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For College Students

Sampling Methods in Statistics

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Population: This refers to the entire data.

Sample: This refers to the part of the population selected by a defined procedure to be representative of the data.

 

 

Sample

Population

Constant

Statistic

Parameter

Size

n

N

Mean

x̄

μ

Standard Deviation

s

σ

Proportions

Lower case. E.g.,  p and q.

Upper case. E.g., P and Q.

 

Types of Sampling

  • Random sampling: In this kind of sampling, each element of the population has the same probability of getting selected in the sample.
    • Simple random sampling with replacement: In simple random sampling with replacement, for the creation of a sample size n, you select an element from the population and then return it to the population. This procedure is repeated n times. Thus, each element of the population can be selected more than once in a sample. This is used when the population size is small.
    • Simple random sampling without replacement: In simple random sampling without replacement, for the creation of a sample size n, you select an element from the population and don’t return it to the population. The selection of elements from the population is repeated n times. This is used when the population size is large.
    • Stratified random sampling: In stratified random sampling, the population is divided into strata on the basis of common characteristics. The elements are then selected from these strata.
    • Cluster sampling: In cluster sampling, the population is divided into clusters, and then, a simple random sample of these clusters is selected.
    • Systematic sampling: In systematic sampling, a starting point is selected in the population, and then, the elements are selected at regular, fixed intervals.

 

  • Non-random sampling: In this kind of sampling, each element of the population does not have the same probability of getting selected in the sample.
    • Convenience sampling: In convenience sampling, the researcher selects the elements from the population on the basis of the convenient accessibility of these elements.
    • Judgemental sampling: In judgemental sampling, the researcher selects the elements on the basis of his judgement and bias.
    • Quota sampling: The population is divided into groups or quotas, on the basis of which you select the sample. Quota sampling is, to a certain extent, similar to random sampling; the sampling procedure is more or less the same in both the cases, except the quota is fixed in quota sampling. That is,  you don't consider the entire population, just a section of it to create a quota.
    • Snowball sampling: In the case of snowball sampling, a small sample is first selected, say a sample of five people. Then, each of the five members can suggest five names, and those five can suggest five more each. This creates a snowball effect.

 

What is the difference between stratified random sampling and cluster sampling?

In stratified random sampling, the whole population is divided into strata based on common characteristics, and then, elements are selected from each stratum. In cluster sampling, on the other hand, the whole population is divided into clusters, and then, some of the clusters are chosen randomly to create a sample.