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Today, Inshallah, we are going to start Chapter 7.

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Chapter 7 talks about sampling and sampling

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distributions. The objectives for this chapter are

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number one we have different methods actually we

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have two methods probability and non-probability

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samples and we are going to distinguish between

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these two sampling methods. So again, in this

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chapter, we will talk about two different sampling

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methods. One is called probability sampling and

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the other is non-probability sampling. Our goal is

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to distinguish between these two different

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sampling methods. The other learning objective

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will be We'll talk about the concept of the

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sampling distribution. That will be next time,

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inshallah. The third objective is compute

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probabilities related to sample mean. In addition

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to that, we'll talk about how can we compute

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probabilities regarding the sample proportion. And

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as I mentioned last time, There are two types of

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data. One is called the numerical data. In this

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case, we can use the sample mean. The other type

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is called qualitative data. And in this case, we

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have to use the sample proportion. So for this

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chapter, we are going to discuss how can we

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compute the probabilities for each one, either the

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sample mean or the sample proportion. The last

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objective of this chapter is to use the central

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limit theorem which is the famous one of the most

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famous theorem in this book which is called again

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CLT central limit theorem and we are going to show

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what are the what is the importance of this

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theorem so these are the mainly the four

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objectives for this chapter Now let's see why we

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are talking about sampling. In other words, most

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of the time when we are doing study, we are using

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a sample. instead of using the entire population.

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Now there are many reasons behind that. One of

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these reasons is selecting a sample is less time

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consuming than selecting every item in the

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population. I think it makes sense that suppose we

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have a huge population, that population consists

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of thousands of items. So that will take more time

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If you select 100 of their population. So time

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consuming is very important. So number one,

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selecting sample is less time consuming than using

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all the entire population. The second reason,

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selecting samples is less costly than selecting a

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variety of population. Because if we have large

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population, in this case you have to spend more

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money in order to get the data or the information

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from that population. So it's better to use these

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samples. The other reason is the analysis. Our

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sample is less cumbersome and more practical than

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analysis of all items in the population. For these

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reasons, we have to use a sample. For this reason,

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we have to talk about sampling methods. Let's

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start with sampling process. That begins with a

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seminal frame. Now suppose my goal is to know the

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opinion of IUG students about a certain subject.

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So my population consists of all IUG students. So

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that's the entire population. And you know that,

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for example, suppose our usual students is around,

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for example, 20,000 students. 20,000 students is a

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big number. So it's better to select a sample from

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that population. Now, the first step in this

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process, we have to determine the frame. of that

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population. So my frame consists of all IU

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students, which has maybe males and females. So my

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frame in this case is all items, I mean all

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students at IUG. So that's the frame. So my frame

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consists

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of all students.

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So the definition of

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the semantic frame is a listing of items that make

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up the population. The items could be individual,

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could be students, could be things, animals, and

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so on. So frames are data sources such as a

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population list. Suppose we have the names of IUDs

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humans. So that's my population list. Or

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directories, or maps, and so on. So that's the

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frame we have to know about the population we are

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interested in. Inaccurate or biased results can

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result if frame excludes certain portions of the

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population. For example, suppose here, as I

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mentioned, We are interested in IUG students, so

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my frame and all IU students. And I know there are

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students, either males or females. Suppose for

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some reasons, we ignore males, and just my sample

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focused on females. In this case, females.

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don't represent the entire population. For this

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reason, you will get inaccurate or biased results

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if you ignore a certain portion. Because here

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males, for example, maybe consists of 40% of the

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IG students. So it makes sense that this number or

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this percentage is a big number. So ignoring this

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portion, may lead to misleading results or

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inaccurate results or biased results. So you have

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to keep in mind that you have to choose all the

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portions of that frame. So inaccurate or biased

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results can result if a frame excludes certain

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portions of a population. Another example, suppose

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we took males and females. But here for females,

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females have, for example, four levels. Level one,

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level two, level three, and level four. And we

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ignored, for example, level one. I mean, the new

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students. We ignored this portion. Maybe this

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portion is very important one, but by mistake we

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ignored this one. The remaining three levels will

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not represent the entire female population. For

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this reason, you will get inaccurate or biased

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results. So you have to select all the portions of

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the frames. Using different frames to generate

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data can lead to dissimilar conclusions. For

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example, Suppose again I am interested in IEG

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students.

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And I took the frame that has all students at

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University of Gaza, Universities of Gaza.

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And as we know that Gaza has three universities,

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big universities, Islamic University, Lazar

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University, and Al-Aqsa University. So we have

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three universities. And my frame here, suppose I

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took all students at these universities, but my

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study focused on IU students. So my frame, the

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true one, is all students at IUG. But I taught all

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students at universities in Gaza. So now we have

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different frames.

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And you want to know what are the opinions of the

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smokers about smoking. So my population now is

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just...

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So that's my thing.

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I suppose I talk to a field that has one atom.

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Oh my goodness. They are very different things.

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The first one consists of only smokers. They are

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very interested in you. The other one consists

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of... Anonymous. I thought maybe... Smoker or non

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-smokers. For this reason, you will get...

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Conclusion, different results.

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So now,

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the sampling frame is a listing of items that make

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up the entire population. Let's move to the types

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of samples. Mainly there are two types of

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sampling. One is cold. Non-probability samples.

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The other one is called probability samples. The

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non-probability samples can be divided into two

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segments. One is called judgment and the other

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convenience. So we have judgment and convenience

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non-probability samples. The other type which is

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random probability samples has four segments or

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four parts. The first one is called simple random

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sample. The other one is systematic. The second

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one is systematic random sample. The third one is

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certified. The fourth one cluster random sample.

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So there are two types of sampling. Probability

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and non-probability. Non-probability has four

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methods here, simple random samples, systematic,

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stratified, and cluster. And the non-probability

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samples has two types, judgment and convenience.

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Let's see the definition of each type of samples.

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Let's start with non-probability sample. In non

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-probability sample, items included or chosen

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without regard to their probability of occurrence.

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So that's the definition of non-probability. For

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example.

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So again, non-probability sample, it means you

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select items without regard to their probability

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of occurrence. For example, suppose females

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consist of 70% of IUG students and males, the

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remaining percent is 30%. And suppose I decided to

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select a sample of 100 or 1000 students from IUG.

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Suddenly, I have a sample that has 650 males and

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350 females. Now, this sample, which has these

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numbers, for sure does not represent the entire

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population. Because females has 70%, and I took a

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random sample or a sample of size 350. So this

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sample is chosen without regard to the probability

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here. Because in this case, I should choose males

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with respect to their probability, which is 30%.

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But in this case, I just choose different

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proportions. Another example. Suppose

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Again, I am talking about smoking.

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And I know that some people are smoking and I just

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took this sample. So I took this sample based on

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my knowledge. So it's without regard to their

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probability. Maybe suppose I am talking about

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political opinions about something. And I just

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took the experts of that subject. So my sample is

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not a probability sample. And this one has, as we

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mentioned, has two types. One is called

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convenience sampling. In this case, items are

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selected based only on the fact that they are

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easy. So I choose that sample because it's easy.

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Inexpensive,

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inexpensive, or convenient to sample. If I choose

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my sample because it is easy or inexpensive, I

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think it doesn't make any sense, because easy. is

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not a reason to select that sample. Inexpensive I

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think is also is not that big reason. But if you

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select a sample because these items are convenient

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to assemble, it makes sense. So convenient sample

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can be chosen based on easy, inexpensive or

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convenient to assemble. On the other hand, In

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judgment sample, you get the opinions of pre

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-selected experts in the subject matter. For

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example, suppose we are talking about the causes

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of certain disease. Suppose we are talking about

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cancer.

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If I know the expert for this type of disease,

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that means you have judgment sample because you

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decided Before you select a sample that your

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sample should contain only the expert in

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cancer disease. So that's the judgment sampling.

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So in this case, I didn't take all the doctors in

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this case, I just taught the expert in cancer

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disease. So that's called non-probability samples.

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You have to make sense to distinguish between

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convenience sampling and judgment sample. So for

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judgment, you select a sample based on the prior

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information you have about the subject matter.

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Suppose I am talking about something related to

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psychology, so I have to take the expert in

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psychology. Suppose I am talking about expert in

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sports, so I have to take a sample from that

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segment and so on. But the convenient sample means

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that you select a sample maybe that is easy for

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you, or less expensive, or that sample is

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convenient. For this reason, it's called non

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-probability sample because we choose that sample

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without regard to their probability of occurrence.

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The other type is called probability samples. In

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this case, items are chosen on the basis of non

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-probabilities. For example, here, if males

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has or represent 30%, and females represent 70%,

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and the same size has a thousand. So in this case,

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you have to choose females with respect to their

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probability. Now 70% for females, so I have to

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choose 700 for females and the remaining 300 for

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males. So in this case, I choose the items, I mean

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I choose my samples regarding to their

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probability.

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So in probability sample items and the sample are

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chosen on the basis of known probabilities. And

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again, there are two types. of probability

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samples, simple random sample, systematic,

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stratified, and cluster. Let's talk about each one

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in details. The first type is called a probability

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sample. Simple random sample. The first type of

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probability sample is the easiest one. Simple

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random sample. Generally is denoted by SRS, Simple

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Random Sample. Let's see how can we choose a

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sample that is random. What do you mean by random?

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In this case, every individual or item from the

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frame has an equal chance of being selected. For

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example, suppose number of students in this class

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number of students is 52 so

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each one, I mean each student from

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1 up to 52 has the same probability of being

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selected. 1 by 52. 1 by 52. 1 divided by 52. So

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00:21:23,860 --> 00:21:27,980
each one has this probability. So the first one

259
00:21:27,980 --> 00:21:31,820
has the same because if I want to select for

260
00:21:31,820 --> 00:21:37,680
example 10 out of you. So the first one has each

261
00:21:37,680 --> 00:21:42,400
one has probability of 1 out of 52. That's the

262
00:21:42,400 --> 00:21:47,160
meaning ofEach item from the frame has an equal

263
00:21:47,160 --> 00:21:54,800
chance of being selected. Selection may be with

264
00:21:54,800 --> 00:21:58,800
replacement. With replacement means selected

265
00:21:58,800 --> 00:22:02,040
individuals is returned to the frame for

266
00:22:02,040 --> 00:22:04,880
possibility selection, or without replacement

267
00:22:04,880 --> 00:22:08,600
means selected individuals or item is not returned

268
00:22:08,600 --> 00:22:10,820
to the frame. So we have two types of selection,

269
00:22:11,000 --> 00:22:14,360
either with... So with replacement means item is

270
00:22:14,360 --> 00:22:18,080
returned back to the frame, or without population,

271
00:22:18,320 --> 00:22:21,400
the item is not returned back to the frame. So

272
00:22:21,400 --> 00:22:26,490
that's the two types of selection. Now how can we

273
00:22:26,490 --> 00:22:29,810
obtain the sample? Sample obtained from something

274
00:22:29,810 --> 00:22:33,470
called table of random numbers. In a minute I will

275
00:22:33,470 --> 00:22:36,430
show you the table of random numbers. And other

276
00:22:36,430 --> 00:22:40,130
method of selecting a sample by using computer

277
00:22:40,130 --> 00:22:44,890
random number generators. So there are two methods

278
00:22:44,890 --> 00:22:48,310
for selecting a random number. Either by using the

279
00:22:48,310 --> 00:22:51,950
table that you have at the end of your book or by

280
00:22:51,950 --> 00:22:56,550
using a computer. I will show one of these and in

281
00:22:56,550 --> 00:22:59,650
the SPSS course you will see another one which is

282
00:22:59,650 --> 00:23:03,690
by using a computer. So let's see how can we

283
00:23:03,690 --> 00:23:11,730
obtain a sample from table of

284
00:23:11,730 --> 00:23:12,590
random number.

285
00:23:16,950 --> 00:23:22,090
I have maybe different table here. But the same

286
00:23:22,090 --> 00:23:28,090
idea to use that table. Let's see how can we

287
00:23:28,090 --> 00:23:34,990
choose a sample by using a random number.

288
00:23:42,490 --> 00:23:47,370
Now, for example, suppose in this class As I

289
00:23:47,370 --> 00:23:51,090
mentioned, there are 52 students.

290
00:23:55,110 --> 00:23:58,650
So each one has a number, ID number one, two, up

291
00:23:58,650 --> 00:24:05,110
to 52. So the numbers are 01, 02, all the way up

292
00:24:05,110 --> 00:24:10,790
to 52. So the maximum digits here, two, two

293
00:24:10,790 --> 00:24:11,110
digits.

294
00:24:15,150 --> 00:24:18,330
1, 2, 3, up to 5, 2, 2, so you have two digits.

295
00:24:19,470 --> 00:24:23,710
Now suppose I decided to take a random sample of

296
00:24:23,710 --> 00:24:28,550
size, for example, N instead. How can I select N

297
00:24:28,550 --> 00:24:32,570
out of U? In this case, each one has the same

298
00:24:32,570 --> 00:24:36,790
chance of being selected. Now based on this table,

299
00:24:37,190 --> 00:24:44,230
you can pick any row or any column. Randomly. For

300
00:24:44,230 --> 00:24:51,630
example, suppose I select the first row. Now, the

301
00:24:51,630 --> 00:24:56,570
first student will be selected as student number

302
00:24:56,570 --> 00:25:03,650
to take two digits. We have to take how many

303
00:25:03,650 --> 00:25:08,770
digits? Because students have ID card that

304
00:25:08,770 --> 00:25:13,930
consists of two digits, 0102 up to 52. So, what's

305
00:25:13,930 --> 00:25:17,010
the first number students will be selected based

306
00:25:17,010 --> 00:25:22,130
on this table? Forget about the line 101.

307
00:25:26,270 --> 00:25:27,770
Start with this number.

308
00:25:42,100 --> 00:25:50,900
So the first one, 19. The second, 22. The third

309
00:25:50,900 --> 00:25:51,360
student,

310
00:25:54,960 --> 00:26:04,000
19, 22. The third, 9. The third, 9. I'm taking the

311
00:26:04,000 --> 00:26:16,510
first row. Then fifth. 34 student

312
00:26:16,510 --> 00:26:18,710
number 05

313
00:26:24,340 --> 00:26:29,500
Now, what's about seventy-five? Seventy-five is

314
00:26:29,500 --> 00:26:33,660
not selected because the maximum I have is fifty

315
00:26:33,660 --> 00:26:46,180
-two. Next. Sixty-two is not selected. Eighty

316
00:26:46,180 --> 00:26:53,000
-seven. It's not selected. 13. 13. It's okay.

317
00:26:53,420 --> 00:27:01,740
Next. 96. 96. Not selected. 14. 14 is okay. 91.

318
00:27:02,140 --> 00:27:12,080
91. 91. Not selected. 95. 91. 45. 85. 31. 31.

319
00:27:15,240 --> 00:27:21,900
So that's 10. So students numbers are 19, 22, 39,

320
00:27:22,140 --> 00:27:26,980
50, 34, 5, 13, 4, 25 and take one will be

321
00:27:26,980 --> 00:27:30,940
selected. So these are the ID numbers will be

322
00:27:30,940 --> 00:27:35,480
selected in order to get a sample of 10. You

323
00:27:35,480 --> 00:27:40,500
exclude

324
00:27:40,500 --> 00:27:43,440
that one. If the number is repeated, you have to

325
00:27:43,440 --> 00:27:44,340
exclude that one.

326
00:27:51,370 --> 00:27:57,270
is repeated, then excluded.

327
00:28:02,370 --> 00:28:07,370
So the returned number must be excluded from the

328
00:28:07,370 --> 00:28:14,030
sample. Let's imagine that we have not 52

329
00:28:14,030 --> 00:28:19,130
students. We have 520 students.

330
00:28:25,740 --> 00:28:32,520
Now, I have large number, 52, 520 instead of 52

331
00:28:32,520 --> 00:28:36,080
students. And again, my goal is to select just 10

332
00:28:36,080 --> 00:28:42,220
students out of 120. So each one has ID with

333
00:28:42,220 --> 00:28:46,220
number one, two, all the way up to 520. So the

334
00:28:46,220 --> 00:28:53,160
first one, 001. 002 all the way up to 520 now in

335
00:28:53,160 --> 00:28:56,480
this case you have to choose three digits start

336
00:28:56,480 --> 00:29:00,060
for example you don't have actually to start with

337
00:29:00,060 --> 00:29:03,060
row number one maybe column number one or row

338
00:29:03,060 --> 00:29:06,140
number two whatever is fine so let's start with

339
00:29:06,140 --> 00:29:10,460
row number two for example row number 76

340
00:29:14,870 --> 00:29:19,950
It's not selected. Because the maximum number I

341
00:29:19,950 --> 00:29:25,110
have is 5 to 20. So, 746 shouldn't be selected.

342
00:29:26,130 --> 00:29:29,430
The next one, 764.

343
00:29:31,770 --> 00:29:38,750
Again, it's not selected. 764, 715. Not selected.

344
00:29:38,910 --> 00:29:42,310
Next one is 715.

345
00:29:44,880 --> 00:29:52,200
099 should be 0 that's

346
00:29:52,200 --> 00:29:54,940
the way how can we use the random table for using

347
00:29:54,940 --> 00:29:58,800
or for selecting simple random symbols so in this

348
00:29:58,800 --> 00:30:03,480
case you can choose any row or any column then you

349
00:30:03,480 --> 00:30:06,620
have to decide how many digits you have to select

350
00:30:06,620 --> 00:30:10,500
it depends on the number you have I mean the

351
00:30:10,500 --> 00:30:16,510
population size If for example Suppose I am

352
00:30:16,510 --> 00:30:20,270
talking about IUPUI students and for example, we

353
00:30:20,270 --> 00:30:26,530
have 30,000 students at this school And again, I

354
00:30:26,530 --> 00:30:28,570
want to select a random sample of size 10 for

355
00:30:28,570 --> 00:30:35,190
example So how many digits should I use? 20,000

356
00:30:35,190 --> 00:30:42,620
Five digits And each one, each student has ID

357
00:30:42,620 --> 00:30:51,760
from, starts from the first one up to twenty

358
00:30:51,760 --> 00:30:56,680
thousand. So now, start with, for example, the

359
00:30:56,680 --> 00:30:59,240
last row you have.

360
00:31:03,120 --> 00:31:08,480
The first number 54000 is not. 81 is not. None of

361
00:31:08,480 --> 00:31:08,740
these.

362
00:31:12,420 --> 00:31:17,760
Look at the next one. 71000 is not selected. Now

363
00:31:17,760 --> 00:31:22,180
9001. So the first number I have to select is

364
00:31:22,180 --> 00:31:27,200
9001. None of the rest. Go back.

365
00:31:30,180 --> 00:31:37,790
Go to the next one. The second number, 12149

366
00:31:37,790 --> 00:31:45,790
and so on. Next will be 18000 and so on. Next row,

367
00:31:46,470 --> 00:31:55,530
we can select the second one, then 16, then 14000,

368
00:31:55,890 --> 00:32:00,850
6500 and so on. So this is the way how can we use

369
00:32:00,850 --> 00:32:08,110
the random table. It seems to be that tons of work

370
00:32:08,110 --> 00:32:13,450
if you have large sample. Because in this case,

371
00:32:13,530 --> 00:32:16,430
you have to choose, for example, suppose I am

372
00:32:16,430 --> 00:32:22,390
interested to take a random sample of 10,000. Now,

373
00:32:22,510 --> 00:32:28,370
to use this table to select 10,000 items takes

374
00:32:28,370 --> 00:32:33,030
time and effort and maybe will never finish. So

375
00:32:33,030 --> 00:32:33,950
it's better to use

376
00:32:38,020 --> 00:32:42,100
better to use computer

377
00:32:42,100 --> 00:32:47,140
random number generators. So that's the way if we,

378
00:32:47,580 --> 00:32:51,880
now we can use the random table only if the sample

379
00:32:51,880 --> 00:32:57,780
size is limited. I mean up to 100 maybe you can

380
00:32:57,780 --> 00:33:03,160
use the random table, but after that I think it's

381
00:33:03,160 --> 00:33:08,670
just you are losing your time. Another example

382
00:33:08,670 --> 00:33:14,390
here. Now suppose my sampling frame for population

383
00:33:14,390 --> 00:33:23,230
has 850 students. So the numbers are 001, 002, all

384
00:33:23,230 --> 00:33:28,490
the way up to 850. And suppose for example we are

385
00:33:28,490 --> 00:33:33,610
going to select five items randomly from that

386
00:33:33,610 --> 00:33:39,610
population. So you have to choose three digits and

387
00:33:39,610 --> 00:33:44,990
imagine that this is my portion of that table.

388
00:33:45,850 --> 00:33:51,570
Now, take three digits. The first three digits are

389
00:33:51,570 --> 00:34:00,330
492. So the first item chosen should be item

390
00:34:00,330 --> 00:34:10,540
number 492. should be selected next one 800 808

391
00:34:10,540 --> 00:34:17,020
doesn't select because the maximum it's much

392
00:34:17,020 --> 00:34:21,100
selected because the maximum here is 850 now next

393
00:34:21,100 --> 00:34:26,360
one 892 this

394
00:34:26,360 --> 00:34:32,140
one is not selected next

395
00:34:32,140 --> 00:34:43,030
item four three five selected now

396
00:34:43,030 --> 00:34:50,710
seven seven nine should be selected finally zeros

397
00:34:50,710 --> 00:34:53,130
two should be selected so these are the five

398
00:34:53,130 --> 00:34:58,090
numbers in my sample by using selected by using

399
00:34:58,090 --> 00:35:01,190
the random sample any questions?

400
00:35:04,160 --> 00:35:07,780
Let's move to another part.

401
00:35:17,600 --> 00:35:22,380
The next type of samples is called systematic

402
00:35:22,380 --> 00:35:25,260
samples.

403
00:35:29,120 --> 00:35:35,780
Now suppose N represents the sample size, capital

404
00:35:35,780 --> 00:35:40,520
N represents

405
00:35:40,520 --> 00:35:42,220
the population size.

406
00:35:46,660 --> 00:35:49,900
And let's see how can we choose a systematic

407
00:35:49,900 --> 00:35:54,040
random sample from that population. For example,

408
00:35:55,260 --> 00:35:57,180
suppose

409
00:35:59,610 --> 00:36:05,010
For this specific slide, there are 40 items in the

410
00:36:05,010 --> 00:36:11,370
population. And my goal is to select a sample of

411
00:36:11,370 --> 00:36:16,210
size 4 by using systematic random sampling. The

412
00:36:16,210 --> 00:36:23,290
first step is to find how many individuals will be

413
00:36:23,290 --> 00:36:28,990
in any group. Let's use this letter K.

414
00:36:31,820 --> 00:36:36,940
divide N by, divide frame of N individuals into

415
00:36:36,940 --> 00:36:42,900
groups of K individuals. So, K equal capital N

416
00:36:42,900 --> 00:36:48,840
over small n, this is number of items in a group.

417
00:36:51,570 --> 00:36:56,510
So K represents number of subjects or number of

418
00:36:56,510 --> 00:37:02,750
elements in a group. So for this example, K equals

419
00:37:02,750 --> 00:37:09,710
40 divided by 4, so 10. So the group, each group

420
00:37:09,710 --> 00:37:11,670
has 10 items.

421
00:37:16,630 --> 00:37:23,140
So each group has 10 items.

422
00:37:27,420 --> 00:37:33,860
So group number 1, 10 items, and others have the

423
00:37:33,860 --> 00:37:38,660
same number. So first step, we have to decide how

424
00:37:38,660 --> 00:37:42,110
many items will be in the group. And that number

425
00:37:42,110 --> 00:37:45,330
equals N divided by small n, capital N divided by

426
00:37:45,330 --> 00:37:48,910
small n. In this case, N is 40, the sample size is

427
00:37:48,910 --> 00:37:54,170
4, so there are 10 items in each individual. Next

428
00:37:54,170 --> 00:38:02,850
step, select randomly the first individual from

429
00:38:02,850 --> 00:38:08,620
the first group. For example, here. Now, how many

430
00:38:08,620 --> 00:38:13,360
we have here? We have 10 items. So, numbers are

431
00:38:13,360 --> 00:38:19,060
01, 02, up to 10. I have to choose one more number

432
00:38:19,060 --> 00:38:23,680
from these numbers, from 1 to 10, by using the

433
00:38:23,680 --> 00:38:27,600
random table again. So, I have to go back to the

434
00:38:27,600 --> 00:38:33,730
random table and I choose two digits. Now the

435
00:38:33,730 --> 00:38:36,490
first one is nineteen, twenty-two, thirty-nine,

436
00:38:37,130 --> 00:38:43,450
fifty, thirty-four, five. So I have to see. So

437
00:38:43,450 --> 00:38:46,230
number one is five. What's the next one? The next

438
00:38:46,230 --> 00:38:54,190
one just add K. K is ten. So next is fifteen. Then

439
00:38:54,190 --> 00:38:58,010
twenty-five, then thirty-four.

440
00:39:02,900 --> 00:39:08,840
Number size consists of four items. So the first

441
00:39:08,840 --> 00:39:12,740
number is chosen randomly by using the random

442
00:39:12,740 --> 00:39:17,260
table. The next number just add the step. This is

443
00:39:17,260 --> 00:39:24,340
step. So my step is 10 because number one is five.

444
00:39:25,300 --> 00:39:27,800
The first item I mean is five. Then it should be

445
00:39:27,800 --> 00:39:31,780
15, 25, 35, and so on if we have more than that.

446
00:39:33,230 --> 00:39:37,730
Okay, so that's for, in this example, he choose

447
00:39:37,730 --> 00:39:42,790
item number seven. Random selection, number seven.

448
00:39:43,230 --> 00:39:50,010
So next should be 17, 27, 37, and so on. Let's do

449
00:39:50,010 --> 00:39:50,710
another example.

450
00:39:58,590 --> 00:40:06,540
Suppose there are In this class, there are 50

451
00:40:06,540 --> 00:40:12,400
students. So the total is 50.

452
00:40:15,320 --> 00:40:26,780
10 students out of 50. So my sample is 10. Now

453
00:40:26,780 --> 00:40:30,260
still, 50 divided by 10 is 50.

454
00:40:33,630 --> 00:40:39,650
So there are five items or five students in a

455
00:40:39,650 --> 00:40:45,370
group. So we have five in

456
00:40:45,370 --> 00:40:51,490
the first group and then five in the next one and

457
00:40:51,490 --> 00:40:56,130
so on. So we have how many groups? Ten groups.

458
00:40:59,530 --> 00:41:04,330
So first step, you have to find a step. Still it

459
00:41:04,330 --> 00:41:07,930
means number of items or number of students in a

460
00:41:07,930 --> 00:41:16,170
group. Next step, select student at random from

461
00:41:16,170 --> 00:41:22,010
the first group, so random selection. Now, here

462
00:41:22,010 --> 00:41:28,610
there are five students, so 01, I'm sorry, not 01,

463
00:41:29,150 --> 00:41:35,080
1, 2, 3, 4, 5, so one digit. Only one digit.

464
00:41:35,800 --> 00:41:39,420
Because I have maximum number is five. So it's

465
00:41:39,420 --> 00:41:42,920
only one digit. So go again to the random table

466
00:41:42,920 --> 00:41:48,220
and take one digit. One. So my first item, six,

467
00:41:48,760 --> 00:41:52,580
eleven, sixteen, twenty-one, twenty-one, all the

468
00:41:52,580 --> 00:41:55,500
way up to ten items.

469
00:42:13,130 --> 00:42:18,170
So I choose student number one, then skip five,

470
00:42:19,050 --> 00:42:22,230
choose number six, and so on. It's called

471
00:42:22,230 --> 00:42:26,130
systematic. Because if you know the first item,

472
00:42:28,550 --> 00:42:32,690
and the step you can know the rest of these.

473
00:42:37,310 --> 00:42:41,150
Imagine that you want to select 10 students who

474
00:42:41,150 --> 00:42:48,010
entered the cafe shop or restaurant. You can pick

475
00:42:48,010 --> 00:42:54,790
one of them. So suppose I'm taking number three

476
00:42:54,790 --> 00:43:00,550
and my step is six. So three, then nine, and so

477
00:43:00,550 --> 00:43:00,790
on.

478
00:43:05,830 --> 00:43:13,310
So that's systematic assembly. Questions? So

479
00:43:13,310 --> 00:43:20,710
that's about random samples and systematic. What

480
00:43:20,710 --> 00:43:23,550
do you mean by stratified groups?

481
00:43:28,000 --> 00:43:33,080
Let's use a definition and an example of a

482
00:43:33,080 --> 00:43:34,120
stratified family.

483
00:43:58,810 --> 00:44:05,790
step one. So again imagine we have IUG population

484
00:44:05,790 --> 00:44:11,490
into two or more subgroups. So there are two or

485
00:44:11,490 --> 00:44:16,010
more. It depends on the characteristic you are

486
00:44:16,010 --> 00:44:19,690
using. So divide population into two or more

487
00:44:19,690 --> 00:44:24,210
subgroups according to some common characteristic.

488
00:44:24,730 --> 00:44:30,280
For example suppose I want to divide the student

489
00:44:30,280 --> 00:44:32,080
into gender.

490
00:44:34,100 --> 00:44:38,840
So males or females. So I have two strata. One is

491
00:44:38,840 --> 00:44:43,000
called males and the other is females. Now suppose

492
00:44:43,000 --> 00:44:47,460
the characteristic I am going to use is the levels

493
00:44:47,460 --> 00:44:51,500
of a student. First level, second, third, fourth,

494
00:44:51,800 --> 00:44:56,280
and so on. So number of strata here depends on

495
00:44:56,280 --> 00:45:00,380
actually the characteristic you are interested in.

496
00:45:00,780 --> 00:45:04,860
Let's use the simple one that is gender. So here

497
00:45:04,860 --> 00:45:12,360
we have females. So IUV students divided into two

498
00:45:12,360 --> 00:45:18,560
types, strata, or two groups, females and males.

499
00:45:19,200 --> 00:45:22,870
So this is the first step. So at least you should

500
00:45:22,870 --> 00:45:26,750
have two groups or two subgroups. So we have IELTS

501
00:45:26,750 --> 00:45:29,630
student, the entire population, and that

502
00:45:29,630 --> 00:45:34,370
population divided into two subgroups. Next,

503
00:45:35,650 --> 00:45:39,730
assemble random samples. Keep careful here with

504
00:45:39,730 --> 00:45:45,770
sample sizes proportional to strata sizes. That

505
00:45:45,770 --> 00:45:57,890
means suppose I know that Female consists

506
00:45:57,890 --> 00:46:02,470
of

507
00:46:02,470 --> 00:46:09,770
70% of Irish students and

508
00:46:09,770 --> 00:46:11,490
males 30%.

509
00:46:15,410 --> 00:46:17,950
the sample size we are talking about here is for

510
00:46:17,950 --> 00:46:21,550
example is a thousand so I want to select a sample

511
00:46:21,550 --> 00:46:24,990
of a thousand seed from the registration office or

512
00:46:24,990 --> 00:46:31,190
my information about that is males represent 30%

513
00:46:31,190 --> 00:46:37,650
females represent 70% so in this case your sample

514
00:46:37,650 --> 00:46:43,650
structure should be 70% times

515
00:46:50,090 --> 00:46:59,090
So the first

516
00:46:59,090 --> 00:47:03,750
group should have 700 items of students and the

517
00:47:03,750 --> 00:47:06,490
other one is 300,000.

518
00:47:09,230 --> 00:47:11,650
So this is the second step.

519
00:47:14,420 --> 00:47:17,740
Sample sizes are determined in step number two.

520
00:47:18,540 --> 00:47:22,200
Now, how can you select the 700 females here?

521
00:47:23,660 --> 00:47:26,180
Again, you have to go back to the random table.

522
00:47:27,480 --> 00:47:31,660
Samples from subgroups are compiled into one. Then

523
00:47:31,660 --> 00:47:39,600
you can use symbol random sample. So here, 700. I

524
00:47:39,600 --> 00:47:45,190
have, for example, 70% females. And I know that I

525
00:47:45,190 --> 00:47:51,370
use student help. I have ideas numbers from 1 up

526
00:47:51,370 --> 00:47:59,070
to 7, 14. Then by using simple random, simple

527
00:47:59,070 --> 00:48:01,070
random table, you can.

528
00:48:09,490 --> 00:48:15,190
So if you go back to the table, the first item,

529
00:48:16,650 --> 00:48:23,130
now look at five digits. Nineteen is not selected.

530
00:48:24,830 --> 00:48:27,510
Nineteen. I have, the maximum is fourteen

531
00:48:27,510 --> 00:48:31,890
thousand. So skip one and two. The first item is

532
00:48:31,890 --> 00:48:37,850
seven hundred and fifty-six. The first item. Next

533
00:48:37,850 --> 00:48:43,480
is not chosen. Next is not chosen. Number six.

534
00:48:43,740 --> 00:48:44,580
Twelve.

535
00:48:47,420 --> 00:48:50,620
Zero. Unsure.

536
00:48:52,880 --> 00:48:58,940
So here we divide the population into two groups

537
00:48:58,940 --> 00:49:03,440
or two subgroups, females and males. And we select

538
00:49:03,440 --> 00:49:07,020
a random sample of size 700 based on the

539
00:49:07,020 --> 00:49:10,850
proportion of this subgroup. Then we are using the

540
00:49:10,850 --> 00:49:16,750
simple random table to take the 700 females.

541
00:49:22,090 --> 00:49:29,810
Now for this example, there are 16 items or 16

542
00:49:29,810 --> 00:49:35,030
students in each group. And he select randomly

543
00:49:35,030 --> 00:49:40,700
number three, number 9, number 13, and so on. So

544
00:49:40,700 --> 00:49:44,140
it's a random selection. Another example.

545
00:49:46,820 --> 00:49:52,420
Suppose again we are talking about all IUVs.

546
00:50:02,780 --> 00:50:09,360
Here I divided the population according to the

547
00:50:09,360 --> 00:50:17,680
students' levels. Level one, level two, three

548
00:50:17,680 --> 00:50:18,240
levels.

549
00:50:25,960 --> 00:50:28,300
One, two, three and four.

550
00:50:32,240 --> 00:50:39,710
So I divide the population into four subgroups

551
00:50:39,710 --> 00:50:43,170
according to the student levels. So one, two,

552
00:50:43,290 --> 00:50:48,030
three, and four. Now, a simple random sample is

553
00:50:48,030 --> 00:50:52,070
selected from each subgroup with sample sizes

554
00:50:52,070 --> 00:50:57,670
proportional to strata size. Imagine that level

555
00:50:57,670 --> 00:51:04,950
number one represents 40% of the students. Level

556
00:51:04,950 --> 00:51:17,630
2, 20%. Level 3, 30%. Just

557
00:51:17,630 --> 00:51:22,850
an example. To make more sense?

558
00:51:34,990 --> 00:51:36,070
My sample size?

559
00:51:38,750 --> 00:51:39,910
3,

560
00:51:41,910 --> 00:51:46,430
9, 15, 4, sorry.

561
00:51:53,290 --> 00:52:00,470
So here, there are four levels. And the

562
00:52:00,470 --> 00:52:04,370
proportions are 48

563
00:52:06,670 --> 00:52:17,190
sample size is 500 so the sample for each strata

564
00:52:17,190 --> 00:52:31,190
will be number 1 40% times 500 gives 200 the next

565
00:52:31,190 --> 00:52:32,950
150

566
00:52:36,200 --> 00:52:42,380
And so on. Now, how can we choose the 200 from

567
00:52:42,380 --> 00:52:46,280
level number one? Again, we have to choose the

568
00:52:46,280 --> 00:52:55,540
random table. Now, 40% from this number, it means

569
00:52:55,540 --> 00:52:59,620
5

570
00:52:59,620 --> 00:53:06,400
,000. This one has 5,000. 600 females students.

571
00:53:07,720 --> 00:53:13,480
Because 40% of females in level 1. And I know that

572
00:53:13,480 --> 00:53:17,780
the total number of females is 14,000. So number

573
00:53:17,780 --> 00:53:23,420
of females in the first level is 5600. How many

574
00:53:23,420 --> 00:53:28,040
digits we have? Four digits. The first one, 001,

575
00:53:28,160 --> 00:53:34,460
all the way up to 560. If you go back, into a

576
00:53:34,460 --> 00:53:39,520
random table, take five, four digits. So the first

577
00:53:39,520 --> 00:53:43,340
number is 1922.

578
00:53:43,980 --> 00:53:48,000
Next is 3950.

579
00:53:50,140 --> 00:53:54,760
And so on. So that's the way how can we choose

580
00:53:54,760 --> 00:53:58,640
stratified samples.

581
00:54:02,360 --> 00:54:08,240
Next, the last one is called clusters. And let's

582
00:54:08,240 --> 00:54:11,400
see now what's the difference between stratified

583
00:54:11,400 --> 00:54:16,500
and cluster. Step one.

584
00:54:25,300 --> 00:54:31,720
Population is divided into some clusters.

585
00:54:35,000 --> 00:54:41,160
Step two, assemble one by assembling clusters

586
00:54:41,160 --> 00:54:42,740
selective.

587
00:54:46,100 --> 00:54:48,640
Here suppose how many clusters?

588
00:54:53,560 --> 00:54:58,080
16 clusters. So there are, so the population has

589
00:55:19,310 --> 00:55:25,820
Step two, you have to choose a simple random

590
00:55:25,820 --> 00:55:31,440
number of clusters out of 16. Suppose I decided to

591
00:55:31,440 --> 00:55:38,300
choose three among these. So we have 16 clusters.

592
00:55:45,340 --> 00:55:49,780
For example, I chose cluster number 411.

593
00:55:51,640 --> 00:56:01,030
So I choose these clusters. Next, all items in the

594
00:56:01,030 --> 00:56:02,910
selected clusters can be used.

595
00:56:09,130 --> 00:56:15,770
Or items

596
00:56:15,770 --> 00:56:18,910
can be chosen from a cluster using another

597
00:56:18,910 --> 00:56:21,130
probability sampling technique. For example,

598
00:56:23,190 --> 00:56:28,840
imagine that We are talking about students who

599
00:56:28,840 --> 00:56:31,460
registered for accounting.

600
00:56:45,880 --> 00:56:50,540
Imagine that we have six sections for accounting.

601
00:56:55,850 --> 00:56:56,650
six sections.

602
00:57:00,310 --> 00:57:05,210
And I just choose two of these, cluster number one

603
00:57:05,210 --> 00:57:08,910
or section number one and the last one. So my

604
00:57:08,910 --> 00:57:12,590
chosen clusters are number one and six, one and

605
00:57:12,590 --> 00:57:19,090
six. Or you can use the one we just talked about,

606
00:57:19,590 --> 00:57:23,340
stratified random sample. instead of using all for

607
00:57:23,340 --> 00:57:29,140
example suppose there are in this section there

608
00:57:29,140 --> 00:57:36,180
are 73 models and the other one there are 80

609
00:57:36,180 --> 00:57:42,300
models and

610
00:57:42,300 --> 00:57:46,720
the sample size here I am going to use case 20

611
00:57:50,900 --> 00:57:56,520
So you can use 10 here and 10 in the other one, or

612
00:57:56,520 --> 00:58:03,060
it depends on the proportions. Now, 70 represents

613
00:58:03,060 --> 00:58:09,580
70 out of 150, because there are 150 students in

614
00:58:09,580 --> 00:58:14,060
these two clusters. Now, the entire population is

615
00:58:14,060 --> 00:58:17,300
not the number for each of all of these clusters,

616
00:58:17,560 --> 00:58:22,310
just number one sixth. So there are 150 students

617
00:58:22,310 --> 00:58:25,090
in these two selected clusters. So the population

618
00:58:25,090 --> 00:58:30,030
size is 150. Make sense? Then the proportion here

619
00:58:30,030 --> 00:58:33,210
is 700 divided by 150 times 20.

620
00:58:35,970 --> 00:58:41,610
The other one, 80 divided by 150 times 20.

621
00:58:51,680 --> 00:58:55,960
So again, all items in the selected clusters can

622
00:58:55,960 --> 00:58:59,400
be used or items can be chosen from the cluster

623
00:58:59,400 --> 00:59:01,500
using another probability technique as we

624
00:59:01,500 --> 00:59:06,640
mentioned. Let's see how can we use another

625
00:59:06,640 --> 00:59:10,860
example. Let's talk about again AUG students.

626
00:59:28,400 --> 00:59:31,800
I choose suppose level number 2 and level number

627
00:59:31,800 --> 00:59:37,680
4, two levels, 2 and 4. Then you can take either

628
00:59:37,680 --> 00:59:43,380
all the students here or just assemble size

629
00:59:43,380 --> 00:59:46,460
proportion to the

630
00:59:50,310 --> 00:59:54,130
For example, this one represents 20%, and my

631
00:59:54,130 --> 00:59:56,730
sample size is 1000, so in this case you have to

632
00:59:56,730 --> 01:00:00,310
take 200 and 800 from that one.

633
01:00:03,050 --> 01:00:04,050
Any questions?