 One of the things you'll be expected to do is actually describe a methodology for choosing a random sample and mechanically there are two ways to do that. One is using a random number table and the second is using a technology like a calculator or a computer. Table B in your book actually is a table of random numbers and there's a link to table B on Moodle. If you don't have a book you can look to table B in Moodle for it. In this video it talks about how to select a random sample using table B. A separate video will talk about the mechanics of generating random numbers on a calculator so that you can use a calculator to do it. But it's quite likely on, well it is certain on our tests and likely on the AP test that you might be asked to describe a methodology for choosing a random sample or for taking a group and randomly dividing it into treatment groups for an experiment. This is part of picking a simple random sample. This also might be part of the other three methods that are actually two of the methods that use random sampling. Systematic sampling and cluster sampling both require you to randomly select individuals within groups in the case of stratified sampling or clusters randomly select clusters in the case of cluster sampling. Now remember the point of random selection is to avoid bias. You saw this slide in a different presentation. Voluntary and convenient sampling don't have randomization in them. We improve those methodologies by introducing randomization and so these four methods use random selection in some form. Alright this is literally a picture of table B in your book. It is a table of random numbers. That is there is no pattern whatsoever to the numbers you see here. Just in terms of using the table note that these are just line numbers. They are not part of the random number pattern here. Sorry I should say random number pattern. They're not part of the random numbers. Your book will say something like go to line 103 and randomly select dot dot dot and the reason your book does that is so that everybody gets the same answer and you can see whether you've done the methodology right by looking up the answer in the back of the book. But it's a table of random digits. In theory you could start anywhere on this table you wanted to conduct random selection. What does it mean to be random? Well it means each entry in the table is equally likely to be any number between zero and nine. Makes sense. And each entry is independent of the next. So the fact that one number is zero has no impact on the next number. So in fact it's possible even in a random number table to have three zeros in a row it's also possible to have three numbers in a row that are different. Okay when choosing a random sample and this is specific to using a random number table it's slightly different when generating your own random numbers. We're going to assign a numerical label to every individual in the population. So let's just deal with something simple. Let's deal with a classroom of 30 students. What this means is that every student in the class is going to get a number assigned to a numerical label. They have to have the same number of digits and then we're going to use the shortest possible number of digits. So if I have a class of 30 I'm going to number them zero one to 30. Not one to 30. Each random number has to have this each number sorry numerical label has to have the same number of digits. The problem with using one to 30 is when we use the random number table it's difficult to know how many numbers I should pick at a time. If everybody has two digit labels then it's easy to go two digits at a time and start picking people. So same number of digits. If I have a hundred people I want to use the shortest number of possible digits. Well you might think okay I'll go zero zero one to 100 but that's actually not the shortest number of possible digits. The shortest is zero zero to 99. That's a hundred numbers and it's the shortest possible number of digits. Once the individuals are labeled then we can use random numbers to select people starting at a certain row. We ignore the breaks in the row numbers so these breaks in the table here are simply meant to make it readable. These two numbers can be taken together as a two digit random number and as I said earlier the line numbers can be ignored. You can also get to the end of a row and go on to the next row. One of the things we have to worry about is repeats. If I'm selecting randomly from within a classroom and I have a certain student who's number 27 what happens if I pick 27 twice off the random number table. Two things might happen. I might ignore the second 27 because I've already selected the person. But if my sampling is with what we call replacement if I pick person 27 and I put them back in it might be okay to pick them again. So that's just a function of what we want to have happen and we have to talk about that. And then we also have to talk about what we're going to do with numbers outside our domain. I've numbered my students from 01 to 30. What if the random number that comes up happens to be 54? Well most likely we're going to ignore that. So when you're asked to define a methodology you're going to talk about how do I number people? How do I handle repeats? And then how do I handle numbers outside the domain? Now how do I number people is pretty straightforward? Repeats depends on whether it's okay to pick the same individual more than once and numbers outside the domain are typically ignored. Then as we pick numbers we'll simply pick numbers or individuals randomly. We'll identify them simply by writing their numbers down. Let me do a few quick examples here. Let's use random numbers to do each of the following. I'm going to randomly select five individuals from our class. I'm going to randomly split 100 volunteers into two treatment groups and I'm going to randomly split 20 into four treatment groups and we can use random numbers to do that. With apologies to students in my class I pulled a few names out of my class here for the purpose of this example. I have say I have 30 people in my class. The selection methodology says number them all. So with the same number of digits we'll have 30 so I'm going to number them like this up to 30. So everybody gets a number I've just had them listed alphabetically that's fine and then I have some people in the middle of my class here and I'm not showing everybody obviously. So I've got 30 people in the class and they all get numbers from 1 to 30 in this case done alphabetically. Let's say I want to pick five. Let's go to line 101 on the random number table. We'll pick two digits at a time because that's how folks have been numbered. So here's number 19. So I've randomly just picked Carly. Let's go to the next two digits 22. Well I've randomly just picked Eric and then I see 39. What do I do? My methodology says that's a number outside my domain so I ignore it. I ignore 50. I ignore 34. 05 pops up. I've randomly selected Jeremy. I ignore 75. I ignore 62. Now it's not happening but what if five popped up again? Well in this case I'm using people for a survey so I'd ignore it because I've already got Jeremy's opinion. 87 pops up, 13 pops up. I don't have person number 13 here but somewhere in my roster is person number 13 and I'll pick them as well. So I've picked people for so far. I want to pick one more. How far do I have to go? 96, 40. Ignore them. Ignore them. 91. Ignore it. Person 25. Oops. I don't have them here either but person 25 here. Not really a person in my class but I might pick Bob and Lou as well. So I've got my five selected that way and it's random. The numbering, labeling wasn't random but that's okay. The selection was random because I used a random number table. Once I picked them all I would write them down. Who's my random sample? 05 Jeremy, 13 Bob, 19 Carly, 22 Eric, 25 Lou. Alright let's talk about a slightly different problem. I've got a hundred subjects I'd like to split into two treatment groups. Now there are a number of ways to do this. Sort of up to your creativity. All are fine as long as there's an element of randomness in it. I've got a hundred people. What would I do? Well the first thing is I would label them with the shortest possible number of digits. So I'm going to number them 00 to 99. Let's just say they're listed alphabetically. What am I going to do now? I need to randomly split them into two groups. The simplest approach. Let's go to the random number table. Again it doesn't matter where you start. I'm just going to start at the beginning for simplicity. The simplest approach is just to start picking folks and because it's random the first folks we pick can all go into group one. Again remember their number 00 to 99. So these first two people I picked 19 and 22 they go into group one and I continue to do this. 39 goes into this group. Person number 50. Person number 34. Nothing's going to be outside my domain here because every two digit number I pick off the random number table is going to be between 00 and 99. If I get a duplicate I'm going to ignore them. If person 19 pops up again I've already got them so I ignore that. And I continue to do this until I get 50 in group one. They've been selected randomly. Once I've done that I have 50 others that haven't been selected. The other 50 automatically go into group two. And that's random. I randomly split 100 subjects into two groups. Similarly then we can use that methodology. Let's say I want to randomly split 20 volunteers into four groups. Now this is a bit more clumsy with the random number table but I've done this on purpose. You'll appreciate the calculator later. I would number them 00 to 19 or I could number them 01 to 20. It doesn't really matter. And then I do the same methodology I just did. I go start to select people. Well there's number 19. They're going to go in group one. The problem here is 22 ignore them. 39 ignore them. 50 ignore them. Those aren't in my range. 34 ignore them. And this becomes a bit more of a hassle. Here's person five. I'll put them there. Ignore the next. Ignore the next. Ignore the next. Here's person 13. I'll put them there. And 20 volunteers. Four groups. I want to keep going. Ignore, ignore, ignore. Ignore, ignore. And you can see the problem with this. I want to keep going until I get five people in the first group. And I'm not going to keep doing this. Here's double zero. Let's say I was using this methodology so I can put person 00. And there I've already got person 19. I'm going to ignore that. 27, 27, 75. And it's not going to happen for me. And I'm not going to waste your time. So at some point here I'd pick one more person at random and they'd be in group one. Once group one is filled I'd work on group two. I'd ignore repeats. Let's try that again. I would ignore repeats. But keep picking people until I had five in group two. Then I'd keep picking until I had five in group three. And the last five would go in group four. It is random. Even though the last five go in group four, the fact that the first 15 would pick randomly makes the last five random as well. So that's methodologies for using your random number table. Hopefully that makes sense. You'll see a few homework problems that require you to go there. Again, there are other ways to do the randomization as long as you follow sort of the guidelines of picking random numbers.