What Is a Sample?
A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.
There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.
- In statistics, a sample is an analytic subset of a larger population.
- The use of samples allows researchers to conduct their studies with more manageable data and in a timely manner.
- Randomly drawn samples do not have much bias if they are large enough, but achieving such a sample may be expensive and time-consuming.
- In simple random sampling, every entity in the population is identical, while stratified random sampling divides the overall population into smaller groups.
A sample is an unbiased number of observations taken from a population. In simple terms, a population is the total number of observations (i.e., individuals, animals, items, data, etc.) contained in a given group or context. A sample, in other words, is a portion, part, or fraction of the whole group, and acts as a subset of the population. Samples are used in a variety of settings where research is conducted. Scientists, marketers, government agencies, economists, and research groups are among those who use samples for their studies and measurements.
Using whole populations for research comes with challenges. Researchers may have problems gaining ready access to entire populations. And, because of the nature of some studies, researchers may have difficulties getting the results they need in a timely fashion. This is why people samples are used. Using a smaller number of people who represent the entire population can still produce valid results while reducing time and resources.
Samples used by researchers must resemble the broader population in order to make accurate inferences or predictions. All the participants in the sample should share the same characteristics and qualities. So, if the study is about male college freshmen, the sample should be a small percentage of males that fit this description. Similarly, if a research group conducts a study on the sleep patterns of single women over 50, the sample should only include women within this demographic.
Consider a team of academic researchers who want to know how many students studied for less than 40 hours for the CFA exam and still passed. Since more than 200,000 people take the exam globally each year, reaching out to each and every exam participant would burn time and resources.
In fact, by the time the data from the population has been collected and analyzed, a couple of years would have passed, making the analysis worthless since a new population would have emerged. What the researchers can do instead is take a sample of the population and get data from this sample.
In order to achieve an unbiased sample, the selection has to be random so everyone from the population has an equal and likely chance of being added to the sample group. This is similar to a lottery draw and is the basis for simple random sampling.
For an unbiased sample, the selection must be random so that everyone in the population has an equal chance of being added to the group.
Types of Sampling
Simple Random Sampling
Simple random sampling is ideal if every entity in the population is identical. If the researchers don’t care whether their sample subjects are all male or all female or a combination of both sexes in some form, simple random sampling may be a good selection technique.
Let's say there were 200,000 test-takers who sat for the CFA exam in 2021, out of which 40% were women and 60% were men. The random sample drawn from the population should, therefore, have 400 women and 600 men for a total of 1,000 test-takers.
But what about cases where knowing the ratio of men to women that passed a test after studying for less than 40 hours is important? Here, a stratified random sample would be preferable to a simple random sample.
Stratified Random Sampling
This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups. These are known as strata. People within the strata share similar characteristics.
What if age was an important factor that researchers would like to include in their data? Using the stratified random sampling technique, they could create layers or strata for each age group. The selection from each stratum would have to be random so that everyone in the bracket has a likely chance of being included in the sample. For example, two participants, Alex and David, are 22 and 24 years old, respectively. The sample selection cannot pick one over the other based on some preferential mechanism. They both should have an equal chance of being selected from their age group. The strata could look something like this:
|Strata (Age)||Number of People in Population||Number to Be Included in Sample|
From the table, the population has been divided into age groups. For example, 30,000 people within the age range of 20 to 24 years old took the CFA exam in 2021. Using this same proportion, the sample group will have (30,000 ÷ 200,000) × 1,000 = 150 test-takers that fall within this group. Alex or David—or both or neither—may be included among the 150 random exam participants of the sample.
There are many more strata that could be compiled when deciding on a sample size. Some researchers might populate the job functions, countries, marital status, etc., of the test-takers when deciding how to create the sample.
Examples of Samples
In 2021, the population of the world was nearly 7.9 billion, out of which 49.6% were female and 50% were male. The total number of people in any given country can also be a population size. The total number of students in a city can be taken as a population, and the total number of dogs in a city is also a population size. Samples can be taken from these populations for research purposes.
Following our CFA exam example, the researchers could take a sample of 1,000 CFA participants from the total 200,000 test-takers—the population—and run the required data on this number. The mean of this sample would be taken to estimate the average of CFA exam takers that passed even though they only studied for less than 40 hours.
The sample group taken should not be biased. This means that if the sample mean of the 1,000 CFA exam participants is 50, the population mean of the 200,000 test-takers should also be approximately 50.
Why Do Analysts Use Samples Instead of Measuring the Population?
Often, a population is too large or extensive in order to measure every member and measuring each member would be expensive and time-consuming. A sample allows for inferences to be made about the population using statistical methods.
What Is a Simple Random Sample?
This sampling method uses respondents or data points that are randomly selected from the larger population. With a large enough sample size, a random sample removes bias.
Why Do Random Samples Allow for Inference?
The laws of statistics imply that accurate measurements and assessments can be made about a population by using a sample. Analysis of variance (ANOVA), linear regression, and more advanced modeling techniques are valid because of the law of large numbers and the central limit theorem.
How Large of a Sample Do You Need?
This will depend on the size of the population and the type of analysis you'd like to do (e.g., what confidence intervals you are using). Power analysis is a technique for mathematically evaluating the smallest sample size needed based on your needs. Another rule of thumb is that your sample should be large enough, but no more than 10% as large as the population.
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Sage Publishing. "Introduction to Statistics, Chapter 1," Pages 4-5.
CFA Institute. "1963 - 2022 Candidate Examination Results."
Virginia Tech Library. "Significant Statistics: 1.5 Sampling Techniques and Ethics."
The World Bank Group. "Population, Female (% of Total Population)."
The World Bank Group. "Population, Male (% of Total Population)."
The World Bank Group. "Population, Total."
A sample statistic (or just statistic) is defined as any number computed from your sample data. Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by random sampling, which is a random experiment.What is sample and its types in statistics? ›
A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.What is a sample in statistics answer? ›
A sample is defined as a smaller and more manageable representation of a larger group. A subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test.What does it meaning to sample statistics? ›
A sample statistic is a figure that is computed from a sample of data. A sample is a piece or set of objects taken from a statistical population. In other words, a sample statistic is just a calculation taken from a sample that is just a piece of a population.What is an example of sample data? ›
The data are the number of books students carry in their backpacks. You sample five students. Two students carry three books, one student carries four books, one student carries two books, and one student carries one book. The numbers of books (three, four, two, and one) are the quantitative discrete data.What is the best example of a sample in statistics? ›
A sample is just a part of a population. For example, let's say your population was every American, and you wanted to find out how much the average person earns. Time and finances stop you from knocking on every door in America, so you choose to ask 1,000 random people. This one thousand people is your sample.What are the 5 types of samples? ›
There are five types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.What is the sample mean *? ›
A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.What is a one sample t test example? ›
For example, imagine a company wants to test the claim that their batteries last more than 40 hours. Using a simple random sample of 15 batteries yielded a mean of 44.9 hours, with a standard deviation of 8.9 hours. Test this claim using a significance level of 0.05.What is the main purpose of sample? ›
The primary goal of sampling is to create a representative sample, one in which the smaller group (sample) accurately represents the characteristics of the larger group (population). If the sample is well selected, the sample will be generalizable to the population. There are many ways to obtain a sample.
There are two main types of sampling: probability sampling and non-probability sampling.What are the 4 types of random sampling? ›
There are four primary, random (probability) sampling methods – simple random sampling, systematic sampling, stratified sampling, and cluster sampling.Why are samples used in statistics? ›
Sampling has a lot of advantages, namely cost efficiency, reduction of efforts, and effective analysis. Cost efficiency is due to the fact that it is cheaper to use a group of people that you have in hand than reaching out to a wider group of people, especially when the population is large.What are the 4 types of data examples? ›
- Nominal data.
- Ordinal data.
- Discrete data.
- Continuous data.
“Sample”- Learn the Difference. The word example is used to mention an illustration, in support of a claim. The word sample is used to denote a specimen or model.What are 3 examples of sample vs population? ›
Population vs. Sample | Definitions, Differences & Examples.
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Collect unbiased data utilizing these four types of random sampling techniques: systematic, stratified, cluster, and simple random sampling.What is the best sample type? ›
Simple random sampling: One of the best probability sampling techniques that helps in saving time and resources, is the Simple Random Sampling method. It is a reliable method of obtaining information where every single member of a population is chosen randomly, merely by chance.What are sample categories? ›
There are two main categories of sampling: probability sampling and non-probability sampling. 1. Probability sampling: In this category of sampling, all members of the population have an equal chance of being selected for a study.Is population mean a sample mean? ›
In statistics, there are two different averages: the sample mean and the population mean. The sample mean only considers a selected number of observations—drawn from the population data. The population mean, on the other hand, considers all the observations in the population—to compute the average value.
The sample mean is a random variable, because its value depends on what the particular random sample happens to be. The expected value of the sample sum is the sample size times the population mean (the average of the numbers in the box).What are the 2 types of two sample t tests? ›
Independent two-sample t-test. Paired sample t-test.What is an example of a two sample t-test? ›
Two Sample t-test: Motivation
Suppose we want to know whether or not the mean weight between two different species of turtles is equal. Since there are thousands of turtles in each population, it would be too time-consuming and costly to go around and weigh each individual turtle.
The 2-sample t-test takes your sample data from two groups and boils it down to the t-value. The process is very similar to the 1-sample t-test, and you can still use the analogy of the signal-to-noise ratio. Unlike the paired t-test, the 2-sample t-test requires independent groups for each sample.What is the most commonly used method of sampling? ›
- Random Sampling. ...
- Stratified Sampling. ...
- Systematic Sampling. ...
- Convenience Sampling. ...
- Quota Sampling. ...
- Purposive Sampling.
Population and Sample Examples
All the students in the class are population whereas the top 10 students in the class are the sample. All the members of the parliament is population and the female candidates present there is the sample.
To summarize: your sample is the group of individuals who participate in your study, and your population is the broader group of people to whom your results will apply. As an analogy, you can think of your sample as an aquarium and your population as the ocean.How do you select a sample? ›
- Step 1: Define the population. Start by deciding on the population that you want to study. ...
- Step 2: Decide on the sample size. Next, you need to decide how large your sample size will be. ...
- Step 3: Randomly select your sample. ...
- Step 4: Collect data from your sample.
Population structure is the breakdown of different groups and amounts of people in an area. It is important as it affects the area itself. There are 4 main characteristics of the population structure: age, gender, ethnicity, and density.What is the rule for sample means? ›
Rule for sample means (p. 363) If numerous samples of the same size are taken, the. frequency curve of means from the various samples. will be approximately bell-shaped.
The theory behind sampling is based on the concept of the simple random sample. In a simple random sample, individuals are selected from the population in a completely random fashion. This implies that all individuals have identical (nonzero) probability of being selected for our sample.How do you write a sample in research example? ›
You need to: (1) describe what you are studying, including the units involved in your sample and the target population; (2) explain the types of sampling technique available to you; (3) state and describe the sampling strategy you used; and (4) justify your choice of sampling strategy.What are the 4 sampling strategies? ›
Four main methods include: 1) simple random, 2) stratified random, 3) cluster, and 4) systematic. Non-probability sampling – the elements that make up the sample, are selected by nonrandom methods. This type of sampling is less likely than probability sampling to produce representative samples.