## Table of Contents:-

## What is sampling

Sampling is a vital element in statistical analysis, enabling researchers to select a specified number of observations from a broader population. Sampling stands as an essential tool in behavioural research, and researchers cannot carry out their work without it. The comprehensive study of the total population is both unattainable and impractical. The practical limitations, such as cost, time, and other factors which are usually operative in the situation, stand in the way of studying the total population. The introduction of sampling serves as a means for researchers to attain research findings that are both economical and accurate.

For example, a fruit merchant does not examine every apple or mango. He inspects only a few of them and decides whether to purchase them or not. The most important aim of sampling is to obtain maximum information about the population under study with the least use of money, labour, and time.

**According to Davis S. Fox**, “in the social science, it is not possible to collect data from every respondent relevant to our study but only from some fractional part is called sampling”.

**According to Cocharn, **“In every branch of science, we lack the resources, to study more than a fragment of the phenomena that might advance our knowledge.” In this definition, a ‘fragment’ is the sample and a ‘phenomena’ is the ‘population’.

## Importance of Sampling

The importance of sampling is as follows:

**1) More Effective: **Investigators can perform their work more effectively as the smaller sample size minimizes the fatigue associated with collecting information.

**2) Saves Time, Money and Effort:** The researcher can save time, money and effort because the subjects involved are small in number giving him a short time to calculate, tabulate, present, analyse, and interpret.

**3) More Accurate: **The involvement of small data minimizes errors in the various stages, including collection, tabulation, presentation, analysis, and interpretation.

**4) Gives More Comprehensive Information: **A smaller sample size leads to a more in-depth study, offering a broader understanding. The reason behind this is that all individuals in the population are equally eligible for inclusion in the sample.

**5) Faster and Cheaper: **Due to the small sample size, data collection, tabulation, presentation, analysis, and interpretation processes are quicker, resulting in reduced expenses.

## Basic Concepts of Sampling

To fully understand the concept of sampling design, it is important to familiarize oneself with a few fundamental terms.

### Target Population

The population or universe represents the entire group of units that serve as the primary focus of the study. Thus, the population could consist of all the persons in the country, or those in a particular geographical location, or a special indigenous or economic group, depending on the purpose and coverage of the study. A population could also consist of non-human units such as farms, houses or business establishments.

**For example, **let’s consider an investigation focused on the grades achieved by students in a statistics class. In this context, we refer to the complete assembly of students who have enrolled in that specific subject class as the “universe.” If that class consists of 50 students, the same 50 students will form the Universe”.

When investigating a set of objects, regardless of their nature, we employ the terms “population” or “universe.” it is important to understand that this concept refers to the aggregation of people, their inherent qualities, or the tangible results derived from their endeavours.

**1) Finite Universe: **When dealing with a group of entities or members that are finite in number, we use the term “finite universe.” For example, the universe of the weights of students in a particular class or the universe of dancers in Rohtak district.

**2) Infinite Universe: **An “infinite universe” is what we designate as a collection with an infinite count of members. For example, the multitude of pressures experienced at different locations within the atmosphere.

### Statistical Population

When conducting statistical analyses, researchers draw inferences from a statistical population, usually by using a random sample drawn from that population. For example, To draw general conclusions about cows, we must specify the particular set of cows we are focusing on.

It’s important to note that selecting a population such as all cows restricts our observations to cows that currently exist or will be born in the future. Due to our limited resources, geography may pose a constraint when it comes to studying cows. A statistical population refers to a collection of measurable quantities or a set of numbers. When every element in the set possesses only one characteristic, like the income of individuals, it constitutes a univariate population.

It is important to understand that a statistical population can be classified as either finite or infinite, depending on whether it consists of a limited or an unlimited number of elements. Again, it is important to note that an arbitrary set does not automatically qualify as a statistical population. For example. the set of cows on a farm at a particular time does not represent a statistical population.

### Sample

Researchers utilize a sample, which is a portion of the population, to make informed judgments about the population’s characteristics. It is a subset containing the characteristics derived from a broader population. Samples become a necessity in statistical testing when the test cannot accommodate all possible members or observations due to the population’s size. A sample should represent the whole population, without any bias towards specific attributes. A simple is a smaller, manageable version of a larger group.

**For example,**

**1) **To assess the quality of a bag of rice, we examine only a portion of it. We refer to the quantity of rice selected from the bag as a sample, while the entire amount of rice inside the bag constitutes the population.

**2)** When estimating the proportion of defective articles in a large consignment, we choose and examine only a portion, specifically a few of them. The selected portion is a sample.

### Census

If you gather comprehensive information about every individual or item within a specific universe or population, the inquiry becomes a complete enumeration. Another common name for complete enumeration is census. For example, in the Census of Population conducted every ten years in India, authorities collect information about every individual residing in the country. This method gives information about every unit of the population with greater accuracy.

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### Difference between Census and Sample

The main differences between the census and sample methods are as follows:

Basis | Census | Sample |

Meaning | Census refers to the periodic collection of information about the populace from the entire population. | Sampling is a systematic approach to collecting information from a sample that is representative of the entire population. |

Reliability of Data | Data from the census is accurate and reliable. | There is a margin of error in data which is obtained from sampling. |

Time Taken | Census is very time-consuming. | Sampling is quick. |

Sampling Variance | The sampling variance is nearly zero since we’re using data from the entire population. | Sampling variance may occur as the data is drawn from a limited portion of the population. |

Scope | All items relating to the universe are investigated. | Only a few items are required. |

Field on investigation | Used in investigations with limited field. | Used for investigation with large fields. |

Homogeneity | Useful where units of the population are heterogeneous. | Proves more useful where population units are homogeneous. |

### Sample Frame

The sampling frame serves as the source of units for the sample. This list comprises every individual within the population, serving as the source for sample selection. For example, if we wish to study the underlying factors that cause patients to be admitted to hospital following an acute asthmatic attack in a given area (your population), then you would need to know the names of all the people in that area who have been admitted into hospital for this reason.

A good sampling frame should be:

**1) Complete: **It should cover all relevant items.

**2) Relevant: **It should contain things directly linked to the research topic.

**3) Up-to-date: **It should incorporate recent additions and changes, and have redundant items cleansed from the list.

**4) Precise:** It should exclude all the items that are not relevant.

### Sample Unit

A sampling element is the entity that undergoes measurements. A sampling element may or may not be the same as a sampling unit. The sampling unit is termed a cluster of branches when it includes multiple population units. When the goal is to measure all population units in a cluster, the sampling elements encompass the population units contained within the sampled clusters. In this case, the sampling element is a subunit of the sampling unit.

To create the sampling frame, it’s important to have a clear definition of the sampling unit. By convention in statistics, a capital “N” is used to refer to the number of sampling units making up the universe and a lowercase “o” for the number of sampling units in the sample itself.

For example, in a family budget enquiry, usually, a family is considered as the sampling unit since it is found to be convenient for sampling and for ascertaining the required information. In a crop survey, we can consider a farm or a cluster of farms managed by a single household as the sampling unit.