**Method of Random Sampling**

There are two methods of random sampling-unrestricted random sampling and restricted random sampling.

Methods of Restricted Random Sampling: There are three methods of restricted random sampling.

(i) Stratified Sampling: This is a method for getting a more efficient sample. In this method, the total population is divided into different groups or classes, which are called Strata. A sample is drawn from each stratum. The advantage is that an efficient sample is obtained by this method. However, note that there must be great homogeneity within each stratum. Also note that there should be clear-cut differences between the strata.

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The method of stratified sampling has many advantages. Firstly, it is more representative of the entire population. That is because we are dividing the population into homogeneous groups so that none of the groups may be missed. Secondly, calculation accuracy is maximum, if the strata are homogeneous. Thirdly, different strata can be selected from one geographical area only; that would mean savings in terms of cost and time.

But this method is not sans limitations either. Firstly, if the strata were not homogeneous, the results obtained from the analysis of the sample would not be reliable. Secondly, it may not be possible to select items from each stratum on a random basis because of absence of skilled researchers.

(ii) Systematic Sampling: In the process of systematic sampling, one unit is selected at random from the population. Additional units are selected at evenly spaced intervals until the sample has been formed. For this purpose, a complete list of population should be made available to the researcher.

This list may be prepared in an order-alphabetical, geographical, numerical, or some other. All the items are serially numbered. The first item is selected at random by the lottery method. Then, subsequent items are selected by taking every Kth item from the list where K is K = n/N.

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Here, K is called Sampling Ratio, N is the size of the universe and n is size of the sample.

There are many advantages of systematic sampling. Firstly, it is a sample and convenient method. Secondly, time consumed by the researcher in sampling procedures is less. Thirdly, results obtained after analysing the samples (obtained by this method) are satisfactory if care is taken to ensure that there are no periodic features associated with the sampling interval).

Fourthly, if populations under study are sufficiently large, then this method of sampling can give results similar to those obtained through a stratified sampling procedure. However, the prominent limitation of this method in that it is less representative of the population if our population has periodicity hidden in it, or if the sample is taken by following a periodicity trend.

(Hi) Multistage Sampling: In this method, random selection is made of primary, immediate and final units from a given population or stratum. There are several stages in this sampling method.

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To begin with, the first-stage units are sampled by the random sampling method. Then, a sample of second-stage units is selected from the first stage units. The method of selection of second-stage units may be similar to or different from the method used for first stage units. We can add more stages, if needed.

There are many advantages of multistage sampling. Firstly, it is a flexible method; flexibility is lacking in other methods of sampling. Secondly, this method enables the researcher to use existing divisions and sub-divisions of the population at different stages.

Thirdly, fieldwork can be concentrated and large areas can be covered. Fourthly, sub-division of only those first-stage samples is done for selecting the second-stage that are included in the sample. Thus, we can conveniently divide the population into reasonably small sampling units.

Sometimes, a limitation is also associated with this method. Multistage sampling is less accurate because of the involvement of a number of stages. Some researchers aver with confidence that a single-stage process might be more accurate than a multistage process.

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Methods of Unrestricted Random Sampling: In this method, each and every unit of the population has an equal opportunity of getting selected in the sample. Personal bias of the market researcher does not enter the selection process. That is because chance only determines which items would be included in the sample.

Suppose that we have a universe with a total of ‘N’ elements. We want a simple random sample of ‘n’ elements. Then, the following statements ‘R’ any of the following has to be true:

(a) All the items of the sample are selected independently of one another.

(b) All the N items of the population have the same chance of being included in the sample.

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(c) After each selection procedure, all the remaining units of the population have the same chance of being selected for the sample.

If we make a sample in such a way that each unit selected from the population is returned before selecting the next unit, then each item has a probability of 1/N for its selection. If selection is done in such a manner that each unit, which is selected, is not returned to the population before making the next draw, then the probability of selection at first draw is 1/N, at the second draw, 1/N-l and at the third draw, l/(N-2) and so on. All possible samples of a given size n are equally likely to be selected.

**In unrestricted random sampling, we shall consider the following methods:**

(i) Lottery Method: In this method of unrestricted sampling, all the items of the universe are numbered, named on separate slips of paper. These slips are folded (to ensure privacy and exclusion of sampling bias). These are put in a drum. The drum is rotated and then, the required number of slips is taken out of it at random. This method is popular in lottery draws, but paper slips should be of same size shape and colours.

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(ii) Tables of Random Numbers: Random numbers are obtained by some mechanism which, when repeated a large number of times, ensures roughly equal frequencies for various combinations of numbers like 00, 01, 99, 999, etc.

Several tables of random numbers are available in markets. Tippett’s Random Number Tables have 41,600 random digits. Fishers and Yates have developed a table of random numbers with 15,000 random digits. Rand Corporation has also issued a table of random members. These numbers are selected by the researcher at random. Tippett’a numbers have been subjected to many tests and investigations. Their randomness has been proved.

There are three advantages of the method of sample selection by random numbers. Firstly, there is no personal bias of the researcher (or selector of numbers) because of the procedure of random selection. Secondly, the random sample represents the universe in a better manner, if we compare this method with judgment sampling. Thirdly, the researcher can check the accuracy of his data because sampling errors follows the principle of chance.

This method has some limitations too. Firstly, we have to keep complete information about the entire universe. Secondly, the size of the sample is very large as compared to that in stratified sampling. Thirdly, cost of collecting data is high because the population is normally living in a large area. Fourthly, time for collecting data is very long.

Fifthly, random sampling by this method can produce many non-random results.