Statistics Sampling Methods

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We are going to be talking about sampling methods.0003

Previously we talked a lot about bias sampling methods and the different kinds of problems that those have.0007

Now we are going to talk about unbiased sampling methods, sort of the good guys.0012

These methods are all called probability sampling methods.0018

As you could tell the biased sampling methods like convenience sampling and judgment sampling methods those are called nonprobability sampling methods.0022

Biased sampling or non-probability sampling methods.0032

Those kinds of sampling methods are ones that we already talked about sampling from volunteers, convenience sampling and also judgment sampling.0047

These kinds of sampling methods, the method itself is not that great.0056

You might in depth with representative of sample, but the problem is the method is not that great and because of that there is always the suspicion of biased.0062

In unbiased sampling or probability sampling the idea is that the sampling method itself is robust and trustworthy.0075

It is not a guarantee that you will end up with a representative sample, but the method is unbiased.0089

So because of that we are more likely to trust this kind of sample than one of these kinds of sampling methods.0096

The basic principle behind all unbiased sampling is the idea of trusting in randomness because you are going to be using randomness.0104

This means that humans are biased, we do not know what kind of biases we are going to introduce.0116

We are not going to be using judgments.0123

We are not going to be just using convenience or whatever is around us.0125

We are not just going to sample from volunteers.0129

We are going to sample randomly and that does not mean randomly as I do not know what is going on.0132

We are going to sample in a probabilistic way such that we get this uniformly random sample.0140

There are five different kinds of probability sampling methods that you should know about.0154

The first one is this, pretend these are all different kinds of people, lakes, or animals or items or whatever or ice cream pints in our population.0159

In a simple random sample what you would do is get a directory or a list of all person in the population.0175

By using random numbers, number of every person of and then by picking random numbers you are going to pick a subset of that population.0190

You will number everybody in 1 through 1000 and then pick random numbers either from a random number generator and end up with a random sample.0204

This is a pretty difficult kind of sampling method because you have to list the entire population first.0232

This is often only used in a limited number of cases.0242

The next is stratified random sampling and this is actually a little closer to judgment sampling,0248

sort of like a mix of judgment sampling and simple random sampling.0255

First what you do is you divide your population into meaningful strata, into meaningful groupings that are somehow important to your study.0260

If size is important then you might separate by size first.0270

If gender is important, if the city is important, if cost is important, whatever it is you stratify, you create strata first, groupings first0274

Once you have created these groupings then you use simple random.0288

Then you list everyone in this little strata, use random numbers in order to pick a subset right and then you do that for this strata and you also do it for the strata.0293

In that way you make sure to have a little bit of each strata in your sample.0316

Cluster sampling is a way of picking clusters first and then you take everybody in there as your sample.0326

One common place that this is used is often in things like sampling from schools.0336

Sampling from schools is often easier than sampling students.0348

It is easier to list all of the elementary schools in your district than to list all of the elementary school students in your district.0352

You might list all of the elementary schools and then you use simple random sampling to sample one of these clusters0361

or two of these clusters or however many you want.0370

Right and then you take everybody in that cluster.0373

Maybe you will study these two elementary schools and study everybody in them.0377

Another kind of cluster sampling is called 2 stage sampling.0385

2 stage sampling is first doing cluster sampling and then next once you have the cluster then you do simple random sampling.0390

You start with cluster sampling.0401

You pick the clusters randomly then once you have the clusters you use simple random where you list everybody in your cluster0403

and then use random numbers in order to pick people in that sample.0419

We might pick just those individuals, not everybody in that cluster.0428

That is the difference between cluster sampling and 2 stage sampling.0433

Cluster sampling only picks the cluster and then you are done.0437

Here you put the cluster once you have the cluster then you do simple random.0440

Finally, we have something called systematic sampling.0447

Here this may be used at a factory and they might choose every case item to some variable and every case items to be picked for sampling.0450

Let us say at Ben & Jerry's ice cream factory and they pick every 230th pint that comes off the factory line to be picked for quality control.0467

For this example, maybe I will pick just 10.0485

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 so they will pick that one.0487

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 they will pick that one.0493

They will systematically go through and pick every 10th pint or 200 pint or 1000 pint.0498

That would be systematic sampling.0508

Let us go into examples.0513

Example 1, a pharmaceutical company sampled their drug to see whether the potency of the pills match the potency claimed on the bottle.0518

Every 20th box off the factory line was pulled out and 3 bottles were picked randomly and then 10 pills were sampled at random.0527

Which types of sampling was this?0537

First there is systematic sampling right.0542

And that is taking every 20th box, equals 20 here.0552

Every 20th box of the factory line was pulled out and then 3 bottles were picked randomly.0557

That cluster.0564

But then 10 pills where sampled randomly from those bottles.0568

That is two stages.0583

That would be both cluster plus simple random.0584

By sampling the 10 pills randomly we do not just mean that they just shoot out 10 their hands0592

instead they would have to take those however many pills are in that box to get random numbers.0598

Take out 10.0610

That is how they need to choose 10 in order to do simple random.0612

Example 2, supposed you want to estimate the average number of capital letters per printed line in order to sample the readability of a book.0619

Describe how to take a two-stage sample from this book.0628

First we need to figure out what the clusters are.0632

You can have clusters B chapters, you can have cluster B lines, paragraphs, or sentences.0636

You do not have to decide what the clusters are.0643

You would have to pick the samples in order to and then you have to pick another subset of those clusters in order to do simple random.0648

Maybe in 2 stage the first way to cluster and so maybe I will pick pages.0664

Pages will be my cluster and so what I will do as I will have all the numbers of the pages and then generate 10 random numbers and then pick those 10 pages.0674

First I will pick the pages then I use simple random in order to pick which lines and then I will count the capital letters.0687

Then pick lines and then I will count capital letters in those lines and get an average.0700

And then I can look at averages, standard deviations, those kinds of stuff once I have that data.0712

Example 3, the American pet lovers association has a directory of 10,000 members.0720

You want to send out a survey to 1000 people randomly.0725

How would you go about doing this?0729

Well in this case we have a directory so we could use just the simple random if we wanted to.0731

I do not know if you wanted to do it and maybe you want to have strata sampling, two separate people0740

into even numbers of dog lovers and cat lovers and bird lovers whatever else.0748

One we could just start off is just doing simple random.0754

You take all 10,000 of those numbers, number them all, generate 1000 random numbers and send surveys out to those 1000 people.0758

Example 4, to see how well US third graders do on arithmetic test, you will choose a simple random sample0770

of children enrolled in the third grade and give them math test .0777

Describe how to change this into a cluster sample plan.0780

When my cluster sample be a more practical plan.0784

Generating a list of all the children enrolled in third grade in the United States may be pretty hard.0789

It might be easier although not easy to make a list of districts first and then out of sampling those districts0795

then we might want to sample schools and then sample third-graders.0810