Introduction

We all quite often use sampling in our life, when we go to purchase food grain or for that matter any other such commodity from the market, we usually examine a handful from the lot to assess the quality of that product.

Sampling consists of taking a subset of a population for analysis to make an inference about the population from which the samples are taken.

Depending on the type of data being analysed and the purpose of the analysis, several methods can be used to collect samples.

Few Terms

Population: A population consists of all elements - individuals, items, or objects, whose characteristics are being studied.

Finite population: Any population whose elements exist at a particular time is a finite population.

Infinite population: A population is said to be infinite, or uncountable, if it is not possible to count the units contained in that population.

Sample: A portion of the population selected for study is referred to as a sample. A sample is a smaller (but representative) collection of units from a population used to determine truths about that population.

Census survey: The collection of information from the elements of a population is called a survey. A survey that includes every element of the target population is called a census. Thus, in census survey, desired information on each and every element in the population is recorded.

Sample survey: A sample survey can be defined as the technique of collecting information from a portion of the population.

The purpose of conducting a sample survey is to make decisions about the population concerned.

It is important that the results obtained from a sample survey closely match the results expected to be obtained by conducting a census; otherwise, decisions based on a sample survey will not be applicable to the referred population.

The quality of a sample statistic, i.e., accuracy, precision and representativeness, is largely affected by the way the elements in the samples are chosen for recording observations, i.e., the method of sampling.

Why sampling?

Sampling can provide reliable information at far less cost than a census

Data can be collected more quickly, so estimates can be published in a timely fashion.

The estimates based on sample surveys may be more accurate than those based on a census because investigators can be more careful when collecting data.

Methods of sampling

A. Probability sampling

Sampling process that utilises some form of random selection. In probability sampling, each unit is drawn with known probability or has a nonzero chance of being selected in the sample.

a. Random sampling

(i) Simple random sampling

Each element of the population has an equal probability of selection.

Applicable when population is small, homogeneous and readily available.

If all possible samples from the population are equally likely to be obtained, then we call it a simple random sample

A simple random sample of ‘n’ items is a sample which satisfies the following two conditions:

1. Every member of the population has the same chance of being included in the sample, and

2. The members of the sample are chosen independent of each other.

(ii) Systematic random sampling or quasi random sampling

It relies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list. Only first element from the population is selected at random and rest of the elements are repeatedly selected in a pre-determined fashion.

Procedure of systematic sampling

1. Prepare a list of elements by assigning numbers to all the units in population from 1 to N, where N = population size.

2. Decide about the required sample size (n).

3. Find out an integer k = N/n.

4. Randomly select an integer between 1 to k, that will be the first unit to be selected.

5. Record observations on the first unit and every kth unit thereafter till the required sample of size n is obtained.

(iii) Circular systematic sampling

• Selection of elements is made in a circular fashion. From the population having elements numbered from 1 to N, starting from the first unit, every kth unit of the population is included in a circular manner in a set of sample.
• Here, k is an integer obtained as k=N/n. In this technique, the total number of possible samples are N.
• A random start ‘r’ is chosen, and the units in the set of sample corresponding to ‘r’ are taken for recording observations.

(iv) Stratified random sampling

• The term 'stratum' literally means 'layer'. A stratified sample is made up of different 'layers' of the population.
• For example, animals of different age groups, people of different socio-economic status, etc.
• For example, animals of different age groups, people of different socio-economic status, etc.
• The whole population is divided into groups called “strata” which are more or less homogeneous within themselves.
• An individual group is called a “stratum” or “sub population” and the procedure of grouping is known as stratification.

The stratified sampling consists of:

1. Partitioning of the heterogeneous population into fairly homogeneous groups (strata),

2. Obtaining a random sample from each stratum independently, and

3. Collection of data on each randomly sampled unit from each group (stratum).

(v) Cluster sampling

• Sometimes the target population is scattered over a wide geographical area.
• Consequently, if a simple random sample is selected, it may be costly to contact each member of the sample.
• In such a case, we divide the population into different geographical clusters and as a first step select a random sample of certain clusters from all clusters. We then take a random sample of certain elements from each selected cluster.
• Sometimes the target population is scattered over a wide geographical area.
• Consequently, if a simple random sample is selected, it may be costly to contact each member of the sample.
• In such a case, we divide the population into different geographical clusters and as a first step select a random sample of certain clusters from all clusters. We then take a random sample of certain elements from each selected cluster.

(vi) Multistage sampling

• Sampling is carried out in stages using smaller and smaller sampling units at each stage is called a multistage sampling.
• Instead of using all the elements contained in the selected clusters, we randomly select elements from each cluster. Constructing the clusters is the first stage and deciding the elements within the cluster to be selected 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.

(vii) Multiphase sampling

Multiphase sampling is a method of sampling in which certain items of information are drawn from the whole units of a sample and certain other items are taken from the subsample, i.e., part of the information is collected from whole sample and part from subsample.

B. Non-probability sampling

• Non-probability sampling depends on our personal judgment. In this method of sampling, the probabilities cannot be assigned to the units accurately.
• Any sampling method is non-probability sampling where some elements of population have either no chance of selection or whose probability of selection cannot be accurately determined.

a. Convenience sampling

This is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, readily available and convenient.

b. Judgement or purposive sampling

The units are considered based on the judgement of the researcher. This sampling is made on the basis of knowledge of a population and the purpose of the study.

The main goal of purposive sampling is to focus on particular characteristics of a population that are of interest, which will best enable researcher to answer his or her research questions.

Example, we as an animal breeder are interested in selecting those animals for breeding which are at the top of their class for a particular characteristic such as body weight, milk yield, reproductive fitness, disease resistance, draft power etc. While, on the other hand, we would like to remove those animals that are poorer in their performance.

Merits and Demerits of Sampling

Merits

• saves time and money
• only practical method or choice available for studying an infinite population.
• enables us to collect a broad range of data

Demerits

• Not suitable if information is required on each and every individual
• Also not advocated in very small populations, as we may not get the representative samples from such a population.