## Probability And Nonprobability Sampling

There are two major types of sampling designs: probability and nonprobability sampling. In probability sampling, the elements in the population have some known chance or probability of being selected as sample subjects. In nonprobability sampling, the elements do not have a known or predetermined chance of being selected as subjects.

## Probability Sampling

When elements in the population have a known chance of being chosen as subjects in the sample, we resort to a probability sampling design. Probability sampling can be either unrestricted (or simple random sampling) or restricted (or complex probability sampling) in nature.

### Unrestricted or Simple Random Sampling

In the unrestricted probability sampling design, more commonly known as simple random sampling, every element in the population has a known and equal chance of being selected as a subject. Let us say there are 1,000 elements in the population, and we need a sample of 100. Suppose we were to drop pieces of paper in a hat, each bearing the name of one of the elements, and we were to draw 100 of those from the hat with our eyes closed. We know that each one of those elements has a 100/1,000 chance of being drawn. In other words, we know that the probability of any one of them being chosen as a subject is. 1, and we also know that each single element in the hat has the same or equal probability of being chosen.

### Restricted or Complex Probability Sampling

As an alternative to the simple random sampling design, several complex probability sampling (restricted probability) designs can be used. These probability sampling procedures offer a viable and sometimes more efficient alternative to the unrestricted design we just discussed. Efficiency is improved in that more information can be obtained for a given sample size using some of the complex probability sampling procedures than the simple random sampling design.

### Systematic Sampling

The systematic sampling design involves drawing every nth element in the population starting with a randomly chosen element between 1 and n. The procedure is exemplified below.

If we want a sample of 35 households from a total population of 260 houses in a particular locality, then we could sample every seventh house starting from a random number from 1 to 7. Let us say that the random number is 7, then houses numbered 7, 14, 21, 28, and so on, would be sampled until the 35 houses are selected.

### Stratified Random Sampling

Stratified random sampling, as its name implies, involves a process of stratification of segregation, followed by random selection of subjects from each stratum. The population is first divided into mutually exclusive groups that are relevant, appropriate, and meaningful in the context of the study. For instance, if the president of a company is concerned about low motivational levels or high absentee rates among the employees, it makes sense to stratify the population of organizational members according to their job levels. When the data are collected and the analysis done, we may find that contrary to expectations, it is the middle-level managers who are not motivated. This information will help the president to focus on action at the right level and devise better ways to motivate this group.

### Proportionate and Disproportionate Stratified Random Sampling

Once the population has been stratified in some meaningful way, a sample of members from each stratum can be drawn using either a simple random sampling or a systematic sampling procedure. The subjects drawn from each stratum can be either proportionate or disproportionate to the number of elements in the stratum. For instance, if an organization employs 10 top managers, 30 middle managers. 50 lower-level managers, 100 supervisors, 500 clerks, and 20 secretaries and a stratified sample of about 140 people is needed for some scientific survey the researcher might decide to include in the sample 20 percent of members from each stratum. That is, members represented in the sample from each stratum will be proportionate to the total number of elements in the respective stratum. This would mean that 2 from the top, 6 from the middle, and 10 from the lower levels of management will be included in the sample. In addition, 20 supervisors, 100 clerks, and 4 secretaries will be represented in the sample.

Disproportionate sampling decisions are made either when some stratum strata are too small or too large, or when there is more variability suspects within a particular stratum. As an example, the educational levels among supervisors, which may be thought of as influencing perceptions, may range from elementary school to master’s degrees. Here, more people will be sampled at the supervisor’s level. Disproportionate sampling is also sometimes done when it is easier, simpler, and less expensive to collect data from one or more strata than from others.

### Cluster Sampling

Groups or chunks of elements that, ideally, would have heterogeneity among the members within each group are chosen for study in cluster sampling. This is in contrast to choosing some elements from the population as in simple random sampling, or stratifying and then choosing members from the strata as in stratified random sampling, or choosing every nth element in the population as in systematic sampling. When several groups with intragroup heterogeneity and intergroup homogeneity are found, then a random sampling of the clusters or groups can ideally be done and information gathered from each of the members in the randomly chosen clusters. Ad hoc organizational committees drawn from various departments to offer inputs to the company president, to enable him to make decisions on product development, budget allocations, marketing strategies, and the like are good examples of different clusters.

### Single-Stage and Multistage Cluster Sampling

We have thus far discussed single-stage cluster sampling, which involves the division of the population into convenient clusters, randomly choosing the required number of clusters as sample subjects, and investigating all the elements in each of the randomly chosen clusters. Cluster sampling can also be done in several stages, and is then called multistage cluster sampling. If we were to do a national survey of the average monthly bank deposits, for instance, cluster sampling would first be used to select the urban, semiurban, and rural geographical locations would be chosen. At the third stage, banks within each area would be chosen. In other words, multistage cluster sampling involves a probability sampling of the primary sampling units, from each of these primary units, a probability sample of the secondary sampling units is then drawn; a third level of probability sampling is done from each of these secondary units, and so on, until we have reached the final stage of break down for the sample units, when we will sample every member in those units.

### Area Sampling

The area sampling design constitutes geographic clusters; that is, when the research pertains to populations within identifiable geographic areas such as countries, city blocks, or particular boundaries within a locality, area sampling can be done. Thus, area sampling is a form of cluster sampling within as area. Sampling the needs of consumers before opening a 24-hour convenience store in a particular part of the town would involve area sampling. Retail store location plans, advertisements focused specifically on local populations, and TV and radio programs beamed at specific areas could all use an area sampling design gather information on the interests, attitudes, predisposition’s, and behaviors of the local area people.

### Double Sampling

This plan is restored to when further information is needed from a subset of the group from which some information has already been collected. A sampling where a sample is used in a study to collect some preliminary information of interest, a later a subsample of this primary sample is used to examine the matter more detail, is called double sampling.

## Nonprobability Sampling

The nonprobability sampling designs, which fit into the broad categories of convenience sampling and purposive sampling.

### Convenience Sampling

As its name implies, convenience sampling involves collecting information from members of the population who are conveniently available to provide it. One would expect that the Pepsi Challenge contest was administered on a convenience sampling basis. Such a contest, with the purpose of determining whether people prefer one product to another, might be held at a mall visited by many shoppers. Those inclined to take the test might form the sample for the study of how many people prefer Pepsi over Coke or product X over product Y. Such a sample is a convenience sample.

### Purposive Sampling

Instead of obtaining information from those who are most conveniently available, it might sometimes become necessary to obtain information from specific target groups. Here, the sampling is confined to specific types of people who can provide the desired information, either because they are the only ones who possess it, or conform to some criteria set by the researcher. This type of sampling – judgment sampling and quota sampling – will now be explained.

### Judgment Sampling

Judgment sampling involves the choice of subjects who are in the best position to provide the information required. For instance, if a researcher wants to find out what it takes for women managers to make it to the top, the only people who can give firsthand information are the women who have risen to the positions of presidents, vice presidents, and important top-level executives in work organizations. By virtue of having gone through the experiences and processes themselves, they might be expected to have expert knowledge and might perhaps be able to provide good data or information to the researcher. Thus, the judgment sampling design is used when a limited number or category of people have the information that is sought. In such cases, any type of probability sampling across a cross-section of the entire population is purposeless and useless.

### Quota Sampling

Quota sampling, a second type of purposive sampling, ensures that certain groups are adequately represented in the study through the assignment of a quota. Generally, the quota fixed for each subgroup is based on the total numbers of each group in the population. However, since this is a nonprobability-sampling plan, the results are not generalizable to the population.

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