Question

What are the differences in the various types of sampling? Discuss the concept of confidence intervals. What factors will you consider when determining sample size?

Answer 1

Probability sampling (Representative samples)

Probability samples are selected in such a way as to be representative of the population. They provide the most valid or credible results because they reflect the characteristics of the population from which they are selected (e.g., residents of a particular community, students at an elementary school, etc.). There are two types of probability samples: random and stratified.

Random sample

The term random has a very precise meaning. Each individual in the population of interest has an equal likelihood of selection. This is a very strict meaning -- you can't just collect responses on the street and have a random sample.

The assumption of an equal chance of selection means that sources such as a telephone book or voter registration lists are not adequate for providing a random sample of a community. In both these cases there will be a number of residents whose names are not listed. Telephone surveys get around this problem by random-digit dialing -- but that assumes that everyone in the population has a telephone. The key to random selection is that there is no bias involved in the selection of the sample. Any variation between the sample characteristics and the population characteristics is only a matter of chance.

Stratified sample

A stratified sample is a mini-reproduction of the population. Before sampling, the population is divided into characteristics of importance for the research. For example, by gender, social class, education level, religion, etc. Then the population is randomly sampled within each category or stratum. If 38% of the population is college-educated, then 38% of the sample is randomly selected from the college-educated population.

Stratified samples are as good as or better than random samples, but they require a fairly detailed advance knowledge of the population characteristics, and therefore are more difficult to construct.

How to Construct a probability (representative) sample

Nonprobability samples (Non-representative samples)

As they are not truly representative, non-probability samples are less desirable than probability samples. However, a researcher may not be able to obtain a random or stratified sample, or it may be too expensive. A researcher may not care about generalizing to a larger population. The validity of non-probability samples can be increased by trying to approximate random selection, and by eliminating as many sources of bias as possible.

Quota sample

The defining characteristic of a quota sample is that the researcher deliberately sets the proportions of levels or strata within the sample. This is generally done to insure the inclusion of a particular segment of the population. The proportions may or may not differ dramatically from the actual proportion in the population. The researcher sets a quota, independent of population characteristics.

Two of each species

Example: A researcher is interested in the attitudes of members of different religions towards the death penalty. In Iowa a random sample might miss Muslims (because there are not many in that state). To be sure of their inclusion, a researcher could set a quota of 3% Muslim for the sample. However, the sample will no longer be representative of the actual proportions in the population. This may limit generalizing to the state population. But the quota will guarantee that the views of Muslims are represented in the survey.

Purposive sample

A purposive sample is a non-representative subset of some larger population, and is constructed to serve a very specific need or purpose. A researcher may have a specific group in mind, such as high level business executives. It may not be possible to specify the population -- they would not all be known, and access will be difficult. The researcher will attempt to zero in on the target group, interviewing whomever is available.

A subset of a purposive sample is a snowball sample -- so named because one picks up the sample along the way, analogous to a snowball accumulating snow. A snowball sample is achieved by asking a participant to suggest someone else who might be willing or appropriate for the study. Snowball samples are particularly useful in hard-to-track populations, such as truants, drug users, etc.

Convenience sample

A convenience sample is a matter of taking what you can get. It is an accidental sample. Although selection may be unguided, it probably is not random, using the correct definition of everyone in the population having an equal chance of being selected. Volunteers would constitute a convenience sample.

The common notation for the parameter in question is . Often, this parameter is the population mean , which is estimated through the sample mean . The level C of aconfidence interval gives the probability that the intervalproduced by the method employed includes the true value of the parameter .

tatisticians use a confidence interval to describe the amount of uncertainty associated with a sample estimate of a population parameter.

How to Interpret Confidence Intervals

Suppose that a 90% confidence interval states that the population mean is greater than 100 and less than 200. How would you interpret this statement?

Some people think this means there is a 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00.

The confidence level describes the uncertainty associated with a sampling method. Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; A 95% confidence level means that 95% of the intervals would include the parameter; and so on.

Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need:

Population Size — How many total people fit your demographic? For instance, if you want to know about mothers living in the US, your population size would be the total number of mothers living in the US. Don’t worry if you are unsure about this number. It is common for the population to be unknown or approximated.

Margin of Error (Confidence Interval) — No sample will be perfect, so you need to decide how much error to allow. The confidence interval determines how much higher or lower than the population mean you are willing to let your sample mean fall. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”

Confidence Level — How confident do you want to be that the actual mean falls within your confidence interval? The most common confidence intervals are 90% confident, 95% confident, and 99% confident.

Standard of Deviation — How much variance do you expect in your responses? Since we haven’t actually administered our survey yet, the safe decision is to use .5 – this is the most forgiving number and ensures that your sample will be large enough.