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SAMPLING Sampling may be defined as the selection of some part of an aggregate or totality, on the basis of which a judgment or inference about the aggregate or totality is made. In other words it is process of obtaining information about an entire population by examining only a part of it.

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Need for Sampling Sampling is used in practice for a variety of reasons such as:- 1. Reduces the time and cost 2. saves labor 3. Quality of a study is often better with sampling than with a complete 4.Coverage 5. Provides much better results 6. Only procedure possible, if the population is infinite.

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There are many types of sampling, most sampling types can be categorized as: a) Probability sampling and b) Non-probability sampling

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**a) Probability sampling:-**

is one in which every unit in the population has a chance ( greater than Zero) of being selected in the sample, and this probability can be accurately determined. The combinations of these traits make it possible to produce unbiased estimates of population totals, by weighing sampled units according to their probability of selection.

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**Probability Sampling is of the following types:**

1.Simple Random sampling 2.Stratified Random sampling 3.Systematic Random sampling 4. Cluster/ Area sampling 5.Multi stage sampling 6.Random sampling with probability proportional to size (PPS) 7.Double sampling and Multiphase sampling 8.Replicated or interpenetrating sampling.

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**Non-Probability sampling:**

Non probability sampling plans are those that provide no basis for estimating how closely the sample characteristics approximate the parameters of the population from which the sample was obtained. In fact the investigator is generally unable to identify the parent population.

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**Non-Probability sampling may be classified into:-**

1.Convenience or Accidental sampling 2.Purposive or judgment sampling 3.Quota sampling 4.Snow – ball sampling

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**Simple Random sampling: -**

A simple random sample is one in which each element of the population has an equal and independent chance of being included in the sample i.e. a sample selected by randomization method is known as simple random sample and this technique is simple random-sampling. Randomization is a method and is done by using a number of techniques as:- a)Tossing a coin b)Throwing a disc c)Lottery method d)Blind folded method e)by using random table of Tipett’s Table

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The Fish Bowl Draw: The simplest and most familiar type of sample selection consists of putting numbers on slips of paper or marbles and depositing them in a large container. The numbers identify and stand for specific elements in the populations and presumably the entire population of elements has been numbered and is represented in the bowl. After mixing the thoroughly, the investigator selects one number at a time, blindfolded until the desired sample size is obtained. This is called a random sample.

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Systematic Sampling: Systematic sampling relies on arranging the target population according to some ordering scheme and then selecting elements at regular start and then proceeds with the selection of every Kth element from the onwards. In this case K= (population size). It is important that the starting point is not automatically the first in the list, but is instead randomly chosen from within the first to the Kth element in the list.

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Example A simple eg:- would be to select every 10th name from the telephone directory (an every 10th sample, also referred to as sampling with a skip of 10).

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Stratified Sampling It is an improvement over the earlier method, when employing this techniques, the researcher divides his population in strata on the basis of some characteristics and from each of these smaller homogenous groups (strata) drawn at random a pre-determined number of Units. Researcher should choose that characteristic or criterion which seems to be more relevant in his research work.

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- a) Dispropationate Stratified Sampling Means that the size of the sample in each Unit is not proportionate to the size of the unit but depends upon considerations involving personal judgment and convenience. b) Proportionate sampling: - Refers to the selection from each sampling unit of a sample that is proportionate to the size of the unit. c) Optimum allocation stratified sampling:- Is representative as well as comprehensive than other stratified samples. It refers to selecting units from each stratum should be in proportion to the corresponding stratum the population. Thus sample obtained is known as optimum allocation stratified sample.

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**These three are clear from the following table as given below**

Levels Disproportionate stratified sampling Proportionate stratified sampling Optimum allocation stratified sampling Population Sample HG 35 25 250 AG 43 50 400 40 L.G 22 350 100 1000

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Cluster sampling: To select the intact group as a whole is known as a cluster sampling. In cluster sampling the sample units contain groups of elements (clusters) instead of individual members or items in the population.eg:- Rather than listing all elementary school children in a given city and random selecting 15 per cent these students for the sample, a researcher lists all of the elementary schools in the city, selects at random 15 percent of these clusters of units, and uses all of the children in the selected schools as the sample.

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**Multi-stage sampling: -**

In this method, sampling is carried out in two or more stages. The population is regarded as being composed of a number of first stage sampling units. Each of them is made up of number of second stage units and so forth. That is, at each stage, a sampling unit is a cluster of the sampling units of the subsequent stage, first, a sample of the first stage sampling is drawn, and then from each of the selected first stage sampling unit, a sample of the second stage sampling units is drawn. The procedure continues down to the final Sampling units or population elements. Appropriate random sampling method is adopted at each stage.

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USAGE Multi-stage sampling is appropriate where the population is scattered over a wider geographical area an no frame or list is available for sampling. It is also useful when a survey has to be made within a limited time and cost budget. Sampling with probability proportionate size (PPS)

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**Sampling with probability proportionate size (PPS):**

This procedure of selecting clusters with probability proportional to size (PPS) is widely used, if one primary cluster has twice, as large a population as another, It is given twice the chance of being selected. If the same number of persons is then selected from each of the selected clusters, the overall probability of any person will be the same. Thus PPS is a better method for securing a representative sample of population elements in multi-stage cluster sampling.

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Illustration: - Suppose the area of a survey in a state consisting of 20 districts. Out of them 4 districts are to be selected with PPS, the measures of size being population. a)List the district in some order and record the population of each Together with cumulative population figures (see Table 2). b) Divide the cumulative total by 2:310 divide by 2 =155 c) Divide the list into two zones 1-155, d) Make a systematic random selection of two districts in each zone. e) Divide the first zone total by 2:155 divided by 2 =77.Draw a random Number between 1 and 77, say, 66. The District 8 is the first sample. f) Add the interval 77 to the random number 66 to give 143, to locate 13 as the second. g) Add the interval 77 to 143 to give 220, to locate district 17 as the Third sample, and h) Add the interval 77 to 220 to give 297, to locate 20 as the fourth sample.

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**Double (or two phases) sampling :**

Refers to the sub-section of the final sample from a pre-selected larger sample, that provides information for providing the final selection. When this procedure is extended to more than two phases of selection it is then called Multi-Phase sampling. This is also known as sequential sampling as sub sampling is done from a main sample in phases. Additional information from sub samples of the full sample may be collected at the same time or later.

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**Replicated or Interpenetrating Sampling**

Multi-Phase Sampling In multi-phase sampling the different phase of observation s relate to sample units of the same type. Replicated or Interpenetrating Sampling Involves selection of a certain number of sub-samples rather than one full sample from population. All the sub samples should be drawn using the same sampling techniques and each is a self-contained and adequate sample of the population.

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Example: In order to study the views of post graduate students of a University on semester system a random sample of 300 students (out of a total populations of 3000 students distributed over different disciplines like , Economics, Sociology, Statistics etc.) Is to be drawn adopting discipline based stratified sampling. Instead of selecting one full sample of 300 students, two sub sample of 150 each or five sub-samples of 60 each may be selected. Whatever may be the number and size of sub-sample, each sub-sample has to be an independent sample with the same sampling method and must be a sample covering the complete population. Each sub sample may be allocated one individual investigator or a team of investigators.

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**Non- probability sampling methods :**

1.Convenience or accidental sampling: It means selecting sample units in a ‘1 hit and miss fashion’. Example: interviewing people whom we happen to meet. This sampling also means selecting whatever sampling units are conveniently available. Example A teacher may select students in his class. This method is also known as accidental sampling because the respondents whom the researcher meets accidentally are included in the sample.

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**Purposive or Judgment Sampling:**

This method means deliberate selection of sample units that conform to some pre-determined criteria. This is also known as judgment sampling. This involves selection of cases which we judge as the most appropriate ones for the given study. It is based on the judgment of the researcher or some expert. It does not aim at searching a cross section of a population.

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Quota Sampling: This is a form of convenient sampling involving selection of quota groups of accessible sampling units by traits such as Sex, Social class etc. In specific proportions, each investigator may be given an assignment of quota groups specified by the pre-determined traits in specific proportions. He can then select accessible persons belonging to those groups in the area assigned to him. Quota sampling is therefore, a method of stratified sampling in which the selection within strata is non-random. Quota sampling is used in studies like marketing survey, opinion polls, and readership survey which do not aim at precision but to get quickly some crude results.

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Snow ball sampling: Is a technique of building up a list or a sample of a special population by using an initial set of its members as informants. For example a researcher wants to study the problem faced by Indians in another country, Say, he may identify an initial group of Indians through some source like Indian Embassy, Then he can ask each one of them to supply names of other Indians known to them and continue this procedure until he gets an exhaustive list from which he can draw a sample or make a census survey. This sampling technique may also be used in socio-metric studies. For example, the members of a social group may be asked to name the persons with whom they have social contacts, each one of the persons so named may also be asked to do so, and so on. The researcher may thus get a constellation of associates and analyze it.

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References: 01.Ram Ahuja Research Methods Rawat Publication, New Delhi 2007, P 02.Krishna Swami (OR) Methodology of research in Social Sciences, Himalaya Publishing House, Bombay. P , 1933 03.Black James A and Champion, Dean J ,John Wiley & Sons Inc, New York p 04.Yogesh Kumar Singh, Fundamentals of Research Methodology and Statistics, New Age International Publications, New Delhi, 2006, P71-92 05.Http://en.wikipedia.org/wiki/sampling (Statistics) 06.Kothari (CR) Research Methodology methods and techniques, 2nd edition, Wishwa Prakashan, New Delhi 2002, P

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