Concepts Pertaining to Sampling:-

1. Universe/Population: From a statistical point of view, the term ‘universe’ refers to the total of the items or units in any field of enquiry, whereas the term ‘popu­lation’ refers to the total of items about which information is desired. The attributes that are the object of study are referred to as charac­teristics and the units possessing them are called as elementary units.

The aggregate of such units is generally described as population. Thus, all units in any field of enquiry constitute universe and all ele­mentary units (on the basis of one characteristic or more) constitute population. Quite often, we do not find any difference between popu­lation and universe, and as such the two terms are taken as inter­changeable. However, a researcher must necessarily define these terms precisely.

The population or universe may be finite or infinite. The popula­tion is said to be finite if it consists of a fixed number of elements so that it is possible to enumerate it in its totality. For example, the population of a city, the number of households in a village, the num­ber of workers in a factory, and the number of students in a university are the examples of finite population. The symbol ‘N’ is generally used to indicate how many elements (or items) are there in case of a finite population.

An infinite population is that population in which it is theoretically impossible to observe all the elements. Thus, in an in­finite population, the number of items is infinite, i.e., we cannot have any idea about the total number of items.

For example, the number of stars in the sky, sand particles at a sea beach, and pebbles in a river­bed. From a practical consideration, the term ‘infinite population’ is used for a population that cannot be enumerated in a reasonable pe­riod of time. This way we use the theoretical concept of infinite population as an approximation of a very large finite population.

2. Sampling Frame: The elementary units or the group of cluster of such units may form the basis of sampling process in which case they are called as sam­pling units. A list containing all such sampling units is known as sampling frame. The sampling frame consists of a list of items from which the sample is to be drawn. For instance, one can use telephone directory as a frame for conducting opinion survey in a city. What­ever the frame may be it should be a good representative of the popu­lation.

3. Sampling Design:

A sample design is a definite plan for obtaining a sample from the sampling frame. It refers to the technique or the procedure the re­searcher would adopt in selecting some sampling units from which inferences from the population are drawn. Sampling design is deter­mined before any data is collected.

4. Statistic(s) and Parameter(s):

A statistic is a characteristic of a sample, whereas a parameter is a characteristic of a population. Thus, when we work out certain meas­ures such as mean, median, mode, etc., from samples, they are called statistics for they describe the characteristics of a sample. But when such measures describe the characteristics of a population, they are known as parameters. For example, the population means (μ) is a pa­rameter, whereas the sample means (X) is a statistic. To obtain the es­timate of a parameter from a statistic constitutes the prime objective of sampling analysis.

5. Sampling Error:

Sampling survey does imply the study of a small portion of popula­tion and as such there would naturally be a certain amount of inaccu­racy in the information collected. This inaccuracy may be termed as sampling error or error variance. In other words, sampling errors are those errors which arise on account of sampling and they generally happen to be random variations (in case of random sampling) in the sample estimates around the true population values. It can be numeri­cally described as under:

Sampling error = Frame error + chance error + response error.

6. Precision:

Precision is a range within which the population average (or other parameters) will lie in accordance with reliability specified in the confidence level as a percentage of the estimate ± or as a numerical quantity. For example, if the estimate is Rs. 4000 and the precision desired is ± 4 per cent, then the true value will be not less than Rs. 3840 and not more than Rs. 4160. This is the range (Rs. 3840 to Rs. 4160) within which the true answer should lie. But if we desire that the estimate should not deviate from the actual value by more than Rs. 200 in either direction, in that case the range would be Rs. 3800 to Rs. 4200.

7. Confidence Level and Significance Level:

The confidence level or reliability is expected percentage of times that the actual value will fall within the stated precision limit. Thus, if we take a confidence level of 95 per cent, then we mean that there are 95 chances in 100 (or .95 in 1) that the sample results represent the true condition of the population within a specified precision range against five chances in 100 (or .05 in 1) that it does not.