What is probability sampling?
Definition: Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability. For a participant to be considered as a probability sample, he/she must be selected using a random selection.
The most critical requirement of probability sampling is that everyone in your population has a known and equal chance of getting selected. For example, if you have a population of 100 people, every person would have odds of 1 in 100 for getting selected. Probability sampling gives you the best chance to create a sample that is truly representative of the population.
Probability sampling uses statistical theory to randomly select a small group of people (sample) from an existing large population and then predict that all their responses will match the overall population.
- Probability & Statistics introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives.
- The probability formula is used to compute the probability of an event to occur. To recall, the likelihood of an event happening is called probability. When a random experiment is entertained, one of the first questions that come in our mind is: What is the probability that a certain event occurs? A probability is a chance of prediction.
What are the types of probability sampling?
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Simple random sampling, as the name suggests, is an entirely random method of selecting the sample. This sampling method is as easy as assigning numbers to the individuals (sample) and then randomly choosing from those numbers through an automated process. Finally, the numbers that are chosen are the members that are included in the sample.
There are two ways in which researchers choose the samples in this method of sampling: The lottery system and using number generating software/ random number table. This sampling technique usually works around a large population and has its fair share of advantages and disadvantages.
Stratified random sampling involves a method where the researcher divides a more extensive population into smaller groups that usually don’t overlap but represent the entire population. While sampling, organize these groups and then draw a sample from each group separately.
A standard method is to arrange or classify by sex, age, ethnicity, and similar ways. Splitting subjects into mutually exclusive groups and then using simple random sampling to choose members from groups.
Members of these groups should be distinct so that every member of all groups get equal opportunity to be selected using simple probability. This sampling method is also called “random quota sampling.”
Random cluster samplingis a way to select participants randomly that are spread out geographically. For example, if you wanted to choose 100 participants from the entire population of the U.S., it is likely impossible to get a complete list of everyone. Instead, the researcher randomly selects areas (i.e., cities or counties) and randomly selects from within those boundaries.
Cluster sampling usually analyzes a particular population in which the sample consists of more than a few elements, for example, city, family, university, etc. Researchers then select the clusters by dividing the population into various smaller sections.Systematic sampling is when you choose every “nth” individual to be a part of the sample. For example, you can select every 5th person to be in the sample. Systematic sampling is an extended implementation of the same old probability technique in which each member of the group is selected at regular periods to form a sample. There’s an equal opportunity for every member of a population to be selected using this sampling technique.
Example of probability sampling
Let us take an example to understand this sampling technique. The population of the US alone is 330 million. It is practically impossible to send a survey to every individual to gather information. Use probability sampling to collect data, even if you collect it from a smaller population.
For example, an organization has 500,000 employees sitting at different geographic locations. The organization wishes to make certain amendments in its human resource policy, but before they roll out the change, they want to know if the employees will be happy with the change or not. However, it’s a tedious task to reach out to all 500,000 employees. This is where probability sampling comes handy. A sample from the larger population i.e., from 500,000 employees, is chosen. This sample will represent the population. Deploy a survey now to the sample.
From the responses received, management will now be able to know whether employees in that organization are happy or not about the amendment.
What are the steps involved in probability sampling?
Follow these steps to conduct probability sampling:
1. Choose your population of interest carefully: Carefully think and choose from the population, people you believe whose opinions should be collected and then include them in the sample.
2. Determine a suitable sample frame: Your frame should consist of a sample from your population of interest and no one from outside to collect accurate data.
3. Select your sample and start your survey: It can sometimes be challenging to find the right sample and determine a suitable sample frame. Even if all factors are in your favor, there still might be unforeseen issues like cost factor, quality of respondents, and quickness to respond. Getting a sample to respond to a probability survey accurately might be difficult but not impossible.
But, in most cases, drawing a probability sample will save you time, money, and a lot of frustration. You probably can’t send surveys to everyone, but you can always give everyone a chance to participate, this is what probability sample is all about.
When to use probability sampling?
Use probability sampling in these instances:
1. When you want to reduce the sampling bias: This sampling method is used when the bias has to be minimum. The selection of the sample largely determines the quality of the research’s inference. How researchers select their sample largely determines the quality of a researcher’s findings. Probability sampling leads to higher quality findings because it provides an unbiased representation of the population.
2. When the population is usually diverse: Researchers use this method extensively as it helps them create samples that fully represent the population. Say we want to find out how many people prefer medical tourism over getting treated in their own country. This sampling method will help pick samples from various socio-economic strata, background, etc. to represent the broader population.
3. To create an accurate sample: Probability sampling help researchers create accurate samples of their population. Researchers use proven statistical methods to draw a precise sample size to obtained well-defined data.
Advantages of probability sampling
Here are the advantages of probability sampling:
Probability 233 Math
1. It’s Cost-effective: This process is both cost and time effective, and a larger sample can also be chosen based on numbers assigned to the samples and then choosing random numbers from the more significant sample.
2. It’s simple and straightforward: Probability sampling is an easy way of sampling as it does not involve a complicated process. It’s quick and saves time. The time saved can thus be used to analyze the data and draw conclusions.
3. It is non-technical: This method of sampling doesn’t require any technical knowledge because of its simplicity. It doesn’t require intricate expertise and is not at all lengthy.
What is the difference between probability sampling and non-probability sampling?
Probability 233 Calculator
Here’s how you differentiate probability sampling from non-probability sampling,
Probability sampling | Non-probability sampling |
|---|---|
| The samples are randomly selected. | Samples are selected on the basis of the researcher’s subjective judgment. |
| Everyone in the population has an equal chance of getting selected. | Not everyone has an equal chance to participate. |
| Researchers use this technique when they want to keep a tab on sampling bias. | Sampling bias is not a concern for the researcher. |
| Useful in an environment having a diverse population. | Useful in an environment that shares similar traits. |
| Used when the researcher wants to create accurate samples. | This method does not help in representing the population accurately. |
| Finding the correct audience is not simple. | Finding an audience is very simple. |
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word 'probability' is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.
There are several competing interpretations of the actual 'meaning' of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution.
A properly normalized function that assigns a probability 'density' to each possible outcome within some interval is called a probability density function (or probability distribution function), and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a distribution function (or cumulative distribution function).
A variate is defined as the set of all random variables that obey a given probabilistic law. It is common practice to denote a variate with a capital letter (most commonly ). The set of all values that can take is then called the range, denoted (Evans et al. 2000, p. 5). Specific elements in the range of are called quantiles and denoted , and the probability that a variate assumes the element is denoted .
Probabilities are defined to obey certain assumptions, called the probability axioms. Let a sample space contain the union () of all possible events , so
and let and denote subsets of . Further, let be the complement of , so that
Then the set can be written as
where denotes the intersection. Then
(4) |
(6) |
(8) |
where is the empty set.
Let denote the conditional probability of given that has already occurred, then
(10) |
(12) |
(14) |
The relationship
holds if and are independent events. A very important result states that
which can be generalized to
SEE ALSO:Bayes' Theorem, Conditional Probability, Countable Additivity Probability Axiom, Distribution Function, Independent Statistics, Likelihood, Probability Axioms, Probability Density Function, Probability Inequality, Statistical Distribution, Statistics, Uniform Distribution
REFERENCES:Probability 233 Definition
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Probability 233 Probability
Ross, S. M. A First Course in Probability, 5th ed. Englewood Cliffs, NJ: Prentice-Hall, 1997.
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Referenced on Wolfram Alpha: ProbabilityCITE THIS AS:Weisstein, Eric W. 'Probability.' FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Probability.html