## Statistical Sampling Techniques

Sampling is a statistical procedure used for the selection of a subset, often called a sample from a larger group called population, mostly for the purpose of estimating characteristics or features of the entire population.

Everyone at one point or the other have done sampling whether or not they were cognizant of it. It could only be that it was not done professionally. A housewife that cooks rice practices sampling when she wants to check if here meal is done. There is no possible way that she can check every single grain in the pot to see if it’s done, so she simply takes a sample of grain to ascertain if the entire pot of rice is done. Sampling is beneficial in a lot of ways, just like the illustration above, sampling techniques are applied in situations where it is not feasible to examine the entire population. Even in some cases where it is feasible, it could be overtly expensive or time-consuming to evaluate each unit in the population.

Assume that you want to get relevant information about a product, phone says, and you need to interview the production managers of those products (phone in this case). While it may be theoretically feasible to know the number of such production managers, it will be difficult to get across to all of them, let alone holding an interview with them. So, in such situations, it’s best to apply some sampling techniques.

However, care must be taken in the selection of a sample, to ensure that it’s a representative of the population and is free from all forms of bias, systematic and otherwise. For instance, a sample that is comprised of only northern residents will not adequately reflect the opinion of the entire residents of a country. This is a major reason for using randomization to obtain unbiased samples.

Sampling can come in many different forms and designs depending on the situation and the purpose of sampling. Popular designs in sampling include but are not limited to Simple Random Sampling, Stratified Random Sampling, and Multilayered random sampling.

### Simple Random Sample

A simple random sample refers to the number of specific units chosen from an entire population for research purposes. The process that gives the specific value is referred to as Simple Random Sampling. It is a method of selecting a sample, i.e., a specific number of units from the entire units in the population in such a manner that every unit of the population has an equal chance of being selected. This approach is best applied when the population is of homogenous characteristics or features.

This process can be carried out in a number of ways;

a. The sample units are chosen without replacement. This means that once a unit is selected, it cannot be added back to the population for subsequent selections. This approach is referred to as Simple Random Sampling without replacement.

b. The selection of the sample units can be made with replacement. This means that a chosen unit can be put back in the population, giving it a chance to be selected again. This approach is referred to as simple Random Sampling with replacement.

Guideto Simple Random Sampling

There are six major steps in creating a simple random sample; they include

1. Defining the Population

2. Choice of Sample Size

3. Population Listing

4. Assign Numbers to each population point or unit

5. Generate random numbers

6. Sample selection

Defining the Population

The first and very important step is to determine the population size. In the illustration above about the production managers of different brands of phones, if we gather that there are 500 brands of phones globally, it would be that our population size is 500. The population size is often denoted by the uppercase letter N

Choice of Sample Size

This has to with the determination of the sample size appropriate for the study. There are standard measures of sample size estimation. But that is not the only way. Sample sizes can also be chosen based on the availability of funds, time left to the completion of the study. These other factors can either higher or lower than figures obtained from the standard procedures. Let’s assume that the sample size for the study above is 100. We denote this by the lowercase letter n.

Population Listing

This step is not particularly statistical, rather managerial. Now that the appropriate sample size has been chosen, the researcher needs to make sure they can actually access the units in their population of the study. In our illustration, you need to make sure that all product managers can be contacted and have an interview scheduled.

Assign numbers to each population points or units

This step involves the assignment of numbers serially from 1 to 500 to each production manager, like an identification tag. (In our example, the series of numbers would be from 1 to 500, where N is the population size).

Generation of random numbers

In this step, we make a list of random numbers that will be used to select a sample of 100 managers from a total of 500 managers. With the advent of computers and software, random numbers can be easily generated using computers as opposed to the analog method of using random number tables.

Sample Selection

From the list of random numbers generated, you can select your sample and carry it with the rest of the research.

A major advantage of Simple Random Sampling is the elimination of potential human bias via the use of probabilistic methods.

#### Stratified Random Sampling

This sampling technique is applicable when it is known in advance that there are certain factors the split the population into groups or sub-populations (these groups are called strata) with common factors, and it is expected that these factors would impact the measurements obtained from the various groups. Then it is only wise that this factor is put into consideration in order to get a sample that adequately represents the population. This process is achieved by taking a proportionally equivalent sample from each sub-population, otherwise called strata. This approach is particularly necessary when the population under study is heterogeneous, but have some homogenous subpopulations that can be isolated. A good example would be to put different tribes of a multi-lingual nation into strata or sub-groups based on the language spoken.

##### Multilayered Random Sampling

This sampling technique mimics both simple random sampling and stratified random sampling. The design of the study is such that a chain of simple random samples is taken in layers. This approach is mostly used for on-site kind of evaluation. A large area, such asa school, might be divided into smaller regions by faculties, and a random sample of these regions (faculties) is chosen. In the second layer, a random sample of yet a smaller area is chosen. This could be departments under the selected faculties. Then in the third layer, a random sample of yet a smaller area is selected, maybe the units in the departments. If at this layer, a sufficiently small area for the research purpose has been obtained, the sampling process may be terminated. Otherwise, smaller units from the third layer may be sampled. This approach is designed to get intodeep areas of the population that might otherwise be omitted.