WEBVTT 1 00:00:02.340 --> 00:00:06.420 Hello students, this is problem 2e. 2 00:00:06.420 --> 00:00:09.030 And this actually is not in our text, 3 00:00:09.030 --> 00:00:12.900 but it has been added because we want to show you guys 4 00:00:12.900 --> 00:00:17.640 how to determine if two factors are independent or not. 5 00:00:17.640 --> 00:00:20.850 So we are continuing to use the same example, 6 00:00:20.850 --> 00:00:22.290 and we want to know now 7 00:00:22.290 --> 00:00:24.900 if the child's hyperlipidemic status 8 00:00:24.900 --> 00:00:28.110 is independent of the parent's status. 9 00:00:28.110 --> 00:00:30.900 So conceptually, this means that the probability 10 00:00:30.900 --> 00:00:34.320 that the child is hyperlipidemic should be the same 11 00:00:34.320 --> 00:00:38.130 regardless of the parent's hyperlipidemia status, 12 00:00:38.130 --> 00:00:40.710 and that will demonstrate independence. 13 00:00:40.710 --> 00:00:43.330 So mathematically, what we want to do here is 14 00:00:44.231 --> 00:00:45.360 look at this probability, 15 00:00:45.360 --> 00:00:46.743 and I'm going to start. 16 00:00:57.450 --> 00:01:02.450 And again, here I am abbreviating hyperlipidemia as HL, 17 00:01:07.260 --> 00:01:08.310 and we are going to use 18 00:01:08.310 --> 00:01:12.720 the both parents being hyperlipidemic, 19 00:01:12.720 --> 00:01:15.183 but we could use the other columns as well. 20 00:01:21.840 --> 00:01:24.330 Okay, let me write a little smaller, 21 00:01:24.330 --> 00:01:25.953 so that they will fit here. 22 00:01:38.670 --> 00:01:40.530 So now, what are these numbers? 23 00:01:40.530 --> 00:01:42.273 So for this one, 24 00:01:43.260 --> 00:01:46.710 and we have gone through this calculation before, 25 00:01:46.710 --> 00:01:51.300 the numerator is going to be 45 plus 42 plus six 26 00:01:51.300 --> 00:01:55.890 because again, the child's hyperlipidemia status 27 00:01:55.890 --> 00:01:59.370 was given in the rows and the parents in the column. 28 00:01:59.370 --> 00:02:02.550 And then we are going to divide this by 223, 29 00:02:02.550 --> 00:02:04.590 which is our entire cohort. 30 00:02:04.590 --> 00:02:05.520 On this side, 31 00:02:05.520 --> 00:02:10.520 it's going to be 45 divided by 45 plus 13. 32 00:02:13.650 --> 00:02:15.780 Again, I like to put the parentheses around 33 00:02:15.780 --> 00:02:18.060 because it helps me remember 34 00:02:18.060 --> 00:02:21.273 that I have to do the addition before I do the division. 35 00:02:22.170 --> 00:02:25.590 So now what I'm gonna do is go and get a different color, 36 00:02:25.590 --> 00:02:28.590 so I can show you where each of these are coming from. 37 00:02:28.590 --> 00:02:31.020 So this is where we are getting 38 00:02:31.020 --> 00:02:33.960 the child status from, right. 39 00:02:33.960 --> 00:02:35.820 Okay, this row, 40 00:02:35.820 --> 00:02:37.710 and that's exactly what we have there. 41 00:02:37.710 --> 00:02:39.670 And then this is our denominator 42 00:02:40.710 --> 00:02:42.330 for the left hand side. 43 00:02:42.330 --> 00:02:44.883 And now, for the right hand side, 44 00:02:48.000 --> 00:02:51.000 I'm going to show you where 45 is coming from. 45 00:02:51.000 --> 00:02:53.190 Of course, it's coming from here, 46 00:02:53.190 --> 00:02:56.433 and the parent status is coming from here, okay. 47 00:02:57.690 --> 00:02:58.523 So, 48 00:03:00.870 --> 00:03:03.063 this is basically what is going on, 49 00:03:04.050 --> 00:03:08.490 and this is how we are doing our calculation. 50 00:03:08.490 --> 00:03:10.260 So now, let's go back, 51 00:03:10.260 --> 00:03:11.853 let me get the black ink, 52 00:03:13.530 --> 00:03:16.470 and I'm going to start doing the calculation. 53 00:03:16.470 --> 00:03:18.960 And when we do the calculation what we see is 54 00:03:18.960 --> 00:03:22.980 from this side, we get 0.42, 55 00:03:22.980 --> 00:03:27.450 and from this side, what we get is 0.78. 56 00:03:27.450 --> 00:03:28.283 So what? 57 00:03:30.643 --> 00:03:34.203 0.78, so basically we can say that they are not equal. 58 00:03:36.780 --> 00:03:38.610 So since they are not equal, 59 00:03:38.610 --> 00:03:41.043 now we can say that they are not independent. 60 00:03:42.150 --> 00:03:47.150 So not equal here means 61 00:03:49.050 --> 00:03:50.913 not independent. 62 00:04:03.390 --> 00:04:08.370 Let me see if I can write this a little more nicely. 63 00:04:08.370 --> 00:04:09.753 So not equal, 64 00:04:15.270 --> 00:04:17.853 not independent. 65 00:04:26.092 --> 00:04:26.925 Okay.