Sampling Technique (Stats165)

 Introduction 

Sampling techniques are methods used to select a portion (sample) from a large group (population) for study. They are widely applied in everyday life.

Example:

• When buying grains, we often check a handful to judge the quality of the entire bag.
• A doctor tests a few drops of blood to determine a person’s overall health.

Population

In statistics, a population refers to the entire set of items or individuals under investigation. It is also called the universe.

A large group of people 

Definition:

A population is the complete collection of all possible observations of a particular type to be investigated.

Examples:

• Total number of students in a school or college.
• Total number of books in a library.
• Total number of houses in a village or town.

Types of Population:

Finite Population:

A population with a countable number of units.

Example: 

• The number of workers in a factory.

The total number of units in a finite population is called the population size.

Infinite Population:

A population with an uncountable or limitless number of units.

Example: 

• The number of people who can watch a television program.

Sample

A sample is a finite subset or a part of a population selected to represent the entire population under study.

The number of units in a sample is known as the sample size.

Blood samples

Sampling Unit

The sampling unit is the basic element or member of the population chosen for sampling. It cannot be further subdivided during selection.

Examples:

• To determine the average family income, the head of the family is a sampling unit.
• To estimate the average rice yield, each farm owner’s field represents a sampling unit.

Sampling Frame

A sampling frame is the list or record that identifies all the sampling units in the population under study. It provides the basis from which samples are drawn.

Examples:

• A list of registered voters.
• A list of households in a community.
• A list of villages in a district.
• A list of farmers in a region.

Reasons for Selecting a Sample

Sampling is inevitable or necessary in the following situations:

1. When complete enumeration is practically impossible. This occurs when the population is infinite or extremely large, making it impossible to study every unit.

Example:

• Measuring the number of fish in an ocean or counting all stars in the galaxy.

     2. When results are required within a short time.

Sampling provides quicker results because it focuses on a small portion of the population rather than the whole.

     3. When the survey area is very wide. For geographically large areas, sampling helps manage data collection efficiently.

Example: 

• Conducting a national survey of schools or farms.

    4. When resources for surveying are limited. Due to constraints of money, manpower, and time, it is often not feasible to conduct a census; hence, sampling is adopted.

     5. When the items or units are destroyed under investigation. Some studies involve testing that damages or destroys the units observed.

Example: 

• Testing the durability of bulbs or the tensile strength of steel samples.

Parameter and Statistic

We can describe both populations and samples using measures such as mean, median, mode, and standard deviation.

When these measures describe the characteristics of a population, they are called parameters.

When they describe the characteristics of a sample, they are called statistics.

Relationship Between Parameters and Statistics

When the parameters of a population are unknown, they are estimated using the values of corresponding statistics derived from a sample.

In general, we use Greek letters (or sometimes capital letters) to represent population parameters, and lowercase Roman letters to represent sample statistics.

Thus:

• 𝑁: Size
• 𝜇: Mean
• 𝜎: Standard deviation 

N,μ,σ are the standard symbols for the size, mean, and standard deviation of a population, respectively.

• 𝑛: Size
• x̄: Mean
• 𝑠: Standard deviation 

n,x̄,s are the standard symbols for the size, mean, and standard deviation of a sample, respectively.

Conclusion 

Sampling is an essential statistical method that allows researchers to study a portion of a population and make valid inferences about the whole. It is preferred when complete enumeration is impossible, time-consuming, costly, or destructive. By selecting a representative sample, reliable results can be obtained efficiently. The accuracy of these results depends on proper sampling techniques and understanding key concepts such as population, sample, parameters, and statistics, where parameters describe the population, and statistics estimate them.

References 

Stat 165 key points by Rahmon Abass Adewale

U24PS Stats165 note

Wikipedia contributors