Download Document

Chapter 8
Sampling and
Randomness
Sampling, Random Sampling, and
Representativeness
• Two definitions of random sampling:
• 1.Random sampling is that method of drawing a
portion (or sample) of a population or universe so
that each member of the population or universe
has an equal chance of being selected.
• 2.The method of drawing samples from a
population such that every possible sample of a
particular size has an equal chance of being
selected is called random sampling, and the
resulting samples are random samples.
• The first definition, then, is a special case of the
second general definition—the special case in
which n=1.
Sampling, Random Sampling, and
Representativeness
• Sampling without replacement
• Sampling with replacement
• A representative sample means that the
sample has approximately the
characteristics of the population relevant to
the research in question.
• The characteristics typical of a population
are those that are the most frequent and
therefore most likely to be present in any
particular random sample.
Randomness
• Randomness means that there is no
known law, capable of being expressed in
language that correctly describes or
explains events and their outcomes.
• In different words, when events are
random we cannot predict them
individually. However, we can predict them
quite successfully in the aggregate.
Randomization
• Randomization means random
assignment.
• While some people believe that random
assignment removes variation, in reality it
only distributes it.
• Individuals with varying characteristics are
spread approximately equally among the
treatments so that variables, have “equal”
effects in the different treatments.
Randomization
• The principle of randomization may be stated as
the following. Since, in random procedures,
every member of a population has an equal
chance of being selected, members with certain
distinguishing characteristics—male or female,
high or low intelligence, conservative or liberal,
and so on—will, if selected, probably be offset in
the long run by the selection of the
characteristics.
• We say that subjects are assigned at random to
experimental groups, and that experimental
treatments are assigned at random to groups.
Sample Size
• Whenever a mean, a percentage, or other statistic
is calculated from a sample, a population value is
being estimated. A question that must be asked is:
How much error is likely to occur in statistics
calculated from samples of differing sizes?
• Figure 8.1
• Table 8.5, 8.6
• Statistics calculated from large samples are more
accurate (other things being equal) than those
calculated from small samples.
Kinds of Samples
• Probability samples use some form of
random sampling in one or more of their
stages.
• Nonprobability samples do not use
random sampling. Their weakness can to
some extent be mitigated by using
knowledge, expertise, and care in
selecting samples, and by replicating
studies with different samples.
Nonprobability sampling
• Quota sampling: The knowledge of the strata
of the population—sex, race, region, and so
on—is used to select sample members that
are representative, “typical,” and suitable for
certain research purpose. But quota
sampling is difficult to accomplish because it
requires accurate information on the
proportions for each quota, and such
information is rarely available.
Nonprobability sampling
• Purposive sampling: purposive sampling is
characterized by the use of judgment and
a deliberate effort to obtain representative
samples by including presumably typical
areas or groups in the sample.
• Accidental sampling: one takes available
sample at hand
Probability sampling
• Stratified sampling: the population is first
divided into strata. Then random samples
are drawn from each strata. This design is
recommended when the population is
composed of sets of dissimilar groups.
Stratified random sampling is often
accomplished through proportional
allocation procedures (PAP).
Probability sampling
• Cluster sampling: A cluster can be defined
as a group of things of the same kind. In
cluster sampling, the universe is
partitioned into clusters. Then the clusters
are sampled randomly. Each element in
the chosen clusters is then measured.
• Cluster sampling is most effective if a
large number of smaller size clusters are
used.
Probability sampling
• Two-stage cluster sampling: we begin with
a cluster sampling as described above.
Then, instead of measuring every element
of the clusters chosen at random, we
select a random sample of the elements
and measure those elements.
Probability sampling
• Systematic sampling: This method assumes that the
universe or population consists of elements that are
ordered in some way. If the population consists of N
elements and we want to choose a sample of size n,
we first need to form the ratio N/n. This ratio is
rounded to a whole number, k, and then used as the
sampling interval. Here the first sample element is
randomly chosen from numbers 1 through k and
subsequent elements are chosen at every kth
interval.
• The representativeness of the sample chosen in
this fashion is dependent upon the ordering of the N
elements of the population.