POPULATION VS SAMPLE - WHICH IS BEST FOR A STATISTICIAN ?

 Aryuman Ganguly, 2148102, Department of Statistics, Christ University

Just as we need to chose left or right, right or wrong the binary options are sometimes very confusing to choose from. Often Statisticians, some under the confusion of whether they will study the whole or just a part of their data. Just as the word whole refers, here with respect to surveys it means totality of all the observations under study the universe, frequently described as the Population. For any kind of analysis the best way of obtaining accurate results is studying each and every element of the population and drawing conclusions from it. But times when Population turns out to be very large the very motive of accurate results falls behind and a lot of factors like time, cost, precision comes into play.

Statisticians to solve this problem brought out a solution that we need not to investigate each and every unit of the population but a specific representative unit of it. Here comes the concept of  Samples. Samples are a part of the population which reflects the properties of the population and the amount of data to be handled is also less, which in turn saves time, cost, complexity etc. Still, what do we mean by representative ? What do we mean by a specific part of the Population ? How to select ? What to select ? Like this comes a lot of questions in mind. So as a statistician what to chose for your survey so that your analysis gives accurate results ? We read that in the subsequent parts.

Let us consider a situation where we want to study of the heights of all the students in a particular section of class 10. Now let us consider there are in total 50 students in that class. Now for our data accuracy we record the heights of all the students and find out the mean height of the class. The results are accurate and perfect but the time consumed is sufficiently high. But all of these do not come into matter as the size of the population is less. But, what if we are dealing with a much larger population say a population consisting of all the class 10 students who are going to appear for their boards exam. Not just sufficiently high, its huge! 

The term used for evaluating a whole population unit by unit is called as Enumeration. The total count of all the units of the population for a certain characteristic is known as complete enumeration, also termed census survey.

Census 

Census method is that method in which data are collected covering every item of the universe or the population relating to the problem under investigation. Census method implies complete enumeration of the universe . Census of the population is the most suitable example of the census method of a statistical enquiry. For the estimation of the country's population, house to house enquiry is conducted and even people living at the road side are connected in India census of the population is conducted every ten years and the last census was conducted in February 2011.

Suitability of the Census Method

1) Small Size of the Population

2) Widely Diverse Items in the Population

3) Requirement of the Intensive Examination of the different items 

4) High Degree of Accuracy and Reliability. 

Merits of the Census Method

1) Reliable and Accurate 

2) Less Biased

3) Extensive Information

4) Study of the Diverse Characteristics 

5) Study of the Complex Investigations 

6) Indirect Investigation.

Demerits of the Census Method

1) Census Method is very costly and therefore it is not used for Ordinary Investigations only government agencies and big companies can afford the cost.

2) A Large Manpower is requires in the Census Method. Training a large number of enumerators becomes essential which is a very difficult process.

3) If the Universe contains a large Number of Items then it may not be possible to cover each and every item.  Census method becomes practically inoperative in such situations.

Solutions to the Problems in Census Method - A Sample Survey

Sample method is that method in which data is collected about the sample on a group of items taken from the population for examination and conclusions are drawn on their basis. Sample method is widely used in our day to day life. A lady in the kitchen for example tests only a grain or two of the rice to know whether the rice is boiled or not. By examining only a few drops of blood a doctor determines a blood group of the person. When only a part called a sample, is selected from the population and examined it is called sample enumeration or sample survey.

Suitability of the Sample Method 

1) When the size of the population is very large

2) Very high degree of accuracy is not needed but a reasonable amount needs to be maintained.

3) Intensive examinations of diverse items are not required

Two Basic Essentials of  a Sample

a) The sample must represent Characteristics of the Population.

b) The sample must be adequate enough to offer reliable conclusions.

As it is mentioned above that selection of a representative sample is an important step so as it better reflects the population and we get accurate conclusions from our results. There are some predefined steps to be included 

a) Statement of Objectives

b) Definition of Population to be studied.

c) Determination of the Sampling Frame and Sampling Units

d) Selection of proper Sampling Design 

e) Organization of Field Work

f) Summary and Analysis of the Data

Probability and Non-Probability Sampling

The Sampling procedures which are commonly used may be broadly classified under 

a) Probability Sampling

This is the method of sampling according to certain laws of the probability in which each unit of the population has some definite probability of being selected in the sample.

b) Non-Probability Sampling

This is the method of selecting the samples in which the choice of selection of sampling units depends entirely on the discretion or judgement of the sampler. This method is also called purposive sampling or judgement sampling. In this procedure the sampler inspects the entire population and selects a sample of typical units which he considers close to the average of the population. 

But the method of sample survey and selecting the samples differ with respect to objective of the enumerator and the population.

Some of the widely used methods of Sampling are:-

1) Random Sampling - Random Sampling is that method of sampling in which each and every item of the universe has equal chance of being selected in the sample.

2) Purposive Sampling - Purposive Sampling is that method in which the investigator himself makes the choice of the sample items which in his opinions are the best representative of the universe.

3) Stratified Sampling - In this method population is divided into different strata having different characteristics and some of the items are selected from each strata so that the entire population gets represented.

4) Systematic Sampling - According to this method units of the  population are numerically, geographically and alphabetically arranged. Every nth item of the numbered items is selected as a sample items.

Other than them there are Cluster sampling, Multi-Stage Sampling, Multi-phase Sampling, Successive Sampling ,Sequential Sampling etc.

Merits of Sample Survey 

1) Economical

2) Time Saving

3) Identification of Errors

4) Suitable for Large Investigation

5) Administrative Convenience 

6) More Scientific

Demerits of Sample Survey

1) It is only a partial investigation of the universe. The investigators bias in the selection of the sample is not ruled out. Accordingly the results may not be biased as well.

2) If the selected sample does not represent the characteristics of the universe the study may end up in wrong conclusions.

3) It is not very easy to select a sample which would represent the characteristics of the entire population.

4) Sometimes the universe may be so diverse that it becomes difficult to frame a sample.

5) Sampling involves a set of technical procedures. One must have the technical knowledge of choosing a representative sample from the universe. Persons who are well versed in the techniques are not easily available.

Application of Census and Survey in Practical Life

There are some agencies both at the national and state level to collect, process and tabulate the statistical data. Some of the agencies at the national level are Census of India, National Sample Survey (NSS), Central Statistics Office (CSO), Registrar General of India (RGI), Directorate General of Commercial Intelligence and Statistics (DGCIS), Labour Bureau, etc.

The Census of India provides the most complete and continuous demographic record of population. The Census is being regularly conducted every ten years since 1881. The first Census after Independence was conducted in 1951. The Census officials collect information on various aspects of population such as the size, density, sex ratio, literacy, migration, rural-urban distribution, etc. Census data is interpreted and analyzed to understand many economic and social issues in India.

The NSS was established by the Government of India to conduct nation- wide surveys on socio-economic issues. The NSS does continuous surveys in successive rounds. The data collected by NSS are released through reports and its quarterly journal Sarvekshana. NSS provides periodic estimates of literacy, school enrolment, utilization of educational services, employment, unemployment, manufacturing and service sector enterprises, morbidity, maternity, child care, utilization of the public distribution system etc. The NSS 60th round survey (January–June 2004) was on morbidity and healthcare. The NSS 68th round survey (2011-12) was on consumer expenditure. The NSS also collects details of industrial activities and retail prices for various goods. They are used by Government of India for planning purposes.

In Conclusion

The Choice of  Census or Sample Survey depends solely on the investigator as according to his needs and objective of the study. The size of the population plays an important role in the selection of the sample. For Populations of size till 100 statisticians suggest to study the entire population for the study to get accurate results and for the ones above that 30% of the units are generally preferred to be taken into the sample.

Samples in general are a all time preferred way over Census keeping in view the investigators Time, Cost, Expertise etc.