# Simple Random and Systematic Random Sampling Author: Ryan Backman
##### Description:

Differentiate between simple random and systematic random sampling.

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Tutorial

## Video Transcription

Hi, this tutorial covers simple random samples. Recall that it is important to use a representative sample when taking a sample from the population. A common type of representative sample is called a simple random sample. It's often abbreviated just as SRS.

Now for a definition. A simple random sample of size n consists of n individuals from a population chosen in a way that every set of individuals has an equal chance of being sampled. This is sometimes the tricky part, so every set of n individuals has an equal chance of being selected.

So take a look at a simple random sample let's take a look at a situation. My wife and I are planning on celebrating our anniversary with a dinner at a fancy restaurant. Unfortunately, we have a difficult time picking a restaurant. We decide to pick two restaurants from a list of 24 fancy Saint Paul restaurants. From the two restaurants selected, my wife and I will be able to choose which restaurant to attend.

Here's the list of 24 restaurants. We'll come back to that list in a second. Now I'm trying to select a simple random sample of size 2, n equals 2, where again and represents the sample size. Remember to take a random sample, I need a probability sampling plan. Determine if the following probabilities sampling plans would yield a simple random sample.

So here are two plans. And we're going to decide whether or not that will give me a simple random sample. So plan 1, pick the 7th and 10th restaurants on the list. So let's investigate that one first. And so what I would do as I would just count down the list 7-- 1, 2, 3, 4, 5, 6, 7. That would up being Faces, the restaurant Faces. And then the 10th-- 8, 9, 10-- Heartland. So those would represent the two restaurants in my sample-- Faces and Heartland. And then we would be able to choose, probably Heartland is a better restaurant.

So we want to thing about now, is that a simple random sample? Well, first of all, does every restaurant have the equal chance of being selected? And really technically, no. Only Faces and Heartland had a chance at being selected. So those two had 100% probability of being selected, where the rest of them had a 0% chance of being selected. OK, so that's certainly not a simple random sample. So that would not be a good probability sampling.

Plan number two, 12 of the 24 restaurants are known to be steakhouses. Put the names of all of the steakhouses in a hat and draw one. Put the names of the remaining restaurants in another hat and draw one. So in this case, every restaurant does have an equal chance of being selected. Now this also is not a simple random sample. And the reason why is that the way that this is set up, there is no way getting two steak houses in my sample, OK.

And remember with a simple random sample every set of n individuals has an equal chance of being selected. So since there's no way to get two steakhouses in the same sample. Plan 2 does not represent a probability sampling plan for obtaining a simple random sample. So those are two ways that do not give you a simple random sample.

Here are two ways that are. Method 1 is what we call the name in a hat method. The names of the members of the population are placed into a hat and n names are drawn. So let's do that. What I have here are all the restaurants cut out. Each of them are the same length. And all 24 are listed here. So what I'm going to do is I'm going to mix them up, really mix them up. And I'm going to put them in a hat. Instead of a hat, though, I have a bike helmet.

So the names go in a hat. Again, they get mixed up. And two of them get selected, generally one at a time. So there's my first member of my sample. This would be the second member of the sample. OK, so as you can see the two that were selected were Jones in the Park and Boca Chico Restaurant. So out of those two my wife and I then could decide where we could spend our afternoon. So that is, again, what is called the name in a hat method.

The second way of taking a simple random sample is to label each individual with a number, then select n unique random numbers using a random number generator or a random digit table. Random number generators or digit tables can be easily found on the internet. So I'm going to show you how to take a simple random sample with a random digit table. Again, what you could do is go online, find a random number generator, and use that to pick your sample.

So again, what we need to do is label each individual with a number, which I have done. So each restaurant is labeled with a unique number, 1 to 24. And now what I need to do is select two random numbers, OK. So again, I could do this using a random number generator. I'd go 1 to 24 and get two numbers selected. You do need to be careful that you don't-- if you have repeated numbers, that you don't pick the same restaurant twice or the same element twice.

So again, I'm going to do this using a random digit table, OK. So generally, they look something like this. So now when you're on your random digit table, it doesn't really matter where you start. Generally when you're picking random numbers, you just want to pick a different spot to start each time.

So what I'm going to do is I'm going to start here. OK, so now what I'm want to do is I want to pick two digit numbers. Since I'm picking the numbers 1 to 24, I need to consider the numbers 01 all the way up to 24. Anything else I can just throw out and select a different random number.

All right, so what I'm going to do first is I'm going to select this those two random digits. So 1 and 7 so that represents 17. So 17 would be part of my sample. OK, remember I'm trying to pick two restaurants here. So now what I'd do is I'd go to slide across two digits and pick the next two digit number. That would be 86. OK. 86 isn't relevant here. So I'm going to throw that out.

My next one here would be 82. OK, again not relevant. So I'll throw that one out. Next would be 49, not relevant. 43, not relevant. 61, not relevant. 79, not relevant. Now our next one is 09. OK, that one is relevant. That is a number between 1 and 24. So that will be the second number in my sample.

All right, so this was an effective way of taking a simple random sample of size 2. So now let's see which restaurants these two numbers match up with. So if I go back to my list of restaurants, 17 and 9. So 17 here is Pazzaluna or excuse me, Osteria I Nonni. And the next one would be The Happy Gnome.

OK, so my wife and I would consider these two restaurants and then decide which one we'd want to go to more. I think I'd preferably like to go to The Happy Gnome. It's a pretty good restaurant.

So that has been your tutorial on simple random samples. Thanks for watching.

## Video Transcription

This tutorial covers systematic random samples. There's a couple different ways of taking a random sample. One way is called the simple random sample, which is abbreviated SRS. Another is a systematic random sample. We're going to concentrate on systematic random samples today.

A systematic random sample is defined as a sample where every kth individual is selected. So what I mean by kth is it could be the fifth person so every fifth person or every 12th person or every 100th person. So for example, suppose you're interested in sampling 20 people, so n equals 20, from a population of 200 standing in line for a movie.

A systematic random sample can be taken by selecting every 10th person in line. So if we take every 10th person from a population of 200, we'll end up with a sample of size 20. So that would be-- so this sample of size 20 would be a systematic random sample.

Just to kind of see how that would work, I have a smaller population here. So my population here is of size 18. So there's 18 little guys here. And let's say I'm looking for a sample of size n equals 6. So what that wouldn't mean is I would need to sample every 3rd person. And then each of those 6 people will become my sample.

So if I sample every third person, I would sample the third person, the sixth person, the ninth person, the 12th person, the 15th person, and the 18th person. So each of these six people would become my sample of n equals 6. So then each of those six people would be surveyed or studied depending on what type of research I was doing.

Now a common question that comes up is, is a systematic random sample also a simple random sample? So we go back to this example. Remember a simple random sample is when every person has an equal chance of being selected and every group of size n has an equal chance of being selected. So what I would say is for this group, depending where I start, everybody has an equal chance of being selected.

But what makes this not a simple random sample is, let's say, these first six people, if we look at these first six people, there's no way using systematic random sampling where these six people will make up my sample. Because of the way systematic sampling is done, there's no way that these six people can form my sample. So because of that, this is not a simple random sample.

So although a systematic random sample is random and generally representative, it's not considered an SRS or simple random sample. The other thing to note is when you're taking a systematic random sample is that it will not be representative if the population is already in some sort of order. So the people kind of have to be mixed up.

If they already are in order, it's probably best then just to do a simple random sample instead of a systematic random sample. But if they are kind of in a mixed order, usually a systematic random sample will give you a representative sample. So that's the tutorial on systematic random sampling. Thanks for watching.

Terms to Know
Random Number Generator

A method of collecting a sample that utilizes technology to select random numbers corresponding to individuals in the population

Random Number Table

A method of collecting a sample to select random numbers corresponding to individuals in the population. Each individual is assigned a number, which are then selected from the table.

Simple Random Sample

A method of selection that guarantees that every sample of a certain size has an equal chance of being the selected sample

Systematic Random Sample

A sampling method where every "k"th individual is selected for the sample (e.g. every 2nd, 4th, 20th individual)

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