Survey Sampling Methods
Sampling method refers to the way that observations
are selected from a
population
to be in the
sample for a
sample survey.
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Population Parameter vs. Sample Statistic
The reason for conducting a sample survey is to estimate the value
of some attribute of a population.
- Population parameter. A population parameter
is the true value of a population attribute.
- Sample statistic. A sample statistic is an
estimate, based on sample data, of a population parameter.
Consider this example. A public opinion pollster wants to know the
percentage of voters that favor a flat-rate income tax. The
actual percentage of all the voters is a population
parameter. The estimate of that percentage, based on
sample data, is a sample statistic.
The quality of a sample statistic (i.e., accuracy, precision,
representativeness) is strongly affected by the
way that sample observations are chosen; that is., by the sampling
method.
Probability vs. Non-Probability Samples
As a group, sampling methods fall into one of two categories.
- Probability samples. With probability
sampling methods, each population element has a known
(non-zero) chance of being chosen for the sample.
- Non-probability samples. With non-probability
sampling methods, we do not know the probability
that each population element will be chosen, and/or we
cannot be sure that each population element has a non-zero
chance of being chosen.
Non-probability sampling methods offer two potential
advantages - convenience
and cost. The main disadvantage is that non-probability sampling
methods do not allow you to estimate the extent to which sample
statistics are likely to differ from population parameters. Only
probability sampling methods permit that kind of analysis.
Non-Probability Sampling Methods
Two of the main types of non-probability sampling methods are
voluntary samples and convenience samples.
- Voluntary sample. A voluntary sample
is made up of people who self-select into the survey. Often,
these folks have a strong interest in the
main topic of the survey.
Suppose, for example, that a news show asks viewers to
participate in an on-line poll. This would be a volunteer
sample. The sample is chosen by the viewers, not by the
survey administrator.
- Convenience sample. A convenience sample is
made up of people who are easy to reach.
Consider the following example. A pollster interviews shoppers
at a local mall. If the
mall was chosen because it was a convenient site from which
to solicit survey participants and/or because it was close to the
pollster's home or business, this would be a convenience
sample.
Probability Sampling Methods
The main types of probability sampling methods are simple random
sampling, stratified sampling, cluster sampling, multistage
sampling, and systematic random sampling. The key benefit
of probability sampling methods is that
they guarantee that the sample chosen is representative of the
population. This ensures that the statistical conclusions will be valid.
- Simple random sampling. Simple random sampling
refers to any sampling method that has the following properties.
- The population consists of N objects.
- The sample consists of n objects.
- If all possible samples of n objects are equally likely
to occur, the sampling method is called simple random
sampling.
There are many ways to obtain a simple random sample.
One way would be the lottery method. Each of the N population members
is assigned a unique number. The numbers are placed in a bowl and
thoroughly mixed. Then, a blind-folded researcher selects n numbers.
Population members having the selected numbers are included
in the sample.
- Stratified sampling. With stratified sampling,
the population is divided into groups, based on some characteristic.
Then, within each group, a probability sample (often a simple random
sample) is selected. In stratified sampling, the groups are
called strata.
As a example, suppose we conduct a national survey. We might divide
the population into groups or strata, based on geography - north,
east, south, and west. Then, within each stratum, we might randomly
select survey respondents.
- Cluster sampling. With cluster sampling, every
member of the population is assigned to one, and only one, group.
Each group is called a cluster. A sample of clusters
is chosen, using a probability method (often simple random sampling).
Only individuals within sampled clusters are surveyed.
Note the difference between cluster sampling and stratified sampling.
With stratified sampling, the sample includes elements from each
stratum. With cluster sampling, in contrast, the sample includes
elements only from sampled clusters.
- Multistage sampling. With multistage sampling,
we select a sample by using combinations of different sampling methods.
For example, in Stage 1, we might use cluster sampling to
choose clusters from a population. Then, in Stage 2, we might use
simple random sampling to select a subset of elements from each
chosen cluster for the final sample.
- Systematic random sampling. With systematic
random sampling, we create a list of every member of the population.
From the list, we randomly select the first sample element from the
first k elements on the population list.
Thereafter, we select every kth element on the list.
This method is different from simple random sampling since
every possible sample of n elements is not equally likely.
Test Your Understanding
Problem
An auto analyst is conducting a satisfaction survey, sampling
from a list of 10,000 new car buyers. The list includes 2,500 Ford
buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers.
The analyst selects a sample of 400 car buyers, by randomly
sampling 100 buyers of each brand.
Is this an example of a simple random sample?
(A) Yes, because each buyer in the sample was randomly sampled.
(B) Yes, because each buyer in the sample had an equal chance of
being sampled.
(C) Yes, because car buyers of every brand were equally represented
in the sample.
(D) No, because every possible 400-buyer sample did not have an
equal chance of being chosen.
(E) No, because the population consisted of purchasers of
four different brands of car.
Solution
The correct answer is (D). A
simple random sample requires that
every
sample
of size n (in this problem, n
is equal to 400) has an equal chance of being selected. In this
problem, there was a 100 percent chance that the sample would
include 100 purchasers of each brand of car. There was
zero percent chance that the sample would include, for example,
99 Ford buyers, 101 Honda buyers, 100 Toyota buyers, and 100
GM buyers. Thus, all possible samples of size 400 did not have
an equal chance of being selected; so this cannot be a simple
random sample.
The fact that each buyer in the sample was randomly sampled is
a necessary condition for a simple random sample, but it is not
sufficient.
Similarly, the fact that each buyer in the sample had an equal
chance of being selected is characteristic of a simple
random sample, but it is not sufficient. The sampling method in
this problem used random sampling and gave each buyer an equal
chance of being selected;
but the sampling method was actually
stratified random sampling.
The fact that car buyers of every brand were equally
represented in the sample is irrelevant to whether the sampling
method was simple random sampling. Similarly, the fact that
population consisted of buyers of different car brands is
irrelevant.