Essentially all psychological research involves sampling—selecting a sample to study from the population of interest. Sampling falls into two broad categories.
**P****rob****a****b****i****l****i****ty ****s****am****pli****n****g** occurs when the researcher can specify the probability that each member of the population will be selected for
the sample.

**No****n****prob****a****b****i****lity ****sa****m****pli****n****g** occurs when the researcher cannot specify these probabilities. Most psychological research involves
nonprobability sampling. Convenience sampling—studying individuals who happen to be nearby and willing to participate—is a very common form of nonprobability sampling used in psychological
research.

Survey researchers, however, are much more likely to use some form of probability sampling. This is because the goal of most survey research is to make accurate estimates about what is true in a particular population, and these estimates are most accurate when based on a probability sample. For example, it is important for survey researchers to base their estimates of election outcomes—which are often decided by only a few percentage points—on probability samples of likely registered voters.

Compared with nonprobability sampling, probability sampling requires a very clear specification of the population, which of course depends on the research questions
to be answered. The population might be all registered voters in the state of Arkansas, all American consumers who have purchased a car in the past year, women in the United States over 40
years old who have received a mammogram in the past decade, or all the alumni of a particular university. Once the population has been specified, probability sampling requires a
**samplingframe**. This is essentially a list of all the members of the population from which to select the respondents. Sampling frames can come from a variety of sources,
including telephone directories, lists of registered voters, and hospital or insurance records. In some cases, a map can serve as a sampling frame, allowing for the selection of cities,
streets, or households.

There are a variety of different probability sampling methods.**Si****m****ple ****ra****n****d****o****m ****s****am****pli****n****g** is done in
such a way that each individual in the population has an equal probability of being selected for the sample. This could involve putting the names of all individuals in the sampling frame into a
hat, mixing them up, and then drawing out the number needed for the sample. Given that most sampling frames take the form of computer files, random sampling is more likely to involve
computerized sorting or selection of respondents. A common approach in telephone surveys is random-digit dialing, in which a computer randomly generates phone numbers from among the possible
phone numbers within a given geographic area.

A common alternative to simple random sampling is **str****a****t****i****fi****e****d ****r****a****n****dom ****sa****m****pl****in****g**, in which the population is divided into different subgroups or “strata” (usually based on demographic characteristics) and then a random
sample is taken from each “stratum.” Stratified random sampling can be used to select a sample in which the proportion of respondents in each of various subgroups matches the proportion in the
population. For example, because about 12.5% of the US population is Black, stratified random sampling can be used to ensure that a survey of 1,000 American adults includes about 125 Black
respondents. Stratified random sampling can also be used to sample extra respondents from particularly small subgroups—allowing valid conclusions to be drawn about those subgroups. For example,
because Asian Americans make up a fairly small percentage of the US population (about 4.5%), a simple random sample of 1,000 American adults might include too few Asian Americans to draw any
conclusions about them as distinct from any other subgroup. If this is important to the research question, however, then stratified random sampling could be used to ensure that enough Asian
American respondents are included in the sample to draw valid conclusions about Asian Americans as a whole.

Yet another type of probability sampling is **clus****t****e****r ****s****a****m****pl****in****g**, in which larger clusters of individuals are randomly sampled and then individuals within each cluster are randomly sampled. For example, to
select a sample of small-town residents in the United States, a researcher might randomly select several small towns and then randomly select several individuals within each town. Cluster
sampling is especially useful for surveys that involve face-to-face interviewing because it minimizes the amount of traveling that the interviewers must do. For example, instead of traveling to
200 small towns to interview 200 residents, a research team could travel to 10 small towns and interview 20 residents of each. The National Comorbidity Survey was done using a form of cluster
sampling.

How large does a survey sample need to be? In general, this depends on two factors. One is the level of confidence in the result that the researcher wants. The larger the sample, the closer any statistic based on that sample will tend to be to the corresponding value in the population. The other factor is the budget of the study. Larger samples provide greater confidence, but they take more time, effort, and money to obtain. Taking these two factors into account, most survey research uses sample sizes that range from about 100 to about 1,000.

## Sample Size and Population Size

Why is a sample of 1,000 considered to be adequate for most survey research—even when the population is much larger than that? Consider, for example, that a sample of only 1,000 registered voters is generally considered a good sample of the roughly 120 million registered voters in the US population—even though it includes only about 0.0008% of the population! The answer is a bit surprising.

One part of the answer is that a statistic based on a larger sample will tend to be closer to the population value and that this can be characterized mathematically. Imagine, for example, that in a sample of registered voters, exactly 50% say they intend to vote for the incumbent. If there are 100 voters in this sample, then there is a 95% chance that the true percentage in the population is between 40 and 60. But if there are 1,000 voters in the sample, then there is a 95% chance that the true percentage in the population is between 47 and 53. Although this “95% confidence interval” continues to shrink as the sample size increases, it does so at a slower rate. For example, if there are 2,000 voters in the sample, then this only reduces the 95% confidence interval to 48 to 52. In many situations, the small increase in confidence beyond a sample size of 1,000 is not considered to be worth the additional time, effort, and money.

Another part of the answer—and perhaps the more surprising part—is that confidence intervals depend only on the size of the sample and not on the size of the population. So a sample of 1,000 would produce a 95% confidence interval of 47 to 53 regardless of whether the population size was a hundred thousand, a million, or a hundred million.

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