RANDOM SAMPLING METHODS

Introduction

Many professions (business, government, engineering, science, social research,

agriculture, etc.) seek the broadest possible factual basis for decision-making. In the absence

of data on the subject, a decision taken is just like leaping into the dark.

Sampling is of fundamental importance for estimating the quality of a lot or

ascertaining its conformity to the requirements of a specification. The economy, reliability

and practicability of the sampling procedures have made them almost indispensable in most

of the industrial and trade applications. However, the reliability of the conclusions drawn on

the basis of the sample depends on its representativeness and the method of its selection. It is

hoped that the sampling methods as per standard, when implemented, would ensure a truly

random and representative sample leading to sound and satisfactory estimation of lot quailty

Sampling is a procedure, where in a fraction of the data is taken from a large set of

data, and the inference drawn from the sample is extended to whole group. The surveyor’s (a

person or a establishment in charge of collecting and recording data) or researchers initial

task is to formulate a rational justification for the use of sampling in his research. If sampling

is found appropriate for a research, the researcher, then:

(1) Identifies the target population as precisely as possible, and in a way that makes sense in

terms of the purpose of study.

(2) Puts together a list of the target population from which the sample will be selected. This

list is termed as a frame (more appropriately list frame) by many statisticians.

(3) Selects the sample, and decide on a sampling technique, and;

(4) Makes an inference about the population.

All these four steps are interwoven and cannot be considered isolated from one another.

Simple random sampling, systematic sampling, stratified sampling fall into the category of

simple sampling techniques. Complex sampling techniques are used, only in the presence of

large experimental data sets; when efficiency is required; and, while making precise

estimates about relatively small groups within large populations.

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SAMPLING TERMINOLOGY1.population : A population is a group of experimental data, persons, etc. (or) the population is a complete set of all possible observations of the type which is to be investigated.eg. Total number of studentsstudying in a school or college, total number of books in a library, total number of houses in a village or town

a. Finite population: A population is said to be finite if it consists of finite number of units.eg. Number of workers in a factory, production of articles in a particular day for a company.

b. Infinite Population: A population is said to be infinite if it has infinite number of units.eg. the number of stars in the sky, the number of people seeing the Television programmes.

c. Population Total is the sum of all the elements in the sample frame. d. Population Mean is the average of all elements in a sample frame or population.

2.Element: An element is an object on which a measurement is made. This could be a voter in a precinct, a product as it comes off the assembly line, or a plant in a field that has either bloomed or not.3.Cluster. :A population is built up of elementary units, which cannot be further decomposed. A group of elementary units is called a cluster.4.Sampling Fraction:The fraction of the population or data selected in a sample is called the Sampling Fraction.

5.Raising Factor : The reciprocal of the sampling fraction is called the Raising Factor. 6.Random sample : A sample, in which every unit has the same probability of selection, is called a random sample. The word random describes the procedure used to select elements

Target population

Study population

sample

Target population is the population of ultimate clinical interest

Study population is subset of the target population to be studied

Samples are the subset of the study population used in clinical research because often not every member of the study population can be studied .

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Element/case

(participants, cars, test items) from a population.If no repetitions are allowed, it is termed as a simple random sample selected without replacement. If repetitions are permitted, the sample is selected with replacement.

7.Sample:Statisticians use the word sample to describe a portion chosen from the population. A finite subset of statistical individuals defined in a population is called a sample. The number of units in asample is called the sample size. The sample is referred to as representative because the characteristics of a properly drawn sample represent the parent population in all ways.

8.Sampling Unit:The constituents of a population which are individuals to be sampled from the population and cannot be further subdivided for the purpose of the sampling at a time are called sampling units.Eg. to know the average income per family, the head of the family is a sampling unit. To know the average yield of rice, each farm owner’ s yield of rice is a sampling unit.

9.Sampling Frame:For adopting any sampling procedure it is essential to have a list identifying each sampling unit by a number. Such a list or map is called sampling frame. Eg.A list of voters, a list of house holders, a list of villages in a district, a list of farmers etc. are a few examples of sampling frame.A sample is a collection of sampling units drawn from a frame or frames. Data are obtained from the sample and are used to describe characteristics of the population.

Example 1 : Suppose we are interested in what students in a particular high school think about the drilling for oil in our national wildlife preserves. The elements are the high school students and the population is the students who attend this high school. The sampling units could be the students as individuals with the frame the alphabetical listing of all students enrolled in the school. The sampling units could be homerooms, since each student has one and only one homeroom, and the frame the class list for homerooms.Example 2 : Suppose we are interested in what voters in a particular precinct think about the drilling for oil in our national wildlife preserves. The elements are the registered voters in the precinct. The population is the collection of registered voters. The sampling units will likely be households in which there may be several registered voters. The frame is a list of households in the precinct

10.Parameters And Statistics:We can describe samples and populations by using measures such as the mean, median, mode and standard deviation. When these terms describe the characteristics of a population, they are called parameters. When they describe the characteristics of a sample, they are called statistics.

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