Sampling and Surveys
Sampling method refers to the way that observations are selected from a population to be in the sample for a sample survey.
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.
Sample statistic
A population parameter is the true value of a population attribute.
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 Response sample. A voluntary response 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. Gives every possible sample of a given size the same chance to be chosen. 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. Another is using a random digit table. You can also use RandInt on the calculator.
Stratified random 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.
Bias in Survey Sampling
In survey sampling, bias refers to the tendency of a sample statistic to systematically over- or under-estimate a population parameter.
Bias Due to Unrepresentative Samples
A good sample is representative. This means that each sample point represents the attributes of a known number of population elements.
Bias often occurs when the survey sample does not accurately represent the population. The bias that results from an unrepresentative sample is
called selection bias. Some common examples of selection bias are described below.
Undercoverage. Undercoverage occurs when some members of the population are inadequately represented in the sample. A classic example of
undercoverage is the Literary Digest voter survey, which predicted that Alfred Landon would beat Franklin Roosevelt in the 1936 presidential
election. The survey sample suffered from undercoverage of low-income voters, who tended to be Democrats.
How did this happen? The survey relied on a convenience sample drawn from telephone directories and car registration lists. In 1936, people who
owned cars and telephones tended to be more affluent. Undercoverage is often a problem with convenience samples.
Nonresponse bias. Sometimes, individuals chosen for the sample are unwilling or unable to participate in the survey. Nonresponse bias is the bias
that results when respondents differ in meaningful ways from nonrespondents. The Literary Digest survey illustrates this problem. Respondents
tended to be Landon supporters; and nonrespondents, Roosevelt supporters. Since only 25% of the sampled voters actually completed the mail-in
survey, survey results overestimated voter support for Alfred Landon. The Literary Digest experience illustrates a common problem with mail
surveys. Response rate is often low, making mail surveys vulnerable to nonresponse bias.
Voluntary response bias. Voluntary response bias occurs when sample members are self-selected volunteers, as in voluntary response samples. An
example would be call-in radio shows that solicit audience participation in surveys on controversial topics (abortion, affirmative action, gun control,
etc.). The resulting sample tends to overrepresent individuals who have strong opinions.
Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every
element of the population has a known, non-zero probability of being selected. Random sampling helps produce representative samples by
eliminating voluntary response bias and guarding against undercoverage bias. All probability sampling methods rely on random sampling.
Bias Due to Measurement Error
A poor measurement process can also lead to bias. In survey research, the measurement process includes the environment in which the survey is
conducted, the way that questions are asked, and the state of the survey respondent.
Response bias refers to the bias that results from problems in the measurement process. Some examples of response bias are given below.
Wording of or Leading questions. The wording of the question may be loaded in some way to unduly favor one response over another. For
example, a satisfaction survey may ask the respondent to indicate where she is satisfied, dissatisfied, or very dissatisfied. By giving the respondent
one response option to express satisfaction and two response options to express dissatisfaction, this survey question is biased toward getting a
dissatisfied response.
Sampling Error and Survey Bias
A survey produces a sample statistic, which is used to estimate a population parameter. If you repeated a survey many times, using different samples
each time, you would get a different sample statistic with each replication. And each of the different sample statistics would be an estimate for the
same population parameter.
If the statistic is unbiased, the average of all the statistics from all possible samples will equal the true population parameter; even though any
individual statistic may differ from the population parameter. The variability among statistics from different samples is called sampling error.
Increasing the sample size tends to reduce the sampling error; that is, it makes the sample statistic less variable. However, increasing sample size
does not affect survey bias. A large sample size cannot correct for the methodological problems (undercoverage, nonresponse bias, etc.) that produce
survey bias. The Literary Digest example discussed above illustrates this point. The sample size was very large - over 2 million surveys were
completed; but the large sample size could not overcome problems with the sample - undercoverage and nonresponse bias.
Test Your Understanding of This Lesson
Problem
Which of the following statements are true?
I. Random sampling is a good way to reduce response bias.
II. To guard against bias from undercoverage, use a convenience sample.
III. Increasing the sample size tends to reduce survey bias.
IV. To guard against nonresponse bias, use a mail-in survey.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) None of the above.
Solution
The correct answer is (E). None of the statements is true. Random sampling provides strong protection against bias from undercoverage bias and voluntary response
bias; but it is not effective against response bias. A convenience sample does not protect against undercoverage bias; in fact, it sometimes causes undercoverage bias.
Increasing sample size does not affect survey bias. And finally, using a mail-in survey does not prevent nonresponse bias. In fact, mail-in surveys are quite vulnerable to
nonresponse bias.