WEBVTT 1 00:00:01.710 --> 00:00:02.910 Hello students. 2 00:00:02.910 --> 00:00:06.813 Welcome to Biostats ER, Example 3, Chapter 7. 3 00:00:08.340 --> 00:00:09.930 In this example, we will learn 4 00:00:09.930 --> 00:00:12.060 how to perform hypothesis testing 5 00:00:12.060 --> 00:00:16.290 for two sample independent continuous outcome data. 6 00:00:16.290 --> 00:00:21.000 The problem is from our textbook, Problem 30. 7 00:00:21.000 --> 00:00:23.580 And the problem states, a study is performed 8 00:00:23.580 --> 00:00:25.740 to examine the relationship between 9 00:00:25.740 --> 00:00:29.490 the concentration of plasma antioxidant vitamins 10 00:00:29.490 --> 00:00:31.290 and cancer risk. 11 00:00:31.290 --> 00:00:32.490 The table shows data 12 00:00:32.490 --> 00:00:34.710 for plasma vitamin A concentration 13 00:00:34.710 --> 00:00:36.600 in stomach cancer patients 14 00:00:36.600 --> 00:00:40.980 and controls, participants similar to the cancer patients, 15 00:00:40.980 --> 00:00:42.570 but free of disease. 16 00:00:42.570 --> 00:00:46.530 Is there a significant difference in the mean concentration 17 00:00:46.530 --> 00:00:49.200 of plasma antioxidant vitamins 18 00:00:49.200 --> 00:00:53.190 between the patients with stomach cancer and controls? 19 00:00:53.190 --> 00:00:54.870 Run the appropriate test 20 00:00:54.870 --> 00:00:57.753 at a 5% level of significance. 21 00:01:01.710 --> 00:01:06.300 So here the two samples are independent 22 00:01:06.300 --> 00:01:10.080 because this is an example of a case control study. 23 00:01:10.080 --> 00:01:13.650 The outcome, plasma vitamin A concentration, 24 00:01:13.650 --> 00:01:16.050 is measured on a continuous scale, 25 00:01:16.050 --> 00:01:18.390 and here we will use a t-test 26 00:01:18.390 --> 00:01:21.360 because the sample size for the stomach cancer patients 27 00:01:21.360 --> 00:01:23.043 is less than 30. 28 00:01:26.070 --> 00:01:30.060 So with that, we will move forward with step one, 29 00:01:30.060 --> 00:01:32.250 where we will set up the hypothesis 30 00:01:32.250 --> 00:01:35.310 and determine the level of significance. 31 00:01:35.310 --> 00:01:36.843 So the hypothesis here, 32 00:01:38.490 --> 00:01:40.470 for null will state 33 00:01:40.470 --> 00:01:43.710 that the means are equal and mu1 is equal to mu2. 34 00:01:43.710 --> 00:01:47.010 And the alternative will state that the means are not equal 35 00:01:47.010 --> 00:01:49.620 and mu1 is not equal to mu2. 36 00:01:49.620 --> 00:01:52.773 The level of significance here is 0.05. 37 00:01:56.430 --> 00:01:59.193 Now for step two, as per the guidelines, 38 00:02:01.920 --> 00:02:04.170 if the ratio of the sample variance 39 00:02:04.170 --> 00:02:06.540 is between 0.5 and two, 40 00:02:06.540 --> 00:02:09.900 the assumption of equality of population variance 41 00:02:09.900 --> 00:02:12.150 is considered appropriate. 42 00:02:12.150 --> 00:02:17.073 Therefore, when we check the ratio of the variance, 43 00:02:19.050 --> 00:02:21.960 we find out that it is 0.62, 44 00:02:21.960 --> 00:02:24.750 which is between 0.5 and two. 45 00:02:24.750 --> 00:02:26.283 Therefore, we can proceed. 46 00:02:28.020 --> 00:02:29.280 Here, I have provided you 47 00:02:29.280 --> 00:02:31.830 with the t-test that we will be using 48 00:02:31.830 --> 00:02:36.390 and the degrees of freedom will be calculated 49 00:02:36.390 --> 00:02:40.980 by adding the two sample sizes, n1 plus n2, 50 00:02:40.980 --> 00:02:45.393 and then deducting two because we have two samples. 51 00:02:46.800 --> 00:02:51.570 And then we will get our degree of freedom, which is 68. 52 00:02:51.570 --> 00:02:54.150 Then we will set up the decision rule. 53 00:02:54.150 --> 00:02:57.360 And based on the degrees of freedom being 68 54 00:02:57.360 --> 00:03:00.570 and alpha being 0.05, 55 00:03:00.570 --> 00:03:03.580 we will reject null if our t calculated 56 00:03:04.770 --> 00:03:08.970 is less than or equal to negative 1.995, 57 00:03:08.970 --> 00:03:11.760 or if our t calculated is greater than 58 00:03:11.760 --> 00:03:14.163 or equal to positive 1.995. 59 00:03:15.780 --> 00:03:17.140 Now we will move forward 60 00:03:18.690 --> 00:03:21.540 and compute the test statistics. 61 00:03:21.540 --> 00:03:24.570 First we will calculate the Sp, 62 00:03:24.570 --> 00:03:28.600 and here the n1 is 20 63 00:03:30.690 --> 00:03:33.390 and the s1 is 0.15. 64 00:03:33.390 --> 00:03:35.193 The n2 is 50, 65 00:03:36.060 --> 00:03:37.233 and the s2 is 0.19. 66 00:03:41.880 --> 00:03:46.350 And for the denominator, n1 again is 20, 67 00:03:46.350 --> 00:03:47.490 n2 is 50. 68 00:03:47.490 --> 00:03:49.500 And then we will deduct two. 69 00:03:49.500 --> 00:03:51.510 So once we perform the calculation, 70 00:03:51.510 --> 00:03:54.930 we find out that Sp is 0.18. 71 00:03:54.930 --> 00:03:59.300 Then we will move to our calculation 72 00:04:01.200 --> 00:04:04.920 to obtain the t-value. 73 00:04:04.920 --> 00:04:07.440 And here for the numerator, 74 00:04:07.440 --> 00:04:10.830 we will insert the two mean values, 75 00:04:10.830 --> 00:04:14.163 2.41 and 2.78. 76 00:04:15.660 --> 00:04:19.890 And then for the denominator, we'll insert Sp, 77 00:04:19.890 --> 00:04:21.540 which is 0.18 78 00:04:21.540 --> 00:04:26.340 and then the n1, 79 00:04:26.340 --> 00:04:27.630 which is 20, 80 00:04:27.630 --> 00:04:29.760 and n2, which is 50. 81 00:04:29.760 --> 00:04:31.983 Once we perform the calculation here, 82 00:04:35.310 --> 00:04:37.410 we obtain our t calculated, 83 00:04:37.410 --> 00:04:42.330 which is negative 7.77. 84 00:04:42.330 --> 00:04:46.800 Now in step five, we are going to reach our conclusion. 85 00:04:46.800 --> 00:04:48.630 And here we will reject null 86 00:04:48.630 --> 00:04:51.270 because negative 7.77 87 00:04:51.270 --> 00:04:55.740 is actually less than negative 1.995. 88 00:04:55.740 --> 00:04:58.530 So we have statistically significant evidence 89 00:04:58.530 --> 00:05:01.050 at the alpha of 0.05 90 00:05:01.050 --> 00:05:04.713 to show that there is a significant difference 91 00:05:07.470 --> 00:05:11.340 in the mean concentration of plasma antioxidant vitamins 92 00:05:11.340 --> 00:05:14.793 between patients with stomach cancer and controls. 93 00:05:27.180 --> 00:05:29.490 Thank you for your time and attention 94 00:05:29.490 --> 00:05:31.263 and I'll see you in the next video.