1 00:00:04,670 --> 00:00:08,210 Today, Inshallah, we are going to start Chapter 7. 2 00:00:09,830 --> 00:00:14,910 Chapter 7 talks about sampling and sampling 3 00:00:14,910 --> 00:00:22,690 distributions. The objectives for this chapter are 4 00:00:22,690 --> 00:00:27,610 number one, we have different methods, actually we 5 00:00:27,610 --> 00:00:31,330 have two methods: probability and non-probability 6 00:00:31,330 --> 00:00:34,750 samples, and we are going to distinguish between 7 00:00:35,420 --> 00:00:40,700 these two sampling methods. So again, in this 8 00:00:40,700 --> 00:00:44,980 chapter, we will talk about two different sampling 9 00:00:44,980 --> 00:00:49,480 methods. One is called probability sampling and 10 00:00:49,480 --> 00:00:52,940 the other is non-probability sampling. Our goal is 11 00:00:52,940 --> 00:00:56,520 to distinguish between these two different 12 00:00:56,520 --> 00:00:59,280 sampling methods. The other learning objective 13 00:00:59,280 --> 00:01:04,400 will be, We'll talk about the concept of the 14 00:01:04,400 --> 00:01:06,700 sampling distribution. That will be next time, 15 00:01:06,800 --> 00:01:09,960 inshallah. The third objective is compute 16 00:01:09,960 --> 00:01:15,480 probabilities related to sample mean. In addition 17 00:01:15,480 --> 00:01:18,160 to that, we'll talk about how can we compute 18 00:01:18,160 --> 00:01:22,920 probabilities regarding the sample proportion. And 19 00:01:22,920 --> 00:01:27,130 as I mentioned last time, There are two types of 20 00:01:27,130 --> 00:01:30,270 data. One is called the numerical data. In this 21 00:01:30,270 --> 00:01:33,470 case, we can use the sample mean. The other type 22 00:01:33,470 --> 00:01:36,630 is called qualitative data. And in this case, we 23 00:01:36,630 --> 00:01:39,330 have to use the sample proportion. So for this 24 00:01:39,330 --> 00:01:41,690 chapter, we are going to discuss how can we 25 00:01:41,690 --> 00:01:46,370 compute the probabilities for each one, either the 26 00:01:46,370 --> 00:01:50,090 sample mean or the sample proportion. The last 27 00:01:50,090 --> 00:01:55,770 objective of this chapter is to use the central 28 00:01:55,770 --> 00:01:58,190 limit theorem which is the famous one of the most 29 00:01:58,190 --> 00:02:02,130 famous theorem in this book which is called again 30 00:02:02,130 --> 00:02:05,690 CLT, central limit theorem, and we are going to show 31 00:02:05,690 --> 00:02:09,310 what are the, what is the importance of this 32 00:02:09,310 --> 00:02:11,930 theorem, so these are the mainly the four 33 00:02:11,930 --> 00:02:16,610 objectives for this chapter. Now let's see why we 34 00:02:16,610 --> 00:02:20,270 are talking about sampling. In other words, most 35 00:02:20,270 --> 00:02:23,850 of the time when we are doing study, we are using 36 00:02:23,850 --> 00:02:27,700 a sample instead of using the entire population. 37 00:02:28,640 --> 00:02:32,080 Now there are many reasons behind that. One of 38 00:02:32,080 --> 00:02:37,840 these reasons is selecting a sample is less time 39 00:02:37,840 --> 00:02:40,940 consuming than selecting every item in the 40 00:02:40,940 --> 00:02:44,060 population. I think it makes sense that suppose we 41 00:02:44,060 --> 00:02:46,560 have a huge population, that population consists 42 00:02:46,560 --> 00:02:53,140 of thousands of items. So that will take more time 43 00:02:54,440 --> 00:03:00,220 If you select 100 of their population. So time 44 00:03:00,220 --> 00:03:02,140 consuming is very important. So number one, 45 00:03:03,000 --> 00:03:05,780 selecting sample is less time consuming than using 46 00:03:05,780 --> 00:03:10,280 all the entire population. The second reason, 47 00:03:10,880 --> 00:03:14,640 selecting samples is less costly than selecting a 48 00:03:14,640 --> 00:03:17,280 variety of population. Because if we have large 49 00:03:17,280 --> 00:03:19,560 population, in this case you have to spend more 50 00:03:19,560 --> 00:03:23,540 money in order to get the data or the information 51 00:03:23,540 --> 00:03:27,940 from that population. So it's better to use these 52 00:03:27,940 --> 00:03:33,300 samples. The other reason is the analysis. Our 53 00:03:33,300 --> 00:03:37,260 sample is less cumbersome and more practical than 54 00:03:37,260 --> 00:03:40,880 analysis of all items in the population. For these 55 00:03:40,880 --> 00:03:45,820 reasons, we have to use a sample. For this reason, 56 00:03:45,880 --> 00:03:53,080 we have to talk about sampling methods. Let's 57 00:03:53,080 --> 00:03:58,540 start with sampling process. That begins with a 58 00:03:58,540 --> 00:04:05,320 sampling frame. Now suppose my goal is to know the 59 00:04:05,320 --> 00:04:13,960 opinion of IUG students about a certain subject. 60 00:04:16,260 --> 00:04:24,120 So my population consists of all IUG students. So 61 00:04:24,120 --> 00:04:27,370 that's the entire population. And you know that, 62 00:04:27,590 --> 00:04:31,750 for example, suppose our usual students is around, 63 00:04:32,430 --> 00:04:39,890 for example, 20,000 students. 20,000 students is a 64 00:04:39,890 --> 00:04:45,490 big number. So it's better to select a sample from 65 00:04:45,490 --> 00:04:49,270 that population. Now, the first step in this 66 00:04:49,270 --> 00:04:55,700 process, we have to determine the frame of that 67 00:04:55,700 --> 00:05:01,320 population. So my frame consists of all IU 68 00:05:01,320 --> 00:05:04,740 students, which has maybe males and females. So my 69 00:05:04,740 --> 00:05:09,560 frame in this case is all items, I mean all 70 00:05:09,560 --> 00:05:15,380 students at IUG. So that's the frame. So my frame 71 00:05:15,380 --> 00:05:18,720 consists 72 00:05:18,720 --> 00:05:22,220 of all students. 73 00:05:27,630 --> 00:05:32,370 So the definition of 74 00:05:32,370 --> 00:05:36,010 the sampling frame is a listing of items that make 75 00:05:36,010 --> 00:05:39,350 up the population. The items could be individual, 76 00:05:40,170 --> 00:05:44,490 could be students, could be things, animals, and 77 00:05:44,490 --> 00:05:49,650 so on. So frames are data sources such as a 78 00:05:49,650 --> 00:05:54,840 population list. Suppose we have the names of IUDs 79 00:05:54,840 --> 00:05:58,840 humans. So that's my population list. Or 80 00:05:58,840 --> 00:06:02,160 directories, or maps, and so on. So that's the 81 00:06:02,160 --> 00:06:05,520 frame, we have to know about the population we are 82 00:06:05,520 --> 00:06:10,900 interested in. Inaccurate or biased results can 83 00:06:10,900 --> 00:06:16,460 result if frame excludes certain portions of the 84 00:06:16,460 --> 00:06:20,620 population. For example, suppose here, as I 85 00:06:20,620 --> 00:06:24,180 mentioned, we are interested in IUG students, so 86 00:06:24,180 --> 00:06:29,280 my frame and all IU students. And I know there are 87 00:06:29,280 --> 00:06:35,900 students, either males or females. Suppose for 88 00:06:35,900 --> 00:06:40,880 some reasons, we ignore males, and just my sample 89 00:06:40,880 --> 00:06:45,080 focused on females. In this case, females. 90 00:06:48,700 --> 00:06:51,900 don't represent the entire population. For this 91 00:06:51,900 --> 00:06:57,720 reason, you will get inaccurate or biased results 92 00:06:57,720 --> 00:07:02,000 if you ignore a certain portion. Because here 93 00:07:02,000 --> 00:07:08,580 males, for example, maybe consists of 40% of the 94 00:07:08,580 --> 00:07:12,960 IG students. So it makes sense that this number or 95 00:07:12,960 --> 00:07:16,980 this percentage is a big number. So ignoring this 96 00:07:16,980 --> 00:07:21,160 portion, may lead to misleading results or 97 00:07:21,160 --> 00:07:26,160 inaccurate results or biased results. So you have 98 00:07:26,160 --> 00:07:29,600 to keep in mind that you have to choose all the 99 00:07:29,600 --> 00:07:33,740 portions of that frame. So inaccurate or biased 100 00:07:33,740 --> 00:07:38,700 results can result if a frame excludes certain 101 00:07:38,700 --> 00:07:43,180 portions of a population. Another example, suppose 102 00:07:43,180 --> 00:07:48,680 we took males and females. But here for females, 103 00:07:49,240 --> 00:07:56,020 females have, for example, four levels: Level one, 104 00:07:56,400 --> 00:07:59,980 level two, level three, and level four. And we 105 00:07:59,980 --> 00:08:05,560 ignored, for example, level one. I mean, the new 106 00:08:05,560 --> 00:08:09,520 students. We ignored this portion. Maybe this 107 00:08:09,520 --> 00:08:12,860 portion is very important one, but by mistake we 108 00:08:12,860 --> 00:08:18,690 ignored this one. The remaining three levels will 109 00:08:18,690 --> 00:08:22,430 not represent the entire female population. For 110 00:08:22,430 --> 00:08:25,330 this reason, you will get inaccurate or biased 111 00:08:25,330 --> 00:08:31,290 results. So you have to select all the portions of 112 00:08:31,290 --> 00:08:36,610 the frames. Using different frames to generate 113 00:08:36,610 --> 00:08:40,110 data can lead to dissimilar conclusions. For 114 00:08:40,110 --> 00:08:46,020 example, Suppose again I am interested in IEG 115 00:08:46,020 --> 00:08:46,720 students. 116 00:08:49,440 --> 00:08:59,460 And I took the frame that has all students at 117 00:08:59,460 --> 00:09:04,060 the University of Gaza, the Universities of Gaza. 118 00:09:09,250 --> 00:09:12,110 And as we know that Gaza has three universities, 119 00:09:12,350 --> 00:09:15,530 big universities: Islamic University, Lazar 120 00:09:15,530 --> 00:09:18,030 University, and Al-Aqsa University. So we have 121 00:09:18,030 --> 00:09:23,310 three universities. And my frame here, suppose I 122 00:09:23,310 --> 00:09:27,410 took all students at these universities, but my 123 00:09:27,410 --> 00:09:32,470 study focused on IU students. So my frame, the 124 00:09:32,470 --> 00:09:38,250 true one, is all students at IUG. But I taught all 125 00:09:38,250 --> 00:09:42,170 students at universities in Gaza. So now we have 126 00:09:42,170 --> 00:09:44,690 different frames. 127 00:09:48,610 --> 00:09:54,590 And you want to know what are the opinions of the 128 00:09:54,590 --> 00:09:59,910 smokers about smoking. So my population now is 129 00:09:59,910 --> 00:10:00,530 just... 130 00:10:14,030 --> 00:10:19,390 So that's my thing. 131 00:10:21,010 --> 00:10:32,410 I suppose I talk to a field that has one atom. 132 00:10:40,780 --> 00:10:46,040 Oh my goodness. They are very different things. 133 00:10:47,700 --> 00:10:53,720 The first one consists of only smokers. They are 134 00:10:53,720 --> 00:10:58,100 very interested in you. The other one consists 135 00:10:58,100 --> 00:11:06,560 of... anonymous. I thought maybe... smoker or non 136 00:11:06,560 --> 00:11:10,460 -smokers. For this reason, you will get... 137 00:11:17,410 --> 00:11:19,350 Conclusion, different results. 138 00:11:22,090 --> 00:11:28,850 So now, 139 00:11:29,190 --> 00:11:33,610 the sampling frame is a listing of items that make 140 00:11:33,610 --> 00:11:39,510 up the entire population. Let's move to the types 141 00:11:39,510 --> 00:11:44,910 of samples. Mainly there are two types of 142 00:11:44,910 --> 00:11:49,070 sampling: One is called non-probability samples. 143 00:11:50,370 --> 00:11:54,650 The other one is called probability samples. The 144 00:11:54,650 --> 00:11:59,790 non-probability samples can be divided into two 145 00:11:59,790 --> 00:12:04,030 segments: One is called judgment, and the other 146 00:12:04,030 --> 00:12:08,710 convenience. So we have judgment and convenience 147 00:12:08,710 --> 00:12:13,140 non-probability samples. The other type which is 148 00:12:13,140 --> 00:12:17,560 random probability samples, has four segments or 149 00:12:17,560 --> 00:12:21,680 four parts: The first one is called simple random 150 00:12:21,680 --> 00:12:25,680 sample. The other one is systematic. The second 151 00:12:25,680 --> 00:12:28,680 one is systematic random sample. The third one is 152 00:12:28,680 --> 00:12:32,940 stratified. The fourth one, cluster random sample. 153 00:12:33,460 --> 00:12:37,770 So there are two types of sampling: probability 154 00:12:37,770 --> 00:12:41,490 and non-probability. Non-probability has four 155 00:12:41,490 --> 00:12:45,350 methods here: simple random samples, systematic, 156 00:12:45,530 --> 00:12:48,530 stratified, and cluster. And the non-probability 157 00:12:48,530 --> 00:12:53,090 samples has two types: judgment and convenience. 158 00:12:53,670 --> 00:12:58,490 Let's see the definition of each type of samples. 159 00:12:59,190 --> 00:13:03,720 Let's start with non-probability sample. In non 160 00:13:03,720 --> 00:13:07,000 -probability sample, items included or chosen 161 00:13:07,000 --> 00:13:10,800 without regard to their probability of occurrence. 162 00:13:11,760 --> 00:13:14,740 So that's the definition of non-probability. For 163 00:13:14,740 --> 00:13:15,100 example. 164 00:13:23,660 --> 00:13:26,480 So again, non-probability sample, it means you 165 00:13:26,480 --> 00:13:29,580 select items without regard to their probability 166 00:13:29,580 --> 00:13:34,030 of occurrence. For example, suppose females 167 00:13:34,030 --> 00:13:42,430 consist of 70% of IUG students and males, the 168 00:13:42,430 --> 00:13:49,930 remaining percent is 30%. And suppose I decided to 169 00:13:49,930 --> 00:13:56,610 select a sample of 100 or 1000 students from IUG. 170 00:13:58,620 --> 00:14:07,980 Suddenly, I have a sample that has 650 males and 171 00:14:07,980 --> 00:14:14,780 350 females. Now, this sample, which has these 172 00:14:14,780 --> 00:14:19,260 numbers, for sure does not represent the entire 173 00:14:19,260 --> 00:14:25,240 population. Because females has 70%, and I took a 174 00:14:25,240 --> 00:14:30,890 random sample or a sample of size 350. So this 175 00:14:30,890 --> 00:14:35,830 sample is chosen without regard to the probability 176 00:14:35,830 --> 00:14:40,370 here. Because in this case, I should choose males 177 00:14:40,370 --> 00:14:44,110 with respect to their probability, which is 30%. 178 00:14:44,110 --> 00:14:49,330 But in this case, I just choose different 179 00:14:49,330 --> 00:14:54,990 proportions. Another example. Suppose 180 00:14:57,260 --> 00:14:59,920 again, I am talking about smoking. 181 00:15:05,080 --> 00:15:10,120 And I know that some people are smoking and I just 182 00:15:10,120 --> 00:15:14,040 took this sample. So I took this sample based on 183 00:15:14,040 --> 00:15:18,600 my knowledge. So it's without regard to their 184 00:15:18,600 --> 00:15:23,340 probability. Maybe suppose I am talking about 185 00:15:23,340 --> 00:15:28,330 political opinions about something. And I just 186 00:15:28,330 --> 00:15:36,330 took the experts of that subject. So my sample is 187 00:15:36,330 --> 00:15:42,070 not a probability sample. And this one has, as we 188 00:15:42,070 --> 00:15:44,230 mentioned, has two types: One is called 189 00:15:44,230 --> 00:15:49,010 convenience sampling. In this case, items are 190 00:15:49,010 --> 00:15:51,710 selected based only on the fact that they are 191 00:15:51,710 --> 00:15:55,590 easy. So I choose that sample because it's easy. 192 00:15:57,090 --> 00:15:57,690 Inexpensive, 193 00:16:02,190 --> 00:16:09,790 inexpensive, or convenient to sample. If I choose 194 00:16:09,790 --> 00:16:13,430 my sample because it is easy or inexpensive, I 195 00:16:13,430 --> 00:16:18,480 think it doesn't make any sense, because easy is 196 00:16:18,480 --> 00:16:23,780 not a reason to select that sample 223 00:18:17,050 --> 00:18:20,970 segment and so on. But the convenient sample means 224 00:18:20,970 --> 00:18:24,690 that you select a sample maybe that is easy for 225 00:18:24,690 --> 00:18:29,430 you, or less expensive, or that sample is 226 00:18:29,430 --> 00:18:32,980 convenient. For this reason, it's called non 227 00:18:32,980 --> 00:18:36,300 -probability sample because we choose that sample 228 00:18:36,300 --> 00:18:39,540 without regard to their probability of occurrence. 229 00:18:41,080 --> 00:18:48,620 The other type is called probability samples. In 230 00:18:48,620 --> 00:18:54,200 this case, items are chosen on the basis of non 231 00:18:54,200 --> 00:18:58,600 -probabilities. For example, here, if males 232 00:19:02,500 --> 00:19:11,060 has or represent 30%, and females represent 70%, 233 00:19:11,060 --> 00:19:14,840 and the same size has a thousand. So in this case, 234 00:19:14,920 --> 00:19:19,340 you have to choose females with respect to their 235 00:19:19,340 --> 00:19:24,260 probability. Now 70% for females, so I have to 236 00:19:24,260 --> 00:19:29,430 choose 700 for females and the remaining 300 for 237 00:19:29,430 --> 00:19:34,010 males. So in this case, I choose the items, I mean 238 00:19:34,010 --> 00:19:37,970 I choose my samples regarding to their 239 00:19:37,970 --> 00:19:39,050 probability. 240 00:19:41,010 --> 00:19:45,190 So in probability sample items and the sample are 241 00:19:45,190 --> 00:19:48,610 chosen on the basis of known probabilities. And 242 00:19:48,610 --> 00:19:52,360 again, there are two types. of probability 243 00:19:52,360 --> 00:19:55,580 samples, simple random sample, systematic, 244 00:19:56,120 --> 00:19:59,660 stratified, and cluster. Let's talk about each one 245 00:19:59,660 --> 00:20:05,040 in details. The first type is called a probability 246 00:20:05,040 --> 00:20:11,720 sample. Simple random sample. The first type of 247 00:20:11,720 --> 00:20:16,200 probability sample is the easiest one. Simple 248 00:20:16,200 --> 00:20:23,780 random sample. Generally is denoted by SRS, Simple 249 00:20:23,780 --> 00:20:30,660 Random Sample. Let's see how can we choose a 250 00:20:30,660 --> 00:20:35,120 sample that is random. What do you mean by random? 251 00:20:36,020 --> 00:20:41,780 In this case, every individual or item from the 252 00:20:41,780 --> 00:20:47,620 frame has an equal chance of being selected. For 253 00:20:47,620 --> 00:20:52,530 example, suppose number of students in this class 254 00:20:52,530 --> 00:21:04,010 number of students is 52 so 255 00:21:04,010 --> 00:21:11,890 each one, I mean each student from 256 00:21:11,890 --> 00:21:17,380 1 up to 52 has the same probability of being 257 00:21:17,380 --> 00:21:23,860 selected. 1 by 52. 1 by 52. 1 divided by 52. So 258 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 of Each 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 00:3 445 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 chose 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?