Sampling

7.1  Probability versus Non-Probability Sampling

Essentially all psychological research involves sampling—selecting a sample to study from the population of interest. Sampling falls into two broad categories. Probability sampling occurs when the researcher can specify the probability that each member of the population will be selected for the sample. Non-probability sampling occurs when the researcher cannot specify these probabilities. Most psychological research involves non-probability sampling. Convenience sampling—studying individuals who happen to be nearby and willing to participate—is a very common form of non-probability sampling used in psychological research.

Serious researchers, however, are much more likely to use some form of probability sampling. This is because the goal of most 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 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 non-probability 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 sampling frame. 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. Simple random sampling 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 dialling, 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 stratified random sampling, 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 cluster sampling, 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.

7.2  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.

7.3  Sampling Bias

Probability sampling was developed in large part to address the issue of sampling bias. Sampling bias occurs when a sample is selected in such a way that it is not representative of the entire population and therefore produces inaccurate results. This was the reason that the Literary Digest straw poll was so far off in its prediction of the 1936 presidential election. The mailing lists used came largely from telephone directories and lists of registered automobile owners, which overrepresented wealthier people, who were more likely to vote for Landon. Gallup was successful because he knew about this bias and found ways to sample less wealthy people as well.

There is one form of sampling bias that even careful random sampling is subject to. It is almost never the case that everyone selected for the sample actually responds to the survey. Some may have died or moved away, and others may decline to participate because they are too busy, are not interested in the survey topic, or do not participate in surveys on principle. If these survey non-responders differ from survey responders in systematic ways, then this can produce non-response bias. For example, in a mail survey on alcohol consumption, researcher Vivienne Lahaut and colleagues found that only about half the sample responded after the initial contact and two follow-up reminders (Lahaut, Jansen, van de Mheen, & Garretsen, 2002). The danger here is that the half who responded might have different patterns of alcohol consumption than the half who did not, which could lead to inaccurate conclusions on the part of the researchers. So to test for non-response bias, the researchers later made unannounced visits to the homes of a subset of the non-responders—coming back up to five times if they did not find them at home. They found that the original non-responders included an especially high proportion of abstainers (nondrinkers), which meant that their estimates of alcohol consumption based only on the original responders were too high.

Although there are methods for statistically correcting for non-response bias, they are based on assumptions about the non-responders—for example, that they are more similar to late responders than to early responders—which may not be correct. For this reason, the best approach to minimizing non-response bias is to minimize the number of non-responders—that is, to maximize the response rate. There is a large research literature on the factors that affect survey response rates (Groves et al., 2004). In general, in-person interviews have the highest response rates, followed by telephone surveys, and then mail and Internet surveys. Among the other factors that increase response rates are sending potential respondents a short prenotification message informing them that they will be asked to participate in a survey in the near future and sending simple follow-up reminders to non-responders after a few weeks. The perceived length and complexity of the survey also makes a difference, which is why it is important to keep survey questionnaires as short, simple, and on topic as possible. Finally, offering an incentive—especially cash—is a reliable way to increase response rates.

Key Takeaways

·         Research usually involves probability sampling, in which each member of the population has a known probability of being selected for the sample. Types of probability sampling include simple random sampling, stratified random sampling, and cluster sampling.

·         Sampling bias occurs when a sample is selected in such a way that it is not representative of the population and therefore produces inaccurate results. The most pervasive form of sampling bias is non-response bias, which occurs when people who do not respond to the survey differ in important ways from people who do respond. The best way to minimize non-response bias is to maximize the response rate by pre-notifying respondents, sending them reminders, constructing questionnaires that are short and easy to complete, and offering incentives.

References from Chapter 7

Groves, R. M., Fowler, F. J., Couper, M. P., Lepkowski, J. M., Singer, E., & Tourangeau, R. (2004). Survey methodology. Hoboken, NJ: Wiley.

Lahaut, V. M. H. C. J., Jansen, H. A. M., van de Mheen, D., & Garretsen, H. F. L. (2002). Non-response bias in a sample survey on alcohol consumption. Alcohol and Alcoholism, 37, 256–260.