###### B. Samples and Sampling

# Types of Sampling

We may then consider different types of probability samples. Although there are a number of different methods that might be used to create a sample, they generally can be grouped into one of **two** categories: *probability samples* or *non-probability* samples.

### Probability Samples

The idea behind this type is random selection. More specifically, each sample from the population of interest has a known probability of selection under a given sampling scheme. There are **four** categories of probability samples described below.

### Simple Random Sampling

The most widely known type of a random sample is the simple random sample (SRS). This is characterized by the fact that the probability of selection is the same for every case in the population. Simple random sampling is a method of selecting n units from a population of size N such that every possible sample of size an has equal chance of being drawn.

An example may make this easier to understand. Imagine you want to carry out a survey of 100 voters in a small town with a population of 1,000 eligible voters. With a town this size, there are "old-fashioned" ways to draw a sample. For example, we could write the names of all voters on a piece of paper, put all pieces of paper into a box and draw 100 tickets at random. You shake the box, draw a piece of paper and set it aside, shake again, draw another, set it aside, etc. until we had 100 slips of paper. These 100 form our sample. And this sample would be drawn through a simple random sampling procedure - at each draw, every name in the box had the same probability of being chosen.

In real-world social research, designs that employ simple random sampling are difficult to come by. We can imagine some situations where it might be possible - you want to interview a sample of doctors in a hospital about work conditions. So you get a list of all the physicians that work in the hospital, write their names on a piece of paper, put those pieces of paper in the box, shake and draw. But in most real-world instances it is impossible to list everything on a piece of paper and put it in a box, then randomly draw numbers until desired sample size is reached.

There are many reasons why one would choose a different type of probability sample in practice.

#### Example 1

Suppose you were interested in investigating the link between the family of origin and income and your particular interest is in comparing incomes of Hispanic and Non-Hispanic respondents. For statistical reasons, you decide that you need at least 1,000 non-Hispanics and 1,000 Hispanics. Hispanics comprise around 6 or 7% of the population. If you take a simple random sample of all races that would be large enough to get you 1,000 Hispanics, the sample size would be near 15,000, which would be far more expensive than a method that yields a sample of 2,000. One strategy that would be more cost-effective would be to split the population into Hispanics and non-Hispanics, then take a simple random sample within each portion (Hispanic and non-Hispanic).

#### Example 2

Let's suppose your sampling frame is a large city's telephone book that has 2,000,000 entries. To take a SRS, you need to associate each entry with a number and choose n= 200 numbers from N= 2,000,000. This could be quite an ordeal. Instead, you decide to take a random start between 1 and N/n= 20,000 and then take every 20,000th name, etc. This is an example of systematic sampling, a technique discussed more fully below.

#### Example 3

Suppose you wanted to study dance club and bar employees in NYC with a sample of n = 600. Yet there is no list of these employees from which to draw a simple random sample. Suppose you obtained a list of all bars/clubs in NYC. One way to get this would be to randomly sample 300 bars and then randomly sample 2 employees within each bars/club. This is an example of cluster sampling. Here the unit of analysis (employee) is different from the primary sampling unit (the bar/club).

In each of these three examples, a probability sample is drawn, yet none is an example of simple random sampling. Each of these methods is described in greater detail below.

Although simple random sampling is the ideal for social science and most of the statistics used are based on assumptions of SRS, in practice, SRS are rarely seen. It can be terribly inefficient, and particularly difficult when large samples are needed. Other probability methods are more common. Yet SRS is essential, both as a method and as an easy-to-understand method of selecting a sample.

To recap, though, that simple random sampling is a sampling procedure in which every element of the population has the same chance of being selected and every element in the sample is selected by chance.

#### Stratified Random Sampling

In this form of sampling, the population is first divided into two or more mutually exclusive segments based on some categories of variables of interest in the research. It is designed to organize the population into homogenous subsets before sampling, then drawing a random sample within each subset. With stratified random sampling the population of N units is divided into subpopulations of units respectively. These subpopulations, called *strata*, are non-overlapping and together they comprise the whole of the population. When these have been determined, a sample is drawn from each, with a separate draw for each of the different strata. The sample sizes within the strata are denoted by respectively. If a SRS is taken within each stratum, then the whole sampling procedure is described as stratified random sampling.

The primary benefit of this method is to ensure that cases from smaller strata of the population are included in sufficient numbers to allow comparison. An example makes it easier to understand. Say that you're interested in how job satisfaction varies by race among a group of employees at a firm. To explore this issue, we need to create a sample of the employees of the firm. However, the employee population at this particular firm is predominantly white, as the following chart illustrates:

If we were to take a simple random sample of employees, there's a good chance that we would end up with very small numbers of Blacks, Asians, and Latinos. That could be disastrous for our research, since we might end up with too few cases for comparison in one or more of the smaller groups.

Rather than taking a simple random sample from the firm's population at large, in a stratified sampling design, we ensure that appropriate numbers of elements are drawn from each racial group in proportion to the percentage of the population as a whole. Say we want a sample of 1000 employees - we would stratify the sample by race (group of White employees, group of African American employees, etc.), then randomly draw out 750 employees from the White group, 90 from the African American, 100 from the Asian, and 60 from the Latino. This yields a sample that is proportionately representative of the firm as a whole.

Stratification is a common technique. There are many reasons for this, such as:

- If data of known precision are wanted for certain subpopulations, than each of these should be treated as a population in its own right.
- Administrative convenience may dictate the use of stratification, for example, if an agency administering a survey may have regional offices, which can supervise the survey for a part of the population.
- Sampling problems may be inherent with certain sub populations, such as people living in institutions (e.g. hotels, hospitals, prisons).
- Stratification may improve the estimates of characteristics of the whole population. It may be possible to divide a heterogeneous population into sub-populations, each of which is internally homogenous. If these strata are homogenous, i.e., the measurements vary little from one unit to another; a precise estimate of any stratum mean can be obtained from a small sample in that stratum. The estimate can then be combined into a precise estimate for the whole population.
- There is also a statistical advantage in the method, as a stratified random sample nearly always results in a smaller variance for the estimated mean or other population parameters of interest.

#### Systematic Sampling

This method of sampling is at first glance very different from SRS. In practice, it is a variant of simple random sampling that involves some listing of elements - every nth element of list is then drawn for inclusion in the sample. Say you have a list of 10,000 people and you want a sample of 1,000.

Creating such a sample includes three steps:

- Divide number of cases in the population by the desired sample size. In this example, dividing 10,000 by 1,000 gives a value of 10.
- Select a random number between one and the value attained in Step 1. In this example, we choose a number between 1 and 10 - say we pick 7.
- Starting with case number chosen in Step 2, take every tenth record (7, 17, 27, etc.).

More generally, suppose that the N units in the population are ranked 1 to N in some order (e.g., alphabetic). To select a sample of n units, we take a unit at random, from the 1st k units and take every k-th unit thereafter.

The advantages of systematic sampling method over simple random sampling include:

- It is easier to draw a sample and often easier to execute without mistakes. This is a particular advantage when the drawing is done in the field.
- Intuitively, you might think that systematic sampling might be more precise than SRS. In effect it stratifies the population into n strata, consisting of the 1st k units, the 2nd k units, and so on. Thus, we might expect the systematic sample to be as precise as a stratified random sample with one unit per stratum. The difference is that with the systematic one the units occur at the same relative position in the stratum whereas with the stratified, the position in the stratum is determined separately by randomization within each stratum.

#### Cluster Sampling

In some instances the sampling unit consists of a group or cluster of smaller units that we call elements or subunits (these are the units of analysis for your study). There are two main reasons for the widespread application of cluster sampling. Although the first intention may be to use the elements as sampling units, it is found in many surveys that no reliable list of elements in the population is available and that it would be prohibitively expensive to construct such a list. In many countries there are no complete and updated lists of the people, the houses or the farms in any large geographical region.

Even when a list of individual houses is available, economic considerations may point to the choice of a larger cluster unit. For a given size of sample, a small unit usually gives more precise results than a large unit. For example a SRS of 600 houses covers a town more evenly than 20 city blocks containing an average of 30 houses apiece. But greater field costs are incurred in locating 600 houses and in traveling between them than in covering 20 city blocks. When cost is balanced against precision, the larger unit may prove superior.

Important things about cluster sampling:

- Most large scale surveys are done using cluster sampling;
- Clustering may be combined with stratification, typically by clustering within strata;
- In general, for a given sample size n cluster samples are less accurate than the other types of sampling in the sense that the parameters you estimate will have greater variability than an SRS, stratified random or systematic sample.

### Nonprobability Sampling

Social research is often conducted in situations where a researcher cannot select the kinds of probability samples used in large-scale social surveys. For example, say you wanted to study homelessness - there is no list of homeless individuals nor are you likely to create such a list. However, you need to get some kind of a sample of respondents in order to conduct your research. To gather such a sample, you would likely use some form of non-probability sampling.

To reiterate, the primary difference between probability methods of sampling and non-probability methods is that in the latter you do not know the likelihood that any element of a population will be selected for study.

There are **four** primary types of non-probability sampling methods:

#### Availability Sampling

Availability sampling is a method of choosing subjects who are available or easy to find. This method is also sometimes referred to as haphazard, accidental, or convenience sampling. The primary advantage of the method is that it is very easy to carry out, relative to other methods. A researcher can merely stand out on his/her favorite street corner or in his/her favorite tavern and hand out surveys. One place this used to show up often is in university courses. Years ago, researchers often would conduct surveys of students in their large lecture courses. For example, all students taking introductory sociology courses would have been given a survey and compelled to fill it out. There are some advantages to this design - it is easy to do, particularly with a captive audience, and in some schools you can attain a large number of interviews through this method.

The primary problem with availability sampling is that you can never be certain what population the participants in the study represent. The population is unknown, the method for selecting cases is haphazard, and the cases studied probably don't represent any population you could come up with.

However, there are some situations in which this kind of design has advantages - for example, survey designers often want to have some people respond to their survey before it is given out in the "real" research setting as a way of making certain the questions make sense to respondents. For this purpose, availability sampling is not a bad way to get a group to take a survey, though in this case researchers care less about the specific responses given than whether the instrument is confusing or makes people feel bad.

Despite the known flaws with this design, it's remarkably common. Ask a provocative question, give telephone number and web site address ("Vote now at CNN.com), announce results of poll. This method provides some form of statistical data on a current issue, but it is entirely unknown what population the results of such polls represents. At best, a researcher could make some conditional statement about people who are watching CNN at a particular point in time who cared enough about the issue in question to log on or call in.

#### Quota Sampling

Quota sampling is designed to overcome the most obvious flaw of availability sampling. Rather than taking just anyone, you set quotas to ensure that the sample you get represents certain characteristics in proportion to their prevalence in the population. Note that for this method, you have to know something about the characteristics of the population ahead of time. Say you want to make sure you have a sample proportional to the population in terms of gender - you have to know what percentage of the population is male and female, then collect sample until yours matches. Marketing studies are particularly fond of this form of research design.

The primary problem with this form of sampling is that even when we know that a quota sample is representative of the particular characteristics for which quotas have been set, we have no way of knowing if sample is representative in terms of any other characteristics. If we set quotas for gender and age, we are likely to attain a sample with good representativeness on age and gender, but one that may not be very representative in terms of income and education or other factors.

Moreover, because researchers can set quotas for only a small fraction of the characteristics relevant to a study quota sampling is really not much better than availability sampling. To reiterate, you must know the characteristics of the entire population to set quotas; otherwise there's not much point to setting up quotas. Finally, interviewers often introduce bias when allowed to self-select respondents, which is usually the case in this form of research. In choosing males 18-25, interviewers are more likely to choose those that are better-dressed, seem more approachable or less threatening. That may be understandable from a practical point of view, but it introduces bias into research findings.

#### Purposive Sampling

Purposive sampling is a sampling method in which elements are chosen based on purpose of the study. Purposive sampling may involve studying the entire population of some limited group (sociology faculty at Columbia) or a subset of a population (Columbia faculty who have won Nobel Prizes). As with other non-probability sampling methods, purposive sampling does not produce a sample that is representative of a larger population, but it can be exactly what is needed in some cases - study of organization, community, or some other clearly defined and relatively limited group.

#### Snowball Sampling

Snowball sampling is a method in which a researcher identifies one member of some population of interest, speaks to him/her, then asks that person to identify others in the population that the researcher might speak to. This person is then asked to refer the researcher to yet another person, and so on.

Snowball sampling is very good for cases where members of a special population are difficult to locate. For example, several studies of Mexican migrants in Los Angeles have used snowball sampling to get respondents.

The method also has an interesting application to group membership - if you want to look at pattern of recruitment to a community organization over time, you might begin by interviewing fairly recent recruits, asking them who introduced them to the group. Then interview the people named, asking them who recruited them to the group.

The method creates a sample with questionable representativeness. A researcher is not sure who is in the sample. In effect snowball sampling often leads the researcher into a realm he/she knows little about. It can be difficult to determine how a sample compares to a larger population. Also, there's an issue of who respondents refer you to - friends refer to friends, less likely to refer to ones they don't like, fear, etc.