Previous Article – Statistics – Collection of Data
Census and Sampling Techniques of Collection of Data
There are two important techniques of Data collection, (i) Census inquiry implies complete enumeration of each unit of the universe, (ii) In a sample survey, only a small part of the group, is considered, which is taken as representative. For example, the population census in India implies the counting of each and every human being within the country.
In practice sometimes it is not possible to examine every item in the population. Also many a time it is possible to obtain sufficiently accurate results by studying only a part of the “population”. For example, if the marks obtained in statistics by 10 students in an examination are selected at random, say out of 100, then the average marks obtained by 10 students will be reasonably representative of the average marks obtained by all the 100 students. In such a case, the populations will be the marks of the entire group of 100 students and that of 10 students will be a sample.
Objects of Sampling
1. To get as much information as possible of the whole universe by examining only a part of it.
2. To determine the reliability of the estimates. This can be done by drawing successive samples from some parent universe and comparing the results obtained from different samples.
Advantages of Census Method
1. As the entire ‘population’ is studied, the result obtained is most correct.
2. In a census, information is available for each individual item of the population which is not possible in the case of a sample. Thus no information is sacrificed under the census method.
3. If data are to be secured only from a small fraction of the aggregate, their completeness and accuracy can be ensured only by the census method, since greater attention thereby is given to each item.
4. The census mass of data being taken into consideration all the characteristics of the ‘population’ is maintained in the original.
Disadvantages of Census Method
1. The cost of conducting an inquiry by the census method is very high as the whole universe is to be investigated.
2. The census method is not practicable in very big inquiries due to the inconvenience of individual enumeration.
3. In the cases of very big inquiries, the census method can be resorted to by the government agencies only. The application of this method is limited to those who are having adequate financial resources and other facilities at their disposal.
4. As all the items in the universe are to be enumerated, there is a need for training of staff and investigators. Sometimes it becomes very difficult to maintain uniformity of standards when many investigators are involved. Individual preferences and prejudices are there and it becomes very difficult to avoid bias in such type of inquiries.
Advantages of Sampling Method
1. Sample method is less costly since the sample is a small fraction of the total population.
2. Data can be collected and summarized more quickly. This is a vital consideration when the information is urgently needed.
3. A sample produces more accurate results than are ordinarily practicable on a complete enumeration.
4. Personnel of high quality can be employed and given intensive training as the number of much personnel would not be very large.
5. A sample method is not restricted to the Government agencies. Even private agencies can use this method as the financial burden is not heavy. It is much more economical than the census method.
Disadvantages of Sampling Method
1. In a census, information is available for each individual item of the population which is not possible in the case of a sample. Some information has to be sacrificed.
2. If data are to be secured only from a small fraction of the aggregate, their completeness and accuracy can be ensured only through the census method, since greater attention thereby is given to each item.
3. In using the technique of sampling, the investigator may not choose a representative sample. The aim of sampling is that it should afford a sufficiently accurate picture of a large group without the need for a complete enumeration of all the units of the group. If the sample chosen is not representative of the group, the very object of sampling is defeated.
4. The sampling technique is based upon the fundamental assumption that the population to be sampled is homogenous. It is not so, the sampling method should not be adopted unless the population is first divided into groups or “strata” before the selection of the sample is made.
Principle of sampling
There are two important principles on which the theory of sampling is based ;
1. Principle of Statistical Regularity, and
2. Principle of ‘Intertia of Large Numbers’
1. Principle of Statistical Regularity
This principle points out that if a sample is taken at random from a population. It is likely to possess almost the same characteristics as that of the population. By random selection, we mean a selection where each and every item of the population has an equal chance of being selected in the sample. In other words, the selection must not be made by the deliberate exercise of one’s discretion. A sample selected in this manner would be representative of the population. For example, if one intends to make a study of the average weight of the students of Delhi University, it is not necessary to take the weight of each and every student. A few students may be selected at random from every college, their weights taken and the average weight of the University students, in general, may be inferred.
2. Principle of Intertia of Large Numbers
This principle is a corollary of the principle of statistical regularity. This principle is that other things being equal, larger the size of the sample, more accurate the results are likely to be. This is because large numbers are more stable as compared to small ones. For example, if a coin is tossed 10 time we should expect an equal number of heads and tails, i.e., 5 each. But since the experiment is tried a small number of items it is likely that we may not get exactly 5 heads and 5 tails. The result may be a combination of 9 heads and 1 tail or 8 heads and 2 tails or 7 heads and 3 tails etc. If the same experiment is carried out 1,000 times the chance of getting 500 heads and 500 tails would be very higher. The basic reason for such likelihood is that the experiment has been carried out a sufficiently large number of time and possibility of variations in one direction compensates for others.
Method of Sampling
The various methods available for sampling are :
(i) Conscious or Deliberate or Purposive Sampling.
(ii) Random Sampling or Chance Selection.
(iii) Stratified Sampling.
(iv) Systematic Sampling.
(v) Multi-stage Sampling.
(i) Purposive Sampling
Purposive sampling is representative sampling by analyzing carefully the universe inquiry and selecting only those which seem to be most representatives of the characteristics of the universe. If economic conditions of people living in a state are to be studied according to this method, then a few villages and towns may be purposively selected so that intensive study on the principle that they shall be representative of the entire state.
Thus the purposive sampling is a purposive selection by the investigator that depends on the nature and purpose of the inquiry. This method is very much exposed to the dangers of personal prejudices. Also, there is a possibility of certain wrong cases being included in the data under collection, consciously or unconsciously.
However, it may be noted that this method gives a very representative sample data provided neither bias nor prejudices influence the process of data selection.
(ii) Random Sampling
In order to avoid the danger of personal bias and prejudices, a random sample is adopted. Under this method, every item in the universe is given an equal chance of being included in the sample. A random sample is the simplest type of sample. For obtaining such a sample, a certain number of units are selected at random from the universe. But this sampling technique is based upon the fundamental assumption
that the population to be swapped is homogenous. If it is not so, then the stratified sampling is adopted.
(iii) Stratified Sampling
Under this method, the population is first sub-divided into groups or “strata” before the selection of the samples is made. This is done to achieve homogeneity within each group or “stratum”. A stratified sample is nothing but a set of random samples of a number of subpopulations, each representing a single group. The major advantage of such a stratification is that the several sub-divisions of the population which are relevant for purpose of inquiry are adequately represented.
(iv) Systematic Sampling
This method is used where a complete list of the population from which sample is to be drawn is available. The method is to select every rth item*, from the list where ‘r’ refers to the sampling interval. The first item between the first and the rth is selected as random. For example, if a list of 500 students of a college is available and if we want to draw a sample of 100, we must select every fifth item (i.e., r = 5). The first item between one and five shall be selected at random. Suppose it comes out to be 4. Now we shall add five and obtain numbers of the desired sample. Thus the second item would be the 9th students; the third 14th students; the fourth 19 students; and so on.
Sampling interval or r = size of the universe
size of the sample
This method is more convenient to adopt than the random sampling or stratified sampling method. The time and work involved are relatively smaller. But the main drawback of this method is that systematic samples are not always random samples.
(v) Multi-Stage Sampling
As the name implies this method refers to a sampling procedure which is carried out in several stages. At the first stage, the first stage units are sampled by some statistical method, such as random sampling. Then a sample of second stage units is selected from each of the selected first units. Further stages may be added as required.
This method introduces flexibility in the sampling method which is lacking in the other methods. However, a multi-stage sample is less accurate than sample containing the same numbers of final stage units which have been selected by some suitable single stage process.
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