Probability Sampling

Probability Sampling is a sampling technique in which sample from a larger population are chosen using a method based on the theory of probability. For a participant to be considered as a probability sample, he/she must be selected using a random selection.

The most important requirement of probability sampling is that everyone in your population has a known and an equal chance of getting selected. For example, if you have a population of 100 people every person would have odds of 1 in 100 for getting selected. Probability sampling gives you the best chance to create a sample that is truly representative of the population.

Probability sampling uses statistical theory to select randomly, a small group of people (sample) from an existing large population and then predict that all their responses together will match the overall population.

Probability Sampling Example

Let us take an example to understand this sampling technique. The population of the US alone is 330 million, it is practically impossible to send a survey to every individual to gather information but you can use probability sampling to get data which is as good even if it is collected from a smaller population.

For example, consider hypothetically an organization has 500,000 employees sitting at different geographic locations. The organization wishes to make certain amendment in its human resource policy, but before they roll out the change they wish to know if the employees will be happy with the change or not. However, it’s a tedious task to reach out to all 500,000 employees. This is where probability sampling comes handy. A sample from the larger population i.e from 500,000 employees can be chosen. This sample will represent the population. A survey now can be deployed to the sample.

From the responses received, management will now be able to know whether employees in that organization are happy or not about the amendment.

Steps involved in Probability Sampling

1. Choose your population of interest carefully: Carefully think and choose from the population, people you think whose opinions should be collected and then include them in the sample.
2. Determine a suitable sample frame: Your frame should include a sample from your population of interest and no one from outside in order to collect accurate data.
3. Select your sample and start your survey: It can sometimes be challenging to find the right sample and determine a suitable sample frame. Even if all factors are in your favor, there still might be unforeseen issues like cost factor, quality of respondents and quickness to respond. Getting a sample to respond to true probability survey might be difficult but not impossible.

But, in most cases, drawing a probability sample will save you time, money, and a lot of frustration. You probably can’t send surveys to everyone but you can always give everyone a chance to participate, this is what probability sample is all about.

When to use Probability Sampling

1. When the sampling bias has to be reduced: This sampling method is used when the bias has to be minimum. The selection of the sample largely determines the quality of the research’s inference. How researchers select their sample largely determines the quality of a researcher’s findings. Probability sampling leads to higher quality findings because it provides an unbiased representation of the population.
2. When the population is usually diverse: When your population size is large and diverse this sampling method is usually used extensively as probability sampling helps researchers create samples that fully represent the population. Say we want to find out how many people prefer medical tourism over getting treated in their own country, this sampling method will help pick samples from various socio-economic strata, background etc to represent the bigger population.
3. To create an accurate sample: Probability sampling help researchers create an accurate sample of their population. Researchers can use proven statistical methods to draw accurate sample size to obtained well-defined data.

Advantages

1. Its Cost-effective: This process is both cost and time effective and a larger sample can also be chosen based on numbers assigned to the samples and then choosing random numbers from the bigger sample. Work here is done.
2. It is simple and easy: Probability sampling is an easy way of sampling as it does not involve a complicated process. It is quick and saves time. The time saved can thus be used to analyze the data and draw conclusions.
3. It is non-technical: This method of sampling doesn’t require any technical knowledge because of the simplicity with which this can be done. This method doesn’t require complex knowledge and it is not at all lengthy.

Sampling Types 

Simple Sampling

Simple random sampling is defined as a sampling technique where every item in the population has an even chance and likelihood of being selected in the sample. Here the selection of items entirely depends on luck or probability, and therefore this sampling technique is also sometimes known as a method of chances.

Simple random sampling is a fundamental sampling method and can easily be a component of a more complex sampling method. The main attribute of this sampling method is that every sample has the same probability of being chosen.

Random Sampling

Simple random sampling methods

• They prepare a list of all the population members initially, and then each member is marked with a specific number ( for example, there are nth members, then they will be numbered from 1 to N).
• From this population, researchers choose random samples using two ways: random number tables and random number generator software. Researchers prefer a random number generator software, as no human interference is necessary to generate samples.

Advantages of simple random sampling

• It is a fair method of sampling, and if applied appropriately, it helps to reduce any bias involved compared to any other sampling method involved.
• Since it involves a large sample frame, it is usually easy to pick a smaller sample size from the existing larger population.
• The person conducting the research doesn’t need to have prior knowledge of the data he/ she is collecting. One can ask a question to gather the researcher need not be a subject expert.
• This sampling method is a fundamental method of collecting the data. You don’t need any technical knowledge. You only require essential listening and recording skills.
• Since the population size is vast in this type of sampling method, there is no restriction on the sample size that the researcher needs to create. From a larger population, you can get a small sample quite quickly.
• The data collected through this sampling method is well informed; more the samples better is the quality of the data.

Stratified Sampling

Stratified random sampling is a sampling method in which a population group is divided into one or many distinct units called strata, based on shared behaviors or characteristics.

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.

In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be collectively exhaustive and mutually exclusive: every element in the population must be assigned to one and only one stratum. Then simple random sampling is applied within each stratum. The objective is to improve the precision of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population.

The reasons to use stratified sampling rather than simple random sampling include:

• If measurements within strata have lower standard deviation, stratification gives smaller error in estimation.
• For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata.
• It is often desirable to have estimates of population parameters for groups within the population.

Cluster Sampling

In cluster sampling, researchers divide a population into smaller groups known as clusters.  They then randomly select among these clusters to form a sample.

Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed. Researchers usually use pre-existing units such as schools or cities as their clusters.

Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups (known as clusters) and a simple random sample of the groups is selected. The elements in each cluster are then sampled. If all elements in each sampled cluster are sampled, then this is referred to as a “one-stage” cluster sampling plan. If a simple random subsample of elements is selected within each of these groups, this is referred to as a “two-stage” cluster sampling plan. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. For a fixed sample size, the expected random error is smaller when most of the variation in the population is present internally within the groups, and not between the groups.

Multi Stage Sampling

In statistics, multistage sampling is the taking of samples in stages using smaller and smaller sampling units at each stage.

Multistage sampling can be a complex form of cluster sampling because it is a type of sampling which involves dividing the population into groups (or clusters). Then, one or more clusters are chosen at random and everyone within the chosen cluster is sampled.

Using all the sample elements in all the selected clusters may be prohibitively expensive or unnecessary. Under these circumstances, multistage cluster sampling becomes useful. Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use is the second stage. The technique is used frequently when a complete list of all members of the population does not exist and is inappropriate.

There are four multistage steps to conduct multistage sampling:

• Step one: Choose a sampling frame, considering the population of interest. The researcher allocates a number to every group and selects a small sample of relevant separate groups.
• Step two: Select a sampling frame of relevant separate sub-groups. Do this from related, different discrete groups selected in the previous stage.
• Step three: Repeat the second step if necessary.
• Step four: Using some variation of probability sampling, choose the members of the sample group from the sub-groups.

Advantages of multistage sampling

Here are the top 8 benefits obtained from multistage sampling:

• It allows researchers to apply cluster or random sampling after determining the groups.
• Researchers can apply multistage sampling to make clusters and sub-clusters until the researcher reaches the desired size or type of group.
• Researchers can divide the population into groups without restrictions. It allows flexibility to the researchers to choose the sample carefully.
• It is useful while collecting primary data from a geographically dispersed population.
• Cost-effective and time-effective because this method helps cut down the population into smaller groups.
• Finding the right survey sample becomes very convenient for researchers.
• The researcher mindfully chooses the audience. It decreases the issues faced during random sampling.
• It does not need a complete list of all the members of the target population, dramatically reducing sample preparation cost.