Sampling Theory

A population is a collection of all the data points being studied.  A sample is a part of a population. 

 

For example, if we are studying the annual incomes of all the people in India, then the population under study would consist of data points representing the incomes of each and every person in India.  The following would then be possible samples:-

a.                  The annual incomes of all people in Mumbai.

b.                  The annual incomes of all people in India over 40 years of age.

c.                  The annual incomes of the first hundred people in the telephone directory.

 

Samples, being smaller in size than their populations, are easier to study.  Hence, if we want to draw some conclusions about a population, we can do so by studying a suitable sample of the population.  Sampling is advantageous since the population may be too large, a study of the sample may be cheaper than a study of the population, it provides quicker information, it involves lesser work, chances of errors whilst processing data would be less, testing the entire population may not be possible.

 

Types of sampling

 

 

Simple Random Sampling – In this, each possible sample has an equal chance of being selected.  Further, each item in the entire population also has an equal chance of being selected. 

 

Systematic Sampling – Here, each element has an equal chance of being selected, but each sample does not have the same chance of being selected.  Here, the first element of the population is randomly selected to begin the sampling.  But thereafter, the elements are selected according to a systematic plan. 

 

Stratified Sampling – This is generally used when the population is heterogenous.  In this case, the population is first subdivided into several parts or groups called strata according to some relevant characteristics so that each stratum is more or less homogenous.  Each stratum is called a sub-population.  Then a small sample is selected from each stratum at random.  All the sub-samples combined together form the stratified sample.  This represents the population properly.  The process of obtaining and examining a stratified sample to estimate the characteristic of the population is known as stratified sampling.

 

Cluster Sampling – Here the population is divided into clusters or groups and then random sampling is done for each cluster.  Cluster sampling differs from stratified sampling.  In case of stratified sampling, the elements of each stratum are homogenous.  As opposed to this, in cluster sampling the elements of each cluster are not homogenous.  Each cluster is a representative of the population.

 

Judgemental Sampling – Here, the sample is selected according to the judgement of the investigators or experts.  Hence, there is a certain degree of subjectivity in the selection. 

 

Convenience Sampling – Here, the investigator or researcher selects certain elements as samples based on its convenience to him.  An inherent assumption that all groups would have homogenous patters makes one opt for this type of sampling.  If this assumption of homogeneity cannot be made or is made erroneously, then this type of sampling would not give a true representation of the population. 

 

To bring out the different types of sampling, we shall take an example :-

 

Example

 

A retailer of electronic goods wants to study his customer purchases in the city of Mumbai.  For this purpose therefore, his population is all his customers in Mumbai.  Their names and addresses are on the carbon copies of the invoices in her invoice register. 

 

To do a random sampling of her customers, he can put all the carbon copies in a box and draw out a certain number of copies after thoroughly mixing them all up.  The customers so picked would form a random sample.

 

He would randomly select one invoice (or customer), say invoice no. 6, thereafter he would select subsequent invoices according to a systematic plan, say every fifth invoice after invoice no. 6 so that the selected invoices are 6,11,16,21, etc.  These invoices would form a systematic sample.

 

He can analyze the invoice copies according to items purchased, viz. TVs, stereos, VCRs, etc.  Each product's customers would form a strata.  For each stratum, random sampling could be done.  All these sub-samples would form a stratified sample.

 

He can divide the city of Mumbai into four zones, Zone I, II, III and IV.  From the addresses of the customers, he would classify the customers ito each of the four zones.  The he would select every item within randomly selected clusters.  This would form his cluster sample.

 

He can derive a judgemental sample by selecting customers only from Zone III, which he feels, in his opinion would best represent the population.

 

He can also undertake convenience sampling, by picking out those customers which are most convenient for him to select out of the total invoices in his records.

 

Merits of sampling

 

v      Samples, being smaller in size than the population, are easier to study.

v      Sampling is more economical than a comprehensive census in terms of costs, time, effort and resources.

v      Decision making is expedited since the desired observations and results can be achieved more quickly.

v      A complete examination and evaluation can lead to higher number of errors due to fatigue and biases.