# Sampling theory, Introduction, and Reasons to Sample

### Introduction to Sampling Theory

Often we are interested in drawing some valid conclusions (inferences) about a large group of individuals or objects (called population in statistics). Instead of examining (studying) the entire group (population, which may be difficult or even impossible to examine), we may examine (study) only a small part (portion) of the population (an entire group of objects or people). Our objective is to draw valid inferences about certain facts about the population from results found in the sample; a process known as statistical inferences. The process of obtaining samples is called sampling and the theory concerning the sampling is called sampling theory.

Example: We may wish to conclude the percentage of defective bolts produced in a factory during a given 6-day week by examining 20 bolts each day produced at various times during the day. Note that all bolts produced in this case during the week comprise the population, while the 120 selected bolts during 6 days constitute a sample.

In business, medical, social, and psychological sciences, etc., research, sampling theory is widely used for gathering information about a population. The sampling process comprises several stages:

• Defining the population of concern
• Specifying the sampling frame (set of items or events possible to measure)
• Specifying a sampling method for selecting the items or events from the sampling frame
• Determining the appropriate sample size
• Implementing the sampling plan
• Sampling and data collecting
• Data that can be selected

### Reasons to Study a Sample

When studying the characteristics of a population, there are many reasons to study a sample (drawn from the population under study) instead of the entire population such as:

1. Time: it is difficult to contact every individual in the whole population
2. Cost: The cost or expenses of studying all the items (objects or individuals) in a population may be prohibitive
3. Physically Impossible: Some populations are infinite, so it will be physically impossible to check all items in the population, such as populations of fish, birds, snakes, and mosquitoes. Similarly, it is difficult to study the populations that are constantly moving, being born, or dying.
4. Destructive Nature of items: Some items, objects, etc. are difficult to study as during testing (or checking) they are destroyed, for example, a steel wire is stretched until it breaks and the breaking point is recorded to have a minimum tensile strength. Similarly different electric and electronic components are checked and they are destroyed during testing, making it impossible to study the entire population as time, cost and destructive nature of different items prohibit to study of the entire population.
5. Qualified and expert staff: For enumeration purposes, highly qualified and expert staff is required which is sometimes impossible. National and International research organizations, agencies, and staff are hired for enumeration purposive which is sometimes costly, needs more time (as a rehearsal of activity is required), and sometimes it is not easy to recruit or hire highly qualified staff.
6. Reliability: Using a scientific sampling technique the sampling error can be minimized and the non-sampling error committed in the case of a sample survey is also minimal because qualified investigators are included.

Every sampling system is used to obtain some estimates having certain properties of the population under study. The sampling system should be judged by how good the estimates obtained are. Individual estimates, by chance, may be very close or may differ greatly from the true value (population parameter) and may give a poor measure of the merits of the system.

A sampling system is better judged by the frequency distribution of many estimates obtained by repeated sampling, giving a frequency distribution having small variance and mean estimate equal to the true value.

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