WEBVTT 1 00:00:03.036 --> 00:00:03.869 Dear students, 2 00:00:03.869 --> 00:00:05.550 in this example we are going to learn 3 00:00:05.550 --> 00:00:07.890 how to create a confidence interval 4 00:00:07.890 --> 00:00:10.680 for matched samples of continuous data. 5 00:00:10.680 --> 00:00:11.790 We have matched data 6 00:00:11.790 --> 00:00:15.930 when we have matched case-control studies, sibling studies. 7 00:00:15.930 --> 00:00:19.110 Twin studies are data taken on the same individuals 8 00:00:19.110 --> 00:00:20.553 at different points in time. 9 00:00:22.380 --> 00:00:25.320 So for this example, which is a hypothetical example, 10 00:00:25.320 --> 00:00:27.510 we are going to run an experiment. 11 00:00:27.510 --> 00:00:30.270 We recruit a random sample of 10 individuals 12 00:00:30.270 --> 00:00:33.630 and ask them how many times a week they exercise. 13 00:00:33.630 --> 00:00:35.310 Based on the responses, 14 00:00:35.310 --> 00:00:38.190 we realize that most of the individuals, if not all, 15 00:00:38.190 --> 00:00:41.730 might benefit from enrolling into an exercise program. 16 00:00:41.730 --> 00:00:44.190 Hence, we ask them if they're interested to enroll, 17 00:00:44.190 --> 00:00:45.660 and they all agree. 18 00:00:45.660 --> 00:00:48.420 Six months later, we ask them the same question 19 00:00:48.420 --> 00:00:50.490 and collect the data again. 20 00:00:50.490 --> 00:00:52.503 The fictitious data is shown below. 21 00:00:53.490 --> 00:00:54.930 Now, as you have probably realized, 22 00:00:54.930 --> 00:00:58.530 this is an example of matched sample of continuous data, 23 00:00:58.530 --> 00:01:01.230 because these are the same individuals. 24 00:01:01.230 --> 00:01:02.260 In contrast to 25 00:01:04.140 --> 00:01:05.460 the independent samples, 26 00:01:05.460 --> 00:01:07.860 the confidence interval for matched samples 27 00:01:07.860 --> 00:01:09.660 is for the mean difference 28 00:01:09.660 --> 00:01:13.230 as opposed to for the difference in means. 29 00:01:13.230 --> 00:01:17.280 So here first, we have to write the formula, 30 00:01:17.280 --> 00:01:19.440 and I'm going to write it for you here, 31 00:01:19.440 --> 00:01:22.773 because we are looking for the 90% confidence interval. 32 00:01:25.020 --> 00:01:26.523 This will be our formula. 33 00:01:37.050 --> 00:01:39.270 We will use the t distribution here 34 00:01:39.270 --> 00:01:44.270 because our sample size is below 30, it is 10, 35 00:01:44.280 --> 00:01:48.150 and now we know our degrees of freedom is going to be nine. 36 00:01:48.150 --> 00:01:49.650 And from the back of our book, 37 00:01:49.650 --> 00:01:51.360 we get our t critical value, 38 00:01:51.360 --> 00:01:52.490 which is going to be 39 00:01:55.077 --> 00:01:57.510 1.833. 40 00:01:57.510 --> 00:02:00.180 Now what we are going to do is plug all these numbers 41 00:02:00.180 --> 00:02:01.323 into our formula. 42 00:02:24.750 --> 00:02:26.850 So we are going to now do the algebra, 43 00:02:26.850 --> 00:02:29.240 and what we find here is... 44 00:02:36.090 --> 00:02:39.490 Of course, after doing all the algebra 45 00:02:43.950 --> 00:02:45.573 and rounding up our numbers, 46 00:02:50.190 --> 00:02:52.083 this is our confidence interval. 47 00:02:53.550 --> 00:02:55.480 Now, one thing I want you to 48 00:02:58.920 --> 00:03:00.540 understand here is 49 00:03:00.540 --> 00:03:04.713 that our confidence interval here does not include a zero. 50 00:03:06.060 --> 00:03:10.410 Therefore, we can state with 90% confidence 51 00:03:10.410 --> 00:03:14.080 that the mean difference here has changed significantly 52 00:03:15.270 --> 00:03:19.750 before after, or after the individuals enrolled into the 53 00:03:22.350 --> 00:03:23.553 exercise program. 54 00:03:24.420 --> 00:03:28.293 I hope this helps and I will see you in the next video.