4 Sampling

4.1 Foundations of Sampling Sampling is the process of selecting units from a population of interest Most often people, groups, and organizations, but sometimes texts like diaries, Internet discussion boards and blogs, or even graphic images By studying the sample, we can generalize results to the population from which the units were chosen

4.2 Sampling Terminology Figure 4.3 The different groups in the sampling model. Population: The group you want to generalize to and the group you sample from in a study. Theoretical population: A group which, ideally, you would like to sample from. This is usually contrasted with the accessible population. Accessible population: A group you can get access to when sampling. This is usually contrasted with the theoretical population. Sampling frame: The list from which you draw your sample. In some cases, there is no list; you draw your sample based upon an explicit rule. For instance, when doing quota sampling of passers-by at the local mall, you do not have a list per se, and the sampling frame is the population of people who pass by within the time frame of your study and the rule(s) you use to decide whom to select. Sample: The actual units you select to participate in your study.

4.2 Sampling Terminology (cont’d.) Accessible population A group you can get access to when sampling, usually contrasted with the theoretical population Bias A systematic error in an estimate Can be the result of any factor that leads to an incorrect estimate, and can lead to a result that does not represent the true value in the population

4.3 External Validity Generalizing External validity The process of making an inference that the results observed in a sample would hold in the population of interest – if such an inference or conclusion is valid we can say that it has generalizability External validity The degree to which the conclusions in your study would hold for other persons in other places and at other times

4.3a Two Major Approaches to External Validity in Sampling: The Sampling Model Figure 4.4 The sampling model for external validity. The researcher draws a sample for a study from a defined population to generalize the results to the population. Sampling model: A model for generalizing in which you identify your population, draw a fair sample, conduct your research, and finally generalize your results to other populations groups.

4.3a Two Major Approaches to External Validity: The Proximal Similarity Model Figure 4.5 The proximal similarity model for external validity. Proximal Similarity Model: A model for generalizing from your study to other contexts based upon the degree to which the other context is similar to your study context. Gradient of similarity The dimension along which your study context can be related to other potential contexts to which you might wish to generalize. Contexts that are closer to yours along the gradient of similarity of place, time, people, and so on can be generalized to with more confidence that ones that are further away.

4.4 Sampling Methods Nonprobability sampling Probability sampling Sampling that does not involve random selection Probability sampling Sampling that does involve random selection

4.5 Nonprobability Sampling Does not involve random selection Random selection is a process or procedure that assures that the different units in your population are selected by chance Two kinds of nonprobability sampling Accidental Purposive

4.5a Accidental, Haphazard, or Convenience Sampling Sampling by asking for volunteers Sampling by using available participants, such as college students Sampling by interviewing people on the streets The problem: you do not know if your sample represents the population

4.5b Purposive Sampling Several types: 4.5c Modal Instance Sampling 4.5d Expert Sampling: Validity 4.5e Quota Sampling Proportional Quota Sampling Nonproportional Quota Sampling 4.5f Heterogeneity Sampling 4.5g Snowball Sampling: Respondent Driven Sampling Modal instance sampling: Sampling for the most typical case. Expert sampling: A sample of people with known or demonstrable experience and expertise in some area. Validity: The best available approximation of the truth of a given proposition, inference, or conclusion Quota sampling: Any sampling method where you sample until you achieve a specific number of sampled units for each subgroup of a population. Proportional quota sampling: A sampling method where you sample until you achieve a specific number of sampled units for each subgroup of a population, where the proportions in each group are the same. Nonproportional quota sampling: A sampling method where you sample until you achieve a specific number of sampled units for each subgroup of a population, where the proportions in each group are not the same. Heterogeneity sampling: Sampling for diversity or variety. Snowball sampling: A sampling method in which you sample participants based upon referral from prior participants. Respondent Driven Sampling: RDS combines a modified form of chain referral, or snowball, sampling, with a mathematical system for weighting the sample to compensate for its not having been drawn as a simple random sample

4.6a The Sampling Distribution – Statistical Terms Figure 4.11 Statistical terms in sampling Response: A specific measurement value that a sampling unit supplies. Statistic: A value that is estimated from data Population parameter: The mean or average you would obtain if you were able to sample the entire population.

4.6a The Sampling Distribution – A Theoretical Distribution Figure 4.12 The sampling distribution Sampling distribution: The theoretical distribution of an infinite number of samples of the population of interest in your study.

4.6b Sampling Error Standard Deviation Standard Error Sampling Error Standard deviation: The square root of the variance. The standard deviation and variance both measure dispersion, but because the standard deviation is measured in the same units as the original measure and the variance is measured in squared units, the standard deviation is usually the more directly interpretable and meaningful. Standard error: The spread of the averages around the average of averages in a sampling distribution. Sampling error: Error in measurement associated with sampling.

4.6c The Normal Curve In Sampling Figure 4.13 The 68, 95, 99 Percent Rule Normal curve: A common type of distribution where the values of a variable have a bell-shaped histogram or frequency distribution. In a normal distribution, approximately 68 percent of cases occur within one standard deviation of the mean or center, 95 percent of the cases fall within two standard deviations, and 99 percent are within three standard deviations. We call these intervals the 68, 95, and 99 percent confidence intervals.

4.7 Probability Sampling: Procedures 4.7a Definitions: N is the number of cases in the sampling frame n is the number of cases in the sample NCn is the number of combinations (subsets) of n from N f = n/N is the sampling fraction

4.7b Simple Random Sampling Figure 4.15 Simple random sampling. Simple random sampling: A method of sampling that involves drawing a sample from a population so that every possible sample has an equal probability of being selected.

4.7c Stratified Random Sampling Figure 4.16 Stratified random sampling. Stratified Random Sampling: A method of sampling that involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup.

4.7d Systematic Random Sampling Figure 4.17 Systematic random sampling Systematic random sampling: A sampling method where you determine randomly where you want to start selecting in the sampling frame and then follow a rule to select every xth element in the sampling frame list (where the ordering of the list is assumed to be random).

4.7e Cluster (Area) Random Sampling Figure 4.19 A county level map of New York state used for cluster (area) random sampling Cluster random sampling: A sampling method that involves dividing the population into groups called clusters, randomly selecting clusters, and then sampling each element in the selected clusters. This method is useful when sampling a population that is spread across a wide area geographically.

4.7f Multistage Sampling The combining of several sampling techniques to create a more efficient or effective sample than the use of any one sampling type can achieve on its own

4.7g How Big Should the Sample Be? Bigger is better, as it increases the confidence in results However, this has to be balanced with cost and time considerations Sample size is also determined by the sampling technique used

4.8 Threats to External Validity Can the results be generalized to other people? Can the results be generalized to other places? Can the results be generalized to other time periods?

4.9 Improving External Validity Do a good job of drawing a sample from a population Random selection is always better Use proximal similarity effectively Replication When a study is repeated with a different group of people, in a different place, at a different time, and the results of the study are similar, external validity is increased

Discuss and Debate What does the term population really mean? What are some examples of populations? What are the advantages and disadvantages of each sampling technique in this chapter, and when would you choose one technique over another? What is external validity, and what is the best way to strengthen it? Often, students hear the word population, and automatically assume that it must be something very large, like the entire population of the United States. In reality, a population can be any group of people in a given setting. For example, everyone who works for a given company can be a population. All students enrolled in a given university can be a population. Student responses will vary, but the idea is to have them to see that populations do not have to be large groups of people.   Responses will vary. External validity is the ability of the researcher to generalize the results of a study back to the population from which it was drawn. The best way of strengthening external validity is through replication.