# Types of Probability Sampling: Simple Random Sampling, Systematic Sampling, Stratified Random sampling, Area sampling, Cluster Sampling

1. ### Simple Random Sample

Simple random sampling as the name suggests is a completely random method of selecting the sample. This sampling method is as easy as assigning numbers to the individuals (sample) and then randomly choosing from those numbers through an automated process. Finally, the numbers that are chosen are the members that are included in the sample.

There are two ways in which the samples are chosen in this method of sampling: Lottery system and using number generating software/ random number table. This sampling technique usually works around large population and has its fair share of advantages and disadvantages.

Ease of use represents the biggest advantage of simple random sampling. Unlike more complicated sampling methods such as stratified random sampling and probability sampling, no need exists to divide the population into sub-populations or take any other additional steps before selecting members of the population at random.

A simple random sample is meant to be an unbiased representation of a group. It is considered a fair way to select a sample from a larger population, since every member of the population has an equal chance of getting selected.

A sampling error can occur with a simple random sample if the sample does not end up accurately reflecting the population it is supposed to represent. For example, in our simple random sample of 25 employees, it would be possible to draw 25 men even if the population consisted of 125 women and 125 men. For this reason, simple random sampling is more commonly used when the researcher knows little about the population. If the researcher knew more, it would be better to use a different sampling technique, such as stratified random sampling, which helps to account for the differences within the population, such as age, race or gender. Other disadvantages include the fact that for sampling from large populations, the process can be time consuming and costly compared to other methods.

1. ### Systematic Sample

Systematic Sampling is when you choose every “nth” individual to be a part of the sample. For example, you can choose every 5th person to be in the sample. Systematic sampling is an extended implementation of the same old probability technique in which each member of the group is selected at regular periods to form a sample. There’s an equal opportunity for every member of a population to be selected using this sampling technique.

Risks Associated With 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.

1. ### Stratified Random Sample

Stratified Random sampling involves a method where a larger population can be divided into smaller groups that usually don’t overlap but represent the entire population together. While sampling these groups can be organized and then draw a sample from each group separately.

A common method is to arrange or classify by sex, age, ethnicity and similar ways. Splitting subjects into mutually exclusive groups and then using simple random sampling to choose members from groups.

Members in each of these groups should be distinct so that every member of all groups get equal opportunity to be selected using simple probability. This sampling method is also called “random quota sampling.

The main advantage of stratified random sampling is that it captures key population characteristics in the sample. Similar to a weighted average, this method of sampling produces characteristics in the sample that are proportional to the overall population. Stratified random sampling works well for populations with a variety of attributes but is otherwise ineffective if subgroups cannot be formed.

Stratification gives a smaller error in estimation and greater precision than the simple random sampling method. The greater the differences between the strata, the greater the gain in precision.

1. ### Area Sampling

Area sampling is a method of sampling used when no complete frame of reference is available. The total area under investigation is divided into small sub-areas which are sampled at random or according to a restricted process (stratification of sampling). Each of the chosen sub-areas is then fully inspected and enumerated, and may form the basis for further sampling if desired.

Application of Area sampling

The basic idea of area sampling is both simple and powerful. It enjoys wide usage in situations where very high quality data are wanted but for which no list of universe items exists. For instance, many governmental agencies (e.g. Bureau of Labor Statistics) use area sampling.

However, the practical execution of a large scale area sample is highly complex. Typically an area sampling is conducted in multiple stages, with successively smaller area clusters being sub-sampled at each stage.

Example: A national sample of households is often constructed in a series of steps like this:

(i) Create geographic strata, each consisting of a group of counties in more or less close proximity. Fifty or more such strata, containing all of the roughly 3,000 US counties, are commonly used.

(ii) Within each geographic stratum, choose a probability sample of one or more counties (or groups of counties such as metropolitan areas).

(iii) Within each sample county (or group of counties), choose a probability sample of places (cities, towns, etc).

(iv) Within each sample place, select a probability sample of area segments (blocks in cities, area with identifiable boundaries in other places, etc)

(v) Finally, within sample segments choose a probability sample of households.

1. ### Cluster Sampling

Cluster sampling is a way to randomly select participants when they are geographically spread out. For example, if you wanted to choose 100 participants from the entire population of the U.S., it is likely impossible to get a complete list of everyone. Instead, the researcher randomly selects areas (i.e. cities or counties) and randomly selects from within those boundaries.

Cluster sampling usually analyzes a particular population in which the sample consists of more than a few elements, for example, city, family, university etc. The clusters are then selected by dividing the greater population into various smaller sections.

Cluster Sampling: Steps

Some steps and tips to use cluster sampling for market research, are:-

• Sample: Decide the target audience and also the size of the sample.
• Create and evaluate sampling frames: Create a sampling frame by using either an existing frame or creating a new one for the target audience. Evaluate frames on the basis of coverage and clustering and make adjustments accordingly. These groups will be varied considering the population which can be exclusive and comprehensive. Members of a sample are selected individually.
• Determine groups: Determine the number of groups by including the same average members in each group. Make sure each of these groups are distinct from one another.
• Select clusters: Choose clusters randomly for sampling.
• Geographic segmentation: Geographic segmentation is the most commonly used cluster sample.
• Sub-types: Cluster sampling is bifurcated into one-stage and multi-stage subtypes on the basis of the number of steps followed by researchers to form clusters.

Cluster Sampling Methods with Examples

There are two ways to classify cluster sampling. The first way is based on the number of stages followed to obtain the cluster sample and the second way is the representation of the groups in the entire cluster.

The first classification is the most used in cluster sampling. In most cases, sampling by clusters happens over multiple stages. A stage is considered to be the steps taken to get to a desired sample and cluster sampling is divided into single-stage, two-stage, and multiple stages.

(I) Single Stage Cluster Sampling: As the name suggests, sampling will be done just once. An example of Single Stage Cluster Sampling –An NGO wants to create a sample of girls across 5 neighboring towns to provide education. Using single-stage cluster sampling, the NGO can randomly select towns (clusters) to form a sample and extend help to the girls deprived of education in those towns.

(II) Two-Stage Cluster Sampling: A sample created using two-stages is always better than a sample created using a single stage because more filtered elements can be selected which can lead to improved results from the sample. In two-stage cluster sampling, instead of selecting all the elements of a cluster, only a handful of members are selected from each cluster by implementing systematic or simple random sampling. An example of Two-Stage Cluster Sampling –A business owner is inclined towards exploring the statistical performance of her plants which are spread across various parts of the U.S. Considering the number of plants, number of employees per plant and work done from each plant, single-stage sampling would be time and cost consuming. This is when she decides to conduct two-stage sampling. The owner creates samples of employees belonging to different plants to form clusters and then divides it into the size or operation status of the plant. A two-level cluster sampling was formed on which other clustering techniques like simple random sampling were applied to proceed with the calculations.

(III) Multiple Stage Cluster Sampling: For effective research to be conducted across multiple geographies, one needs to form complicated clusters that can be achieved only using multiple-stage cluster sampling technique. Steps of listing and sampling will be used in this sampling method. An example of Multiple Stage Cluster Sampling –Geographic cluster sampling is one of the most extensively implemented cluster sampling technique. If an organization intends to conduct a survey to analyze the performance of smartphones across Germany. They can divide the entire country’s population into cities (clusters) and further select cities with the highest population and also filter those using mobile devices.

There are multiple advantages of using cluster sampling, they are:-

(I) Consumes less time and cost: Sampling of geographically divided groups require less work, time and cost. It’s a highly economical method to observe clusters instead of randomly doing it throughout a particular region by allocating a limited number of resources to those selected clusters.

(II) Convenient access: Large samples can be chosen with this sampling technique and that’ll increase accessibility to various clusters.

(III) Least loss in accuracy of data: Since there can be large samples in each cluster, loss of accuracy in information per individual can be compensated.

(IV) Ease of implementation: Since cluster sampling facilitates information from various areas and groups, it can be easily implemented in practical situations in comparison to other probability sampling methods such as simple random sampling, systematic sampling, and stratified sampling or non-probability sampling methods such as convenience sampling.

In comparison to simple random sampling, cluster sampling can be effective in deciding the characteristics of a group such as population and it can also be implemented without having a sampling frame for all the elements for the entire population.

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