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Types of samples

The best sampling is probability sampling, because it increases the likelihood of obtaining samples that are representative of the population.

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 orstratum. 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.

Non-probability samples are limited with regard to generalization. Because they do not truly represent a population, we cannot make valid inferences about the larger group from which they are drawn. Validity can be increased by approximating random selection as much as possible, and making every attempt to avoid introducing bias into sample selection.

Sampling: Sample size

In a very general sense, the larger the sample, the better -- because larger samples tend to be more similar to the population from which they are drawn. However, if the population of interest is small, then the sample can be relatively small. Large samples require more time for data collection and analysis, and are therefore more costly than smaller ones.

If a treatment is known to have a fairly strong effect, it may show up in an experiment involving a small sample. On the other hand, a small sample for a survey may miss individuals holding a minority point of view. For surveys one has to consider refusal and spoilage rates (incomplete responses, illegible answers, nonsensical replies). In such cases the researcher should aim for a larger sample in order to cover the losses.

Increasing the number of variables and/or their levels requires more participants. For example, comparing attitudes of 20 lower division and 20 upper division college students toward college athletics may be a reasonable number. If the samples of 20 each are broken down into fraternity/sorority vs. non-greek students, the number in each category declines. A gender division leads to only 5 persons per cell -- probably too small for drawing any conclusions.
Level
20 Lower division
20 Upper division
Greek
10 Yes
10 No
10 Yes
10 No
Gender
5 M
5 F
5 M
5 F
5 M
5 F
5 M
5 F