SAMPLING CONCEPTS AND METHODS ASSIGNMENT HELP

Importance, Scope and Advantages of Sampling

Sampling surveys occupy a place of importance particularly in destructive surveys where complete enumeration survey has no scope for its application whatsoever. A certain minimum facilities such as funds trained personnel, transport and communication facilities are needed for complete enumeration as well as sample surveys. But certainly, the extents to which the above mentioned facilities are required in case of sample survey are much smaller than required in case of complete sample surveys are much smaller than required in case of complete enumeration surveys.

Main advantages of sample surveys over complete enumeration surveys can be enumerated in brief, as follows:

• Saving of Time: Comparatively smaller number of unit is studied in sampling method and naturally it requires much lesser time than the census method and naturally it requires much lesser time than the census method. In certain types of surveys, time is the most important factor and the results of the study have to be declared quite early to be of any use at all. In all such surveys sampling is the only method which can be used.
• Reduced Cost: Survey of smaller number of cases not only requires lesser time but also requires lesser money, and the study can be financed with much lesser resources.
• Detailed Study: When the number of units is large, detailed study is impossible. The smaller number of cases in the sample permits more minute observation and detailed study. In business and industrial research sometimes a through and prolonged study has to be undertaken. This is possible only when the number of cases to be studied is small.
• Accuracy of Result: All the above advantages of sampling are not at the cost of accuracy. On the other hand, at times results drawn from sample, surveys are more reliable than the results from census method. If the sample has been properly selected, the results coverage obtained with in a very close range of accuracy.
• Administrative Convenience: Handling of smaller number of units is usually more lenient from administrative point of view. Supervision becomes difficult in case of large number of units.
• Impossibility of the Use of Census Method: In certain cases, the use of census method becomes impossible, it is because the universe is too cast and geographically scattered, so that every unit cannot be contacted. In case of enquiry highly trained personnel or specialized element limited in availability must be used to obtain the data. In such cases, a complete census is almost impracticable.

Sampling with and without replacement:

One or more sampling units selected from a population according to some specified procedure are said to constitute a sample. If the specified procedure of selection of the units permits the selected unit at each draw to go back into the population and allows it to get selected again it is called as SAMPLING WITH REPLACEMENT and the selected unit at each draw is not permitted go back to the population and is not allowed to get selected more than once, it is termed as SAMPLING WITHOUT REPLACEMENT in more cases, sampling without replacement is more efficient than sampling with replacement.

We have seen that while in some cases sample survey are the only means of collecting information, in many other cases they are much more desirable than a complete enumeration surveys not only on account of saving in time, money and efforts etc, but also on account of the fact that times, the results obtained from them are subject to smaller amount of error. Now the question arises how the sample should be selected, i.e., what should be the procedure of selecting the sample? Broadly speaking the sampling producers can be divided in 2 categories:

• Random sampling or probability sampling and
• Non-Random or Purposive of Subjective sampling, and the sample obtained as a result are termed as
  • Random sample or Probability sample and
  • Non-Random of Purposive or Subjective sample.

Simple Random Sampling:

Random sampling has been referred to as a procedure of selecting a sample where in each unit in the population has a predetermined probability of being selected in the sample. Its simplest from when the units are selected unit by unit, insuring equal probability of selection for every unit at each draw is termed ‘SIMPLE RANDOM SAMPLING (SRS). In S.R.S. an equal probability of selection (equal to the reciprocal of the number of available units) is assigned to each available unit at the first and each subsequent draw. If the number of units in the population is N, the probability of selecting any unit from among the remaining available units at the second draw in 1/N – 1 and so on. There are very many situations where there is no justification for given differential treatment to the different units in the population i.e., there exists no ground or reasons on the basis of which different treatment. All the units in the population, therefore, have to be treated alike, In a situation like this, the units to be included in the sample may be selected one by one with equal probability at each draw and the sample so drawn is termed SIMPLE RANDOM SAMPLE.

Advantages of Simple Random Sampling:

The following are the main advantages of simple random sampling.

• It is free from bias and therefore not affected by the choice of the researcher.
• It is generally more representative because each unit has equal chance of being selected.
• It is very simple. The researcher need not exercise his brain in deciding whether a particular unit can be representative or not.
• Assessment of sampling error can be made and it is possible to calculate the limit of error due to sampling.

Disadvantages of Simple Random Sampling:

SRS suffers from the following disadvantages:-

• It is very difficult to have completely catalogued universe and thus selection according to strictly random basis is frequently not possible.
• Cases studied may be too widely dispersed or even impossible to contact and thus adherence in the whole sample may not be possible.
• If units are of different sizes and the population consists of many heterogeneous units simple random sampling method is unsuitable.

Stratified Random Sampling:

Simple Random sample suffers from a drawback that there is always chance, howsoever small it may be, that it might not contain all types of the units and thus may not be true representative of the population. To overcome this problem and to ensure representation of all types of units in the sample, the following procedure is adopted. The population units are classified into a number of groups. These groups are termed ‘Strata’ and the division of the population into strata is termed ‘Stratification’. The above discussion shows that stratification involves a number of issues; the important ones being as mentioned below:

• Choice of stratification Variable: As has been discussed earlier, it should be a variable which is closely related with the main variable under study. Inappropriate choice of stratification variable may give rise to the results which are subject to larger amount of error.
• Allocation of sample size to strata: It is to specify as to how many units should be selected from each stratum so as to obtain a sample of given size n. Though certain order method is available, but generally, method of “Proportional allocation.
• Demarcation of strata: It refers to the specification of points which will separate different strata from each other. This issue is of great importance since the sampling error of the results, obtained depends upon the location of the points of demarcation. Many statisticians have worked on this problem and have suggested method to find out these points.
• Sampling within Strata: Since the selection units from each stratum are to be done independently, it is possible to adopt different sampling procedure in different strata.

Cluster Sampling:

All developments in sampling theory have taken place with the consideration of two aspects sampling error and the cost of the survey. Different sampling techniques have been evolved to deal with different kinds of populations either to minimize the sampling error for a given (fixed) cost of the survey or to minimize the cost of the survey or a given (fixed) value of sampling error.

Systematic Sampling:

Systematic sampling is a procedure of selecting a sampling which though ensures each unit in the population equal probability of inclusion in the sample as is the case in S.R.S. are yet the units are selected systematically unlike the S.R.S. This process of selecting the sample may be easily described. Suppose the population consists of N units and a sample of size n, to be selected. An integer k – N/n is worked out of N and n, k may not be a whole number but, for the sake of simplicity, we will consider the case of its being a whole number.

Multistage Sampling:

Multi-stage sampling is a kind of compromise between the simple Random sampling on one hand and the cluster sampling on the other. Two hand stage sampling can be viewed as a special case of the cluster sampling in which only a few rather than all of the units in the selected clusters are surveyed. Compared with simple random sampling, multistage sampling is lesser expensive and operationally more convenient but from the point of view of error likely to be committed in the estimation of population values, generally, it is lesser efficient. As compared to cluster sampling it is more expensive and operationally lesser convenient but more efficient, from the point of error likely to be committed in the estimation of population values in general. Multi-stage sampling is adopted is most of the large-scale surveys.