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Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Simple random sampling is a common method used to collect data in many different fields. From psychology to economics, simple random sampling can be the most feasible way to get information. Learn all about it in this lesson!

Simple Random Sampling

Adrian is gathering information for a trip he plans to take. He is thinking about moving permanently to a new town. However, he wants to get an idea of how the people in the town feel about the safety of the town. Unfortunately, Adrian does not have the resources to ask every person in the town how they feel about the safety. How should Adrian go about collecting this data?

In this lesson, you will learn about how to use and recognize simple random sampling in statistics. First, let's discuss the meaning of simple random sampling by defining a few key terms.

When you are doing an experiment, you want to gather information about a population. A population is all members of a specific group. For example, the population of Adrian's research will be, quite literally, the population of the town. Sometimes a population is not that geographically contained. If Adrian wanted to know the typical income of a person over 30, then anyone with a job over 30 in the entire world would be in his population. Since Adrian does not have the resources to ask everyone in the town how they feel about safety, he will have to use a sample of the population.

A sample is a part of the population used to describe the whole group. Adrian will want to make sure all demographics are represented in his sample. He doesn't just want the opinion of the teenagers in his town or just the men over 50. He wants to get all demographics equally represented in his sample. To do this, Adrian will need to use random sampling, which is a method of choosing an equally distributed subset from a larger population. This takes us to simple random sampling or SRS, which is a type of random sampling where the variables have an equal and unsystematic chance of selection.

For example, if you were to toss a handful of 6-sided dice on a table, you would have an equal and unsystematic likelihood of getting a one, two, three, four, five, or six. When I say unsystematic, I mean you aren't throwing the dice and then only choosing the number off of every other dice on the table. When you use a system to randomize the selection instead of just taking the random selections as they fall, then you are not using simple random selection.

In Adrian's experiment, Adrian can use a phone book with all of the names of the people in the town as his population group. He can then put each name on a piece of paper and put the papers into a bag. Adrian can blindly select a certain number of names from the bag as part of his simple random sampling.

Now that you understand the meaning of simple random sampling, let's discuss how to use simple random sampling.

Using Simple Random Sampling

Simple random sampling is meant to be a balanced representation of the demographics of the population. When you are discussing a population of people, that means all of the demographics: age, race, religion, ethnicity, socioeconomic status, education level, etc. that are all currently present in the given population.

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Simple random sampling is best used when a researcher does not know a lot about the demographics of the population. For example, if Adrian knew that the population was mostly older, he would choose his sample to skew towards older people. But without doing additional research, Adrian is not familiar with the people in his new town. Therefore, simple random sampling is a good choice for Adrian since he does not know much about the population.

Most often, you will find simple random sampling used without replacement. This means that once Adrian selects a name from the bag, he will not put the name back into the bag to have a chance to be selected a second time. It is understood that simple random sampling is done without replacement. However, when you are replacing an outcome, you would say that you are doing simple random sampling with replacement.

Lesson Summary

Remember, random sampling is a method of choosing an equally distributed subset from a larger population. One type of random sampling is simple random sampling, or SRS, which is a type of random sampling where the variables have an equal and unsystematic chance of selection. When I say unsystematic, I mean there isn't a routine or prescribed method for choosing the sample. Simple random samples are best used for populations where the researcher, like Adrian, is unfamiliar with the given population.

Most simple random samples are assumed to be conducted without replacement, but you can have simple random samples that have the outcomes replaced at each draw, which is called simple random sampling with replacement. Adrian can conduct a simple random sample by putting the names of all the townspeople in a bag and then blindly selecting names out of the bag to create his sample.

Learning Outcomes

Viewing this lesson can prepare you to:

Restate the definitions of population, sample and random sampling

Determine how to conduct simple random sampling

Specify instances in which you would want to use this method of sampling

Display understanding of simple random sampling with replacement

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