Introduction
Every researcher must understand the concept of population vs. Sample.
In statistics, data is critical in determining the validity of the outcome. Data must be relevant, correct, and representative of all classes. While more data is beneficial for obtaining objective results, it is critical to ensure that the data collected is appropriate for the problem at hand.
It is simple to distinguish between a given population and a sample. One essential law of statistics must be remembered: a sample always refers to a smaller group (subset) inside the population.
The following article discusses the differences between population and the sample.
Population vs Sample
The main difference between population and sample is the fact that a population is the complete group of individuals or things that share a similar trait or set of characteristics, whereas a sample is a smaller subset of the population chosen for research.
Both the population and the sample depend on the selection method. A population is all individuals or items having a specific characteristic, whereas a sample is a portion of the population chosen for study. Another crucial distinction between population and sample is precision. Larger samples, in general, yield more exact estimates, but they can also be more expensive or difficult to collect and analyze.
Difference Between Population and Sample in Tabular Form
| BASIS OF COMPARISON | POPULATION | SAMPLE |
| Meaning | The term population refers to a group of all elements that share common features and compose the cosmos. | A sample is a subset of the population chosen for taking part in the study. |
| Size | Usually greater than the sample size. | Smaller in size than the population. |
| Inference | The goal is to comprehend the traits of the entire group. | The purpose is to conclude about the wider population based on the sample's characteristics. |
| Data | Includes all possible data points for the desired feature. | Although there are fewer data points, they are still representative of the population's characteristics. |
| Focus on | Recognizing the qualities. | Making population inferences. |
| Characteristic | Parameter | Statistic |
What Is a Population?
In simple words, population refers to the average of all elements under investigation that have one or more characteristics, such as everyone living in India. The population does not just comprise people, but also animals, events, items, structures, and so on. It can be of any size, and the total amount of members or components in a population is known as population size; for example, if India has a population of 100 million people, the population size (N) is 100 million.
Types of Population
1. Finite Population: A finite population is sometimes referred to as a countable population because the population can be tallied. In other terms, it is defined as the population of all finite individuals or objects. For statistical analysis, a finite population is preferable to an infinite population. Employees of a firm and potential consumers in a market are examples of finite populations.
2. Infinite Population: The infinite population, often known as an uncountable population, is one in which counting units is impossible. The quantity of microbes in the patient's body is an example of an endless population.
3. Accessible Population: An accessible population can be reached by researchers or statisticians. This group is frequently smaller than the entire population and therefore easier to study. For example, if a study focuses on college students in a specific city, the accessible population is the students who attend institutions in that city.
4. Target Population: The target population is the population that is the subject of a specific study or research. The investigator or the study's aims usually specify the target population. For example, if research is planned to evaluate the efficacy of an innovative drug, the group to be studied would be people who have a certain medical problem that the drug is intended to treat.
5. Homogeneous Population: A homogenous population shares comparable qualities or traits. A homogenous population would be a population of plants that all share the same genetic makeup.
6. Heterogeneous Population: A heterogeneous population possesses a variety of characteristics or attributes. A heterogeneous population would contain, for example, a group of animals of various kinds, ages, and genders.
Collecting Data From a Population
Populations are utilized when your research topic demands data from every member of the population or when you have access to data from every member of the population.
It is usually only possible to collect data from a large population when it is small, accessible, and cooperative.
It is usually difficult or impossible to collect information about every individual in larger and more distributed populations. For example, the federal US government uses the US Census to count all individuals living in the country every ten years. This information is utilized to disperse funds across the country.
However, historically, it has been difficult to contact, locate, and encourage participation from marginalized and low-income groups. Due to non-response, the population count is inaccurate and biased towards certain groups, resulting in disproportionate financing across the board.
What Is a Sample?
A sample is a more manageable and smaller representation of a bigger group. A subset of an entire population that shares some of its traits. In statistical testing, a sample is employed when the population size is too big to include all members or observations in the test.
The sample is a random selection of the population that best reflects the entire data collection.
To avoid demographic constraints, you can sometimes gather data from just a portion of the population and then use it as the overall norm. You obtain the necessary information from the study's participants, making the data credible.
The results acquired for the various study groups can be extended to generalize for the public.
Sampling is the process of gathering data from a small subset of the population and then using it to generalize over the complete set.
A Sample Is Used When:
When the population is too huge to collect data
The information gathered is untrustworthy.
The population is fictitious and infinite in size. Consider a study that documents the outcomes of a new medical technique. Because it is unknown how the process will affect people all over the world, a test group is used to see how they react to it.
A Sample Should Generally:
Satisfy all the population's variances as well as a clearly defined selection criterion.
Be completely objective about the attributes of the objects being chosen.
Choose the items of study at random to ensure fairness.
Assume you are seeking a career in the IT field and do an internet search for IT employment. The initial result would be for jobs worldwide. However, you'd like to work in India, so you look for IT jobs in India. This is your demographic. It would be difficult to apply for all the positions on the list. So, you analyze the top 30 positions for which you are qualified and happy, and you apply for those. This is your sample.
Types of Samples
There are two main types of samples. They are
1. PROBABILITY SAMPLING
The population units in probability sampling cannot be chosen at the researcher's choice. This can be handled by following specific processes that ensure that each component of the population has one set probability of being taken into the sample. This procedure is also known as random sampling. The following are some probability sampling techniques:
- Basic random sampling
- Cluster analysis
- Sampling stratification
- Proportionate sample size
- Sample proportionately
- Stratified sampling with optimal allocation
- Sampling in stages
2. NON-PROBABILITY SAMPLING
The population units in non-probability sampling can be chosen at the researcher's discretion. The samples in question will use human judgement to select units and have no mathematical foundation for estimating population characteristics. Some non-probability sampling techniques are as follows:
- Limit sampling
- Samples of judgement
- Purposeful sampling
Collecting Data From a Sample
When a population is large, geographically spread out, or hard to contact, a sample is required. You can use statistical analysis to produce estimates or investigate theories regarding population data by using sample data.
A sample should ideally be drawn at random and reflect the population. Using methods of probability sampling (such as simple sampling at random or stratified sampling) lowers the possibility of sample bias while improving validity internally as well as externally.
Non-probability sampling methods are frequently used by researchers for practical reasons. Non-probability samples are selected for special reasons; they may be easier or less expensive to obtain. Any statistical inferences about the larger population will be poorer than with a probability sample due to non-random selection procedures.
How to Choose High-Quality Sample
Although we ensure that all members of the population have an equal chance of being included in the sample, this does not imply that samples derived from a specific population satisfying the criteria will be identical. They will continue to differ from one another. This change can be minor or significant.
It is also discovered that the accuracy of the data is affected by the sample size. With a smaller sample size, the accuracy is substantially lower than with a larger study group. Thus, if two, three, or more samples are drawn from a population, the larger the samples, the more similar they are.
Population and Sample Example
- The population consists of all people who have ID proof, while the sample consists of people who have a single voter id with them.
- The population consists of all students in the class, whereas the sample consists of the top ten students in the class.
- The population consists of all members of parliament, while the sample consists of the female candidates present.
- We'd like to know which vehicle manufacturer is most popular among drivers aged 40 to 50 in Noida. The population consists of all drivers of the abovementioned ages who live in Noida, and the sample is a random sample of all people with a driver's licence and of that age.
Population and Sample Formula
Population Parameter:
Mean: μ = (ΣX) / N, where (ΣX) is the total of all population values and N is the population size.
Standard deviation: σ = √[(Σ(X-μ) ²) / N], where X is a population value, is the population mean, and N is the population size.
Sample Parameter:
Mean: xÌ„ = (Σx) / n, where Σx is the sum of all sample values and n is the sample size.
Standard deviation: s = √[(Σ(x-xÌ„) ²) / (n-1)], where x is a sample value and xÌ„ are the sample mean
It is worth noting that the formulas for the population parameter and sample statistics are identical, but they are written differently and have somewhat different calculations. The population parameter considers the entire population, whereas the sample statistic considers a subset (i.e., sample) of the population.
Main Differences Between the Population and Sample in Points
The distinction between population and sample can be clearly drawn on the following grounds:
- The population is the collection of every component with common qualities that compose the cosmos. A sample is a subset of the population selected for participation in the study.
- The population is made up of every member of the whole group. A sample, on the other hand, includes only a subset of the population.
- The population feature based on all units is referred to as a parameter, but the measurement of sample observation is referred to as a statistic.
- The process of collecting information from every unit of the population is called a census or total count. In contrast, a sample survey is carried out to collect information from a sample using a sampling procedure.
- The focus of the population is on identifying the features of the elements, whereas the focus of the sample is on generalizing about the features of the population from where the sample was drawn.
Conclusion
Despite the above differences, it is accurate that the sample and population are related, i.e. sample is chosen from the population, so the sample may not exist without the population. Furthermore, the sample's primary goal is to make statistical conclusions about the population that are as exact as possible. The greater the sample size, the greater the level of generalization accuracy.
