WEBVTT 1 00:00:01.830 --> 00:00:02.663 Hello, students. 2 00:00:02.663 --> 00:00:06.090 Welcome to our biostat ER example from Chapter 6. 3 00:00:06.090 --> 00:00:07.830 In this example, we are going to learn 4 00:00:07.830 --> 00:00:11.100 how to calculate the 95% confidence interval 5 00:00:11.100 --> 00:00:12.630 for risk difference. 6 00:00:12.630 --> 00:00:14.790 First, I'm going to read the problem. 7 00:00:14.790 --> 00:00:17.790 The problem here states, "A clinical trial is conducted 8 00:00:17.790 --> 00:00:20.730 to compare an experimental medication to a placebo 9 00:00:20.730 --> 00:00:23.070 to reduce the symptoms of asthma. 10 00:00:23.070 --> 00:00:25.680 200 participants are enrolled to the study 11 00:00:25.680 --> 00:00:27.090 and randomized to receive 12 00:00:27.090 --> 00:00:30.510 either the experimental medication or the placebo. 13 00:00:30.510 --> 00:00:31.500 The primary outcome 14 00:00:31.500 --> 00:00:34.050 is a self-reported reduction of symptoms. 15 00:00:34.050 --> 00:00:35.700 Among 100 participants 16 00:00:35.700 --> 00:00:38.010 who received the experimental medication, 17 00:00:38.010 --> 00:00:40.560 38 report reduction in symptoms 18 00:00:40.560 --> 00:00:45.360 as compared to 21 participants of 100 assigned to placebo." 19 00:00:45.360 --> 00:00:48.930 So for your convenience here, I have generated a table 20 00:00:48.930 --> 00:00:53.010 and inserted the numbers in the respective cells. 21 00:00:53.010 --> 00:00:58.010 So, 38 participants from 100 in the experimental group 22 00:00:58.410 --> 00:01:00.330 reported reduction in symptoms, 23 00:01:00.330 --> 00:01:05.233 whereas 21 participants from the placebo group out of 100 24 00:01:06.780 --> 00:01:09.480 reported reduction in symptoms. 25 00:01:09.480 --> 00:01:12.090 The next thing I have done here is type the formula 26 00:01:12.090 --> 00:01:13.480 that we will be using 27 00:01:14.700 --> 00:01:17.580 to calculate the 95% confidence interval 28 00:01:17.580 --> 00:01:19.320 for risk difference. 29 00:01:19.320 --> 00:01:21.780 The first thing for this formula we have to do 30 00:01:21.780 --> 00:01:24.030 is calculate the p1-hat, 31 00:01:24.030 --> 00:01:26.610 which is x1 divided by n1. 32 00:01:26.610 --> 00:01:30.420 And as you can see, the x1 here is 38, 33 00:01:30.420 --> 00:01:32.700 and the n1 is 100. 34 00:01:32.700 --> 00:01:36.090 So p1-hat is going to be 0.38. 35 00:01:36.090 --> 00:01:38.403 And next we have to calculate p2-hat. 36 00:01:39.720 --> 00:01:44.720 And x2 here is 21, and n2 here again is 100. 37 00:01:44.970 --> 00:01:47.943 So when we do the division, we get 0.21. 38 00:01:48.840 --> 00:01:51.780 Now we have to plug this number into the formula. 39 00:01:51.780 --> 00:01:55.830 So here is 0.38, which is p1-hat, 40 00:01:55.830 --> 00:01:59.160 minus 0.21, which is p2-hat. 41 00:01:59.160 --> 00:02:02.760 Then we have the z value 1.96. 42 00:02:02.760 --> 00:02:07.020 Then again we have the p1-hat, which is 0.38, 43 00:02:07.020 --> 00:02:12.020 and then we have 1 minus p1-hat, which is 0.62, 44 00:02:12.330 --> 00:02:16.263 and then we have 0.21, which is p2-hat, 45 00:02:17.130 --> 00:02:21.063 and 1 minus p2-hat, which is 0.79. 46 00:02:25.020 --> 00:02:29.760 Once we have inserted all the numbers into the formula, 47 00:02:29.760 --> 00:02:34.560 what we have to do is solve the equation algebraically. 48 00:02:34.560 --> 00:02:36.000 And once we do that, 49 00:02:36.000 --> 00:02:41.000 we get that the 95% confidence interval 50 00:02:43.350 --> 00:02:48.247 is going to be 0.046 to 0.294. 51 00:02:49.440 --> 00:02:50.430 So as you can see, 52 00:02:50.430 --> 00:02:53.730 this confidence interval does not include a 1, 53 00:02:53.730 --> 00:02:57.300 therefore, we can state with 95% confidence 54 00:02:57.300 --> 00:03:00.030 that there is a statistically significant difference 55 00:03:00.030 --> 00:03:01.200 between the two groups, 56 00:03:01.200 --> 00:03:03.900 which is the exposed experimental group, 57 00:03:03.900 --> 00:03:08.790 and the unexposed, which is the placebo. 58 00:03:08.790 --> 00:03:10.830 Thank you for your time and attention, 59 00:03:10.830 --> 00:03:12.680 and I will see you in the next video.