WEBVTT 1 00:00:02.820 --> 00:00:06.300 Hello students and welcome to Biostat ER, 2 00:00:06.300 --> 00:00:08.100 Chapter Eight, Example One. 3 00:00:08.100 --> 00:00:11.190 In this example we will learn how to calculate sample size 4 00:00:11.190 --> 00:00:13.830 for one-sample continuous outcome 5 00:00:13.830 --> 00:00:15.843 to perform hypothesis testing. 6 00:00:17.520 --> 00:00:19.500 This problem is not from the textbook 7 00:00:19.500 --> 00:00:21.037 and I will read it first. 8 00:00:21.037 --> 00:00:24.427 "The issue here is that we have collected some data 9 00:00:24.427 --> 00:00:27.697 "and we need to know if our sample mean is different 10 00:00:27.697 --> 00:00:31.267 "from some previous established mean, which is 100. 11 00:00:31.267 --> 00:00:34.447 "We want a hypothesis test with 80% power 12 00:00:34.447 --> 00:00:38.467 "and we know that we will fail to reject the null hypothesis 13 00:00:38.467 --> 00:00:41.047 "within a margin of error of five. 14 00:00:41.047 --> 00:00:44.557 "Therefore, if our mean is between 95 and 105, 15 00:00:44.557 --> 00:00:48.007 "we know that we will fail to reject the null hypothesis. 16 00:00:48.007 --> 00:00:51.067 "From publications for similar studies, 17 00:00:51.067 --> 00:00:56.067 "we know that the standard deviation is between 8.5 and 9.5. 18 00:00:56.137 --> 00:00:58.620 "So how many subjects are required?" 19 00:00:58.620 --> 00:01:01.590 So here I have basically summarized the information 20 00:01:01.590 --> 00:01:05.280 that has been provided and I have also stated the formula. 21 00:01:05.280 --> 00:01:07.470 Now the standard deviation which was obtained 22 00:01:07.470 --> 00:01:12.150 from previous literature, and as you can see it is a range 23 00:01:12.150 --> 00:01:14.730 and we always want you to use the highest value 24 00:01:14.730 --> 00:01:18.630 from this range as it will give us the most variation 25 00:01:18.630 --> 00:01:22.830 and ensure that we have enough subjects in the study 26 00:01:22.830 --> 00:01:25.770 because we always want to error on the side of caution 27 00:01:25.770 --> 00:01:29.280 and ensure that we are enrolling enough subjects. 28 00:01:29.280 --> 00:01:31.680 So as we proceed with the calculation, 29 00:01:31.680 --> 00:01:35.400 we will first calculate the denominator, that is ES. 30 00:01:35.400 --> 00:01:38.760 For ES, the numerator here is the difference 31 00:01:38.760 --> 00:01:40.440 between the means. 32 00:01:40.440 --> 00:01:43.260 Now because we want to fail to reject the null hypothesis 33 00:01:43.260 --> 00:01:45.090 with a margin of error of five. 34 00:01:45.090 --> 00:01:48.060 So this can be the high end minus the mean 35 00:01:48.060 --> 00:01:49.740 or the low end minus the mean, 36 00:01:49.740 --> 00:01:51.780 but the difference must be five. 37 00:01:51.780 --> 00:01:55.020 So we will insert 105 and 100, 38 00:01:55.020 --> 00:01:57.870 but we can also insert 95 and 100. 39 00:01:57.870 --> 00:01:59.640 Both will give us the same result 40 00:01:59.640 --> 00:02:03.090 because we are utilizing the absolute difference. 41 00:02:03.090 --> 00:02:08.010 And here I have inserted 105 and 100 and the sigma, 42 00:02:08.010 --> 00:02:10.680 which is 9.5. 43 00:02:10.680 --> 00:02:15.680 And once we perform the algebra here, we get 0.526. 44 00:02:16.260 --> 00:02:20.580 Now after we calculate the denominator, 45 00:02:20.580 --> 00:02:22.680 we need to calculate the numerator. 46 00:02:22.680 --> 00:02:26.160 So the value for Z, one minus alpha divided by two, 47 00:02:26.160 --> 00:02:29.910 is basically the Z of the 97.5 percentile, 48 00:02:29.910 --> 00:02:32.820 and that is going to be 1.96. 49 00:02:32.820 --> 00:02:35.700 So this is the Z value 50 00:02:35.700 --> 00:02:40.700 for which 97.5% of probability lies below. 51 00:02:40.890 --> 00:02:44.190 So the value of Z one minus beta is going to be 52 00:02:44.190 --> 00:02:46.650 the Z of the 80th percentile 53 00:02:46.650 --> 00:02:50.250 because one minus beta is the power of the study 54 00:02:50.250 --> 00:02:54.393 and that is going to be 0.84. 55 00:02:55.350 --> 00:02:57.240 So, both of these values, of course, 56 00:02:57.240 --> 00:02:58.710 were obtained from the Z table. 57 00:02:58.710 --> 00:03:01.290 So now we are going to insert these numbers 58 00:03:01.290 --> 00:03:03.750 and we are going to perform the algebra 59 00:03:03.750 --> 00:03:07.470 and we will get 28.33. 60 00:03:07.470 --> 00:03:10.380 So we always round off our sample size calculation, 61 00:03:10.380 --> 00:03:12.690 therefore, it is going to be 29, 62 00:03:12.690 --> 00:03:15.960 so 29 subjects are required. 63 00:03:15.960 --> 00:03:17.490 So thank you for your attention 64 00:03:17.490 --> 00:03:19.623 and I'll see you in the next video.