What type of sampling is used when all members of the population have an equal chance of being selected as a sample?

Since it is generally impossible to study an entire population (every individual in a country, all college students, every geographic area, etc.), researchers typically rely on sampling to acquire a section of the population to perform an experiment or observational study. It is important that the group selected be representative of the population, and not biased in a systematic manner. For example, a group comprised of the wealthiest individuals in a given area probably would not accurately reflect the opinions of the entire population in that area. For this reason, randomization is typically employed to achieve an unbiased sample. The most common sampling designs are simple random sampling, stratified random sampling, and multistage random sampling.

Simple Random Sampling

Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection.
(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

Stratified Random Sampling

There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.

A stratified sample is obtained by taking samples from each stratum or sub-group of a population.

When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population.

Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:

a) the cost per observation in the survey may be reduced;
b) estimates of the population parameters may be wanted for each sub-population;
c) increased accuracy at given cost.

Example

Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from these.
(Definition and example taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

Multistage Random Sampling

A multistage random sample is constructed by taking a series of simple random samples in stages. This type of sampling is often more practical than simple random sampling for studies requiring "on location" analysis, such as door-to-door surveys. In a multistage random sample, a large area, such as a country, is first divided into smaller regions (such as states), and a random sample of these regions is collected. In the second stage, a random sample of smaller areas (such as counties) is taken from within each of the regions chosen in the first stage. Then, in the third stage, a random sample of even smaller areas (such as neighborhoods) is taken from within each of the areas chosen in the second stage. If these areas are sufficiently small for the purposes of the study, then the researcher might stop at the third stage. If not, he or she may continue to sample from the areas chosen in the third stage, etc., until appropriately small areas have been chosen.

What Is Systematic Sampling?

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. Despite the sample population being selected in advance, systematic sampling is still thought of as being random if the periodic interval is determined beforehand and the starting point is random.

Key Takeaways

• Systematic sampling is a probability sampling method in which a random sample, with a fixed periodic interval, is selected from a larger population.
• The fixed periodic interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.
• Other advantages of this methodology include eliminating the phenomenon of clustered selection and a low probability of contaminating data.
• Disadvantages include over- or under-representation of particular patterns and a greater risk of data manipulation.

Systematic Sampling

Understanding Systematic Sampling

Since simple random sampling of a population can be inefficient and time-consuming, statisticians turn to other methods, such as systematic sampling. Choosing a sample size through a systematic approach can be done quickly. Once a fixed starting point has been identified, a constant interval is selected to facilitate participant selection.

Systematic sampling is preferable to simple random sampling when there is a low risk of data manipulation. If such a risk is high when a researcher can manipulate the interval length to obtain desired results, a simple random sampling technique would be more appropriate.

Systematic sampling is popular with researchers and analysts because of its simplicity. Researchers generally assume the results are representative of most normal populations unless a random characteristic disproportionately exists with every "nth" data sample (which is unlikely). In other words, a population needs to exhibit a natural degree of randomness along with the chosen metric. If the population has a type of standardized pattern, the risk of accidentally choosing very common cases is more apparent.

Within systematic sampling, as with other sampling methods, a target population must be selected prior to selecting participants. A population can be identified based on any number of desired characteristics that suit the purpose of the study being conducted. Some selection criteria may include age, gender, race, location, education level, and/or profession.

There are several methods of sampling a population for statistical inference; systematic sampling is one form of random sampling.

Examples of Systematic Sampling

As a hypothetical example of systematic sampling, assume that in a population of 10,000 people, a statistician selects every 100th person for sampling. The sampling intervals can also be systematic, such as choosing a new sample to draw from every 12 hours.

As another example, if you wanted to select a random group of 1,000 people from a population of 50,000 using systematic sampling, all the potential participants must be placed in a list and a starting point would be selected. Once the list is formed, every 50th person on the list (starting the count at the selected starting point) would be chosen as a participant, since 50,000/1,000 = 50.

For example, if the selected starting point was 20, the 70th person on the list would be chosen followed by the 120th, and so on. Once the end of the list was reached and if additional participants are required, the count loops to the beginning of the list to finish the count.

In order to conduct systematic sampling, researchers must first know the size of the target population.

Systematic Sampling vs. Cluster Sampling

Systematic sampling and cluster sampling differ in how they pull sample points from the population included in the sample. Cluster sampling breaks the population down into clusters, while systematic sampling uses fixed intervals from the larger population to create the sample.

Systematic sampling selects a random starting point from the population, and then a sample is taken from regular fixed intervals of the population depending on its size. Cluster sampling divides the population into clusters and then takes a simple random sample from each cluster.

Cluster sampling is considered less precise than other methods of sampling. However, it may save costs on obtaining a sample. Cluster sampling is a two-step sampling procedure. It may be used when completing a list of the entire population is difficult. For example, it could be difficult to construct the entire population of the customers of a grocery store to interview.

However, a person could create a random subset of stores, which is the first step in the process. The second step is to interview a random sample of the customers of those stores. This is a simple manual process that can save time and money.

Limitations of Systematic Sampling

One risk that statisticians must consider when conducting systematic sampling involves how the list used with the sampling interval is organized. If the population placed on the list is organized in a cyclical pattern that matches the sampling interval, the selected sample may be biased.

For example, a company's human resources department wants to pick a sample of employees and ask how they feel about company policies. Employees are grouped in teams of 20, with each team headed by a manager. If the list used to pick the sample size is organized with teams clustered together, the statistician risks picking only managers (or no managers at all) depending on the sampling interval.

What Are the Advantages of Systematic Sampling?

Systematic sampling is simple to conduct and easy to understand, which is why it's generally favored by researchers. The central assumption, that the results represent the majority of normal populations, guarantees the entire population is evenly sampled. Also, systematic sampling provides an increased degree of control when compared to other sampling methodologies because of its process. Systematic sampling also carries a low-risk factor because there is a low chance that the data can be contaminated.

What Are the Disadvantages of Systematic Sampling?

The main disadvantage of systematic sampling is that the size of the population is needed. Without knowing the specific number of participants in a population, systematic sampling does not work well. For example, if a statistician would like to examine the age of homeless people in a specific region but cannot accurately obtain how many homeless people there are, then they won't have a population size or a starting point. Another disadvantage is that the population needs to exhibit a natural amount of randomness to it else the risk of choosing similar instances is increased, defeating the purpose of the sample.

How Do Cluster and Systematic Sampling Differ?

Cluster sampling and systematic sampling differ in how they pull sample points from the population included in the sample. Cluster sampling divides the population into clusters and then takes a simple random sample from each cluster. Systematic sampling selects a random starting point from the population, and then a sample is taken from regular fixed intervals of the population depending on its size. Cluster sampling is susceptible to a larger sampling error than is systematic sampling though it may be a cheaper process.

What is the type of sampling when everyone has the equal chance of selection?

Is a kind of sampling where the subject of the population has an equal chance of opportunity to be selected as representative sample?

What sampling technique in which members of the population are listed and samples are selected?