?
• If she were to interview 200 of the students,
  would that be too many?
• If she were to interview just 20 of the students
  would that be too few?
• If she were to interview just the males or just
  the females, would that give her a fair picture?
• If she were to interview only those students who
  considered good at science, would that yield a
  true picture of the total population of 900
  students?

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Four Considerations

• The sample size
• Representativeness and parameters of the sample
• Access to the sample
• The sampling strategy to be used.

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The Sample Size

• A question that often plagues novice researchers
  is just how large their samples for the research
  should be.
• The correct sample size depends on the purpose of
  the study and the nature of the population under
  scrutiny.
• Depending on the kind of analysis to be
  performed, some statistical tests will require
  larger samples.

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An example for the application of sampling in
research using chi-square test
Variable 10-year-old pupils should do one hours homework each weekday evening Variable 10-year-old pupils should do one hours homework each weekday evening Variable 10-year-old pupils should do one hours homework each weekday evening Variable 10-year-old pupils should do one hours homework each weekday evening Variable 10-year-old pupils should do one hours homework each weekday evening Variable 10-year-old pupils should do one hours homework each weekday evening
Strongly disagree Disagree Neither agree nor disagree Agree Strongly agree
10-year-old pupils in the school 25 20 3 8 4
Teachers in the school 6 4 2 4 4

• Note
• Variable
• Subgroups
• Case 5-point scale
• Cell

Chi-square test Five cases or more in 80 of
cells
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Researchers must obtain the minimum sample size
that will accurately represent the population
being targeted.

• With respect to size, will a large sample
  guarantee representativeness? Not necessarily!
• In our first example, the researcher could have
  interviewed a total sample of 450 females and
  still not have represented the male population.
• Will a small size guarantee representativeness?
  Again, not necessarily! The latter falls into the
  trap of saying that 50 percent of those who
  expressed an opinion said that they enjoyed
  science, when the 50 per cent was only one
  student.
• Furthermore, too large a sample might become
  unwieldy and too small a sample might be
  unrepresentative.

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How it should be?

• For populations of equal heterogeneity, the
  larger the population, the larger the sample that
  must be drawn.
• For populations of equal size, the greater the
  heterogeneity on a particular variable, the
  larger the sample that is needed.

To the extent that a sample fails to represent
accurately the population involved, there is
sampling error, discussed later
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Determining Sample Size

• In determining sample size for a probability
  sample one has to consider not only the
  population size but also the confidence level and
  confidence interval.
• The confidence level, usually expressed as a
  percentage (usually 95 per cent or 99 per cent),
  is an index of how sure we can be (95 percent of
  the time or 99 per cent of the time) that the
  responses lie within a given variation range, a
  given confidence interval (e.g. 3 percent)
• The confidence interval is that degree of
  variation or variation range (e.g. 1 per cent,
  or 2 per cent, or 3 per cent) that one wishes
  to ensure.

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A full table of sample sizes for random sample,
with three confidence levels (90 per cent, 95
percent and 99 percent) and three confidence
intervals (5 per cent, 4 per cent and 3 per
cent).
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• Borg and Gall (1979 195) suggest that, as a
  general rule, sample sizes should be large where
• There are many variables
• Only small differences or small relationships are
  expected or predicted
• The sample will be broken down into subgroups
• The sample is heterogeneous in terms of the
  variables under study
• Reliable measures of the dependent variable are
  unavailable.

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Qualitative Data

• their goal usually is not to make inferences
  about the underlying population, but to attempt
  to obtain insights into particular educational,
  social, and familial processes and practices that
  exist within a specific location and context
  (Connolly, 1998)
• Even though qualitative investigations typically
  involve the use of small samples, choice of
  sample size still is an important consideration
  because it determines the extent to which the
  researcher can make generalizations (Onwuegbuzie
  Leech, 2005b)

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Quantitative Data

• level of accuracy
• level of probability
• It is clear that sample size is a matter of
  judgement as well as mathematical precision even
  formula-driven approaches make it clear that
  there are elements of prediction, standard error
  and human judgement involved in determining
  sample size.

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Sampling Error

• Sampling error is often taken to be the
  difference between the sample mean and the
  population mean.
• Usually it does not represent the whole population

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The Standard Error of Proportion

•  

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The Standard Error of Proportion

• How big a sample must I obtain?
• How accurate do I want my results to be?
• Standard Error will decrease if the sample is
  higher

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The Representativeness of the Sample

• Representative sample is a sample that includes
  individuals/participants representative of a
  larger population
• The unrepresentative sample is usually caused by
  different variables of the population and it is
  not considered by researchers.

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The access to the sample

• Access is a key issue and an early factor that
  must be decide in research. Researchers will need
  to ensure that the access is not only permitted
  but also practicable.
• Access might also be denied by the potential
  sample participants themselves for very practical
  reason

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The sampling strategy to be used

• There are two main methods of sampling
• Probability samples
• Non-probability samples

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Probability samples

• Known as random sample, because it draws randomly
  from the wider population
• It will have less risk of bias
• There are several types of probability sample
• Simple random sampling
• Systematic samples.
• Stratified samples.
• Cluster samples.
• Stage samples.
• Multi-phase sample.

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Simple random sampling

• Each member of the population under study has an
  equal chance of being selected and the
  probability of a member of the population being
  selected is unaffected by the selection of other
  members of the population

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Systematic samples

• This method is a modified form of simple random
  sampling. It involves selecting subjects from a
  population list in a systematic rather than a
  random fashion

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Stratified samples

• Stratified sampling involves dividing the
  population into homogenous groups, each group
  containing subjects with similar characteristics.

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Cluster samples

• When the population is large and widely
  dispersed, gathering a simple random sample poses
  administrative problems

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Stage samples

• Stage sampling is an extension of cluster
  sampling. It involves selecting the sample in
  stages, that is, taking samples from samples

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Multi-phase sample

• In a multi-phase sample the purposes change at
  each phase

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Non-probability samples

• the use of nonprobability sample derives from
  the researcher targeting a particular group, that
  it does not represent the wider population it
  simply represents itself.

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• Frequently used in small-scale research,
• for example, as with one or two schools, two or
  three groups of students, or a particular group
  of teachers,
• this is frequently the case for some ethnographic
  research, action research or case study research

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• There are several types of non-probability
  sample
• Convenience
• Quota
• Dimensional
• Purposive
• Snowball

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Convenience sampling

• it is sometimes called, accidental or opportunity
  sampling involves choosing the nearest
  individuals to serve as respondents and
  continuing that process until the required sample
  size has been obtained or those who happen to be
  available and accessible at the time.

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• respondents based on convenience sampling.
  Researchers simply choose the sample from those
  to whom they have easy access

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Quota sampling

• A quota sample strives to represent significant
  characteristics (strata) of the wider population
  unlike stratified sampling it sets out to
  represent these in the proportions in which they
  can be found in the wider population.

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The researcher wishing to devise a quota sample
can proceed in three stages

• 1. Identify those characteristics (factors) which
  appear in the wider population which must also
  appear in the sample, i.e. divide the wider
  population into homogenous and, if possible,
  discrete groups (strata), for example, males and
  females, Asian, Chinese and African Caribbean.
• 2. Identify the proportions in which the selected
  characteristics appear in the wider population,
  expressed as a percentage.
• 3 Ensure that the percentaged proportions of the
  characteristics selected from the wider
  population appear in the sample.

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purposive sampling

• In purposive sampling researchers handpick the
  cases to be included in the sample on the basis
  of their judgement of their typicality or
  possession of the particular characteristics
  being sought.
• It is often used in qualitative research,

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• the sample has been chosen for a specific
  purpose, for example a group of principals and
  senior managers of secondary schools is chosen as
  the research is studying the incidence of stress
  among senior managers

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Dimensional sampling

• One way of reducing the problem of sample size in
  quota sampling is to opt for dimensional
  sampling. Dimensional sampling is a further
  refinement of quota sampling. It involves
  identifying various factors of interest in a
  population and obtaining at least one respondent
  of every combination of those factors. Thus, in a
  study of race relations,
• for example, researchers may wish to distinguish
  first, second and third generation immigrants.
  Their sampling plan might take the form of a
  multidimensional table with ethnic group across
  the top and generation down the side.

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Snowball sampling

• number of individuals who have the
  characteristics in which they are interested.
  These people are then used as informants to
  identify, or put the researchers in touch with
• This method is useful for sampling a population
  where access is difficult, maybe because it is a
  sensitive topic (e.g. teenage solvent abusers)

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Volunteer sampling

• In cases where access is difficult, the
  researcher may have to rely on volunteers, for
  example, personal friends, or friends of friends,
  or participants who reply to a newspaper
  advertisement, or those who happen to be
  interested from a particular school,or those
  attending courses

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Theoretical sampling

• theoretical sampling is the process of data
  collection for generating theory whereby the
  analyst jointly collects, codes, and analyzes his
  sic. data and decides what data to collect next
  and where to find them, in order to develop his
  theory as it emerges.
• (Glaser and Strauss)

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Planning a sampling strategy

• There are several steps in planning the sampling
  strategy
• Decide whether you need a sample, or whether it
  is possible to have the whole population.
• Identify the population, its important features
  (the sampling frame) and its size.
• Identify the kind of sampling strategy you
  require (e.g. which variant of probability and
  non-probability sample you require).
• Ensure that access to the sample is guaranteed.
  If not, be prepared to modify the sampling
  strategy (step 2).
• For probability sampling, identify the confidence
  level and confidence intervals that you require.
  For non-probability sampling, identify the people
  whom you require in the sample.
• Calculate the numbers required in the sample,
  allowing for non-response, incomplete or spoiled
  responses, attrition and sample mortality, i.e.
  build in redundancy.
• Decide how to gain and manage access and contact
  (e.g. advertisement, letter, telephone, email,
  personal visit, personal contacts/friends).
• Be prepared to weight (adjust) the data, once
  collected.