WEBVTT 00:01.420 --> 00:04.840 In this session, we will discuss about hypothesis testing. 00:07.290 --> 00:15.630 They know we have discussed about a normal distribution and we have discussed how we can actually locate 00:15.630 --> 00:23.520 a particular point on a normal distribution and find out the probability of that point occurring and 00:23.730 --> 00:32.550 the probability of anything occurring below a particular point or a percentage of a value of cutting 00:32.800 --> 00:35.970 percentage of values occurring below a particular point. 00:36.210 --> 00:41.640 And we found out how we can find out the confidence interval at a particular confidence level. 00:43.370 --> 00:48.470 Now, hypothesis testing is defined in Boredoms. 00:49.560 --> 00:57.300 So in case of hypothesis testing, we will have to doms one will be the null hypothesis and another 00:57.450 --> 01:00.120 will be the alternate hypothesis. 01:02.150 --> 01:08.360 The null hypothesis will be the sample statistic will be equal to the. 01:09.370 --> 01:10.840 Population cycliste. 01:12.000 --> 01:19.890 So, for example, the null hypothesis, for one example, would be that the average marks after extra 01:19.890 --> 01:23.390 class are same as before the class. 01:23.550 --> 01:25.380 So let's say we have a problem. 01:25.380 --> 01:33.630 We have a situation where we have certain students and these students are being given some sessions, 01:33.660 --> 01:38.420 some extra some classes, and they obtain some marks. 01:38.490 --> 01:41.330 The students are scoring some months after an exam. 01:42.830 --> 01:51.320 So we're trying to come forward if the students will score just the same after some extra classes are 01:51.320 --> 01:52.840 given to the students or not. 01:53.710 --> 02:02.680 OK, so the null hypothesis will be that the student will remain just the same, even after we provide 02:02.680 --> 02:03.960 an extra cost to the string. 02:04.210 --> 02:07.350 So the treatment which we are providing here. 02:07.510 --> 02:14.450 So the null hypothesis always says that we are providing some treatment to the sample. 02:14.740 --> 02:16.830 We are doing something to the sample. 02:17.050 --> 02:20.470 But still, the sample does not show any response. 02:21.220 --> 02:23.760 The sample does not show any change. 02:24.340 --> 02:28.060 So the treatment here is we are providing an extra class. 02:28.300 --> 02:29.410 Still the. 02:30.450 --> 02:36.480 Metric, which we are checking, the value which we are checking, that is the average mass, that average 02:36.480 --> 02:38.490 marks remain just the same. 02:40.010 --> 02:47.870 So this is the null hypothesis, null hypothesis is that whatever we were seeing was happening earlier 02:47.870 --> 02:55.330 before a particular there was a plane that is still applicable even after providing a. 02:57.090 --> 03:07.230 And alternative hypothesis is that even after we have provided an extra class, then there will be a 03:07.380 --> 03:16.200 significant difference of the marks, the average marks in comparison to the marks which were given 03:16.680 --> 03:17.980 before the extra class. 03:18.780 --> 03:27.120 So basically, we are trying to say here is the null hypothesis states that something is just the same 03:27.120 --> 03:29.580 even after a treatment has been provided. 03:29.940 --> 03:34.470 An alternate hypothesis is that there will be a significantly different. 03:36.940 --> 03:40.300 Now, when we say significant difference. 03:41.420 --> 03:50.180 So if I am saying that initially the students marks were to see 15 marks out of 20, so initially students 03:50.180 --> 03:55.040 were scoring 15 months and now students are scoring 16. 03:56.000 --> 04:04.610 So this 16 is not a significant difference, change of a very small value is not a significant difference. 04:04.940 --> 04:13.080 This difference can anyhow be present with the change in the sample or with the confidence interval. 04:13.160 --> 04:19.160 The change we might need, even if we have a confidence in double the value, could be present in the 04:19.160 --> 04:20.250 confidence interval. 04:20.480 --> 04:23.270 So a small change is not a significant change. 04:23.490 --> 04:31.260 A significant change will be if the confidence interval entirely changes, if we are able to say that 04:31.260 --> 04:37.400 in the population with the sample was earlier, representing is now not the same population. 04:37.610 --> 04:45.850 The new machine which we have the new value of the average mean is now let's say 18, so now or 19. 04:45.950 --> 04:49.490 So now the population itself has changed. 04:49.700 --> 04:55.130 So now the population mean has also changed after the treatment which we have provided. 04:56.640 --> 05:02.370 So this is the difference between null hypothesis, an alternate hypothesis that is null hypothesis 05:02.520 --> 05:06.840 that I used to negate a treatment, that the treatment has not impacted anything. 05:07.080 --> 05:12.120 While the alternate hypothesis is to say that the treatment has actually made a significant. 05:14.630 --> 05:22.130 Now, let us look for the how hypothesis distinguished, so hypothesis testing is an infringement procedure 05:22.310 --> 05:27.960 that uses the sample data to evaluate the credibility of hypotheses about a population. 05:28.610 --> 05:35.930 So in this scenario, we will be, first of all, Stoebe, a particular statement and then we will try 05:35.930 --> 05:40.220 to evaluate if that particular statement is correct or not. 05:41.000 --> 05:46.100 Now, remember why we are creating this and why we are evaluating this. 05:46.490 --> 05:49.270 We cannot see a hypothesis is correct. 05:49.700 --> 05:52.760 We can only reject the null hypothesis. 05:52.940 --> 05:59.120 That is, we can only say that the statement is incorrect on the basis of evidence. 05:59.270 --> 06:02.800 We cannot say that the statement is correct in this scenario. 06:03.600 --> 06:09.980 Now, hypothesis is an educated guess about something in the world around you. 06:10.580 --> 06:15.470 It should be testable in nature, either by experiment or by observation. 06:16.480 --> 06:23.710 For example, a new medicine that you think might work or a way of teaching, you might be better on 06:23.710 --> 06:27.320 a possible location of a new species or legacy. 06:27.340 --> 06:33.180 We want to find out if a particular way of we introduce music is not learning. 06:33.370 --> 06:36.870 And we introduce some music in the videos of the beginning. 06:37.060 --> 06:40.290 And will that improve your learning or not? 06:41.230 --> 06:49.690 So obviously, to administer the test or anything which we can put on this can be of hypothesis. 06:58.360 --> 07:06.910 Now, what is hypothesised statement now is we I'm going to propose a hypothesis, it is important to 07:06.910 --> 07:08.130 write the statement. 07:08.980 --> 07:18.330 The statement will look like if I do something, then something may happen to the dependent variable. 07:18.520 --> 07:24.790 That is, if we do something to an independent variable, then something will happen to the dependent 07:24.790 --> 07:25.360 variable. 07:26.600 --> 07:32.780 For example, if I decrease the amount of water given to the hops, then the hopes will increase in 07:32.780 --> 07:33.170 size. 07:34.310 --> 07:43.310 So here the amount of water is the independent variable, while the size of the hub is the dependent 07:43.310 --> 07:47.910 variable, which is increasing with the amount of water which we are giving to it. 07:48.740 --> 07:55.040 Similarly, if I give patients counselling in addition to the medication, then their overall depression 07:55.040 --> 07:56.480 scale will decrease. 07:56.690 --> 08:03.140 Or if I give exam at noon instead of seven, then the students that could be improved so we can have 08:03.140 --> 08:05.870 these kind of different statements created. 08:07.010 --> 08:16.550 Now, a good hypothesis when we always have a if and then statement, and it will include both independent 08:16.550 --> 08:23.810 and dependent variable, and this has to be testable by experiment or survey or any other scientifically 08:23.810 --> 08:24.170 sound. 08:27.250 --> 08:30.550 Now, here we have seen this go before. 08:31.530 --> 08:32.850 Now, we used to. 08:34.240 --> 08:42.900 Analyze this particular plot for finding out the critical region or for finding out the confidence interval, 08:43.660 --> 08:52.500 but now we will be using this to test a hypothesis so we will have a particular significance level. 08:53.810 --> 08:59.660 This significance level will see how significant the value is. 09:00.680 --> 09:03.030 Different from the original value? 09:03.050 --> 09:07.500 How much significant difference is present in the value and the original value? 09:07.910 --> 09:12.490 So in this scene, what happens is we will have a mean value. 09:12.500 --> 09:16.280 We will have some value which is present inside this gold. 09:16.340 --> 09:19.790 We will have some value which is present in this distribution. 09:20.950 --> 09:28.000 So let us say we want to say that we have a student, we have those group of students who were learning 09:28.220 --> 09:31.660 was studying for an average three hours. 09:32.860 --> 09:38.410 So the average three hours that the students were learning, where was the mean value? 09:39.630 --> 09:45.530 So are student loans for three hours in average, so the mean value becomes three here. 09:47.310 --> 09:56.460 Now we want to find out if the change in the learning pattern, if we want to change the learning pattern 09:56.460 --> 10:04.860 of those students and introduce us to a scenario where we will train students by converting the lectures 10:04.860 --> 10:10.740 into music, so we will convert the content of the lectures into a music form. 10:10.920 --> 10:17.610 And then we want to check if the average learning time of the students, which they learn continuously 10:17.610 --> 10:18.570 changes or not. 10:19.290 --> 10:27.140 So what we can do is we can we will have the original data where the mean of the average learning time 10:27.150 --> 10:31.260 will be three years and we provide treatment. 10:31.530 --> 10:37.830 But just we change the learning process by introducing music in the lectures. 10:38.140 --> 10:48.030 And we check that if the mean of the new students, the new mean of the learning time of the students 10:48.240 --> 10:49.350 has changed or not. 10:50.070 --> 10:51.810 So now let's see. 10:51.990 --> 10:56.430 The new game is actually three point five hours now. 10:56.430 --> 11:01.500 The student loan for three point five hours instead of three years. 11:02.990 --> 11:03.440 So. 11:04.410 --> 11:13.260 How we accept and how we reject this hypothesis is actually depending on if this three point five hours 11:13.410 --> 11:17.340 actually falls in this significant region or not. 11:18.490 --> 11:20.740 And this, again, is defined by the. 11:21.650 --> 11:27.770 Confidence which we want to have by the significant difference which we want to have, the full value 11:27.770 --> 11:28.820 which you want to set. 11:29.770 --> 11:36.940 So if the percentage value we want to have a zero point zero five, then it should fall in this particular 11:36.940 --> 11:37.350 region. 11:37.720 --> 11:44.830 If we want to have the confidence of zero point zero one info value, then it will fall in this particular 11:44.830 --> 11:45.240 region. 11:45.460 --> 11:52.230 And if you want to have even less in confidence, then it will fall in this region. 11:53.980 --> 11:56.980 So based on that, we will have different values. 12:00.720 --> 12:01.980 So let us check for the. 12:03.520 --> 12:10.510 Now, the general structure of hypothesis testing, so all this hypothesis testing will have null hypothesis, 12:10.510 --> 12:17.680 alternate hypotheses on the data, which we will have, the null hypothesis again will be a statement 12:17.860 --> 12:21.900 about the population barometer, which we want to prove is wrong. 12:22.300 --> 12:28.870 And alternate hypothesis is a general statement about the population barometer, which is opposed to 12:29.170 --> 12:31.090 this null hypothesis. 12:31.330 --> 12:37.120 So the null hypothesis and the alternate hypothesis have to be opposite statements. 12:37.390 --> 12:45.340 These statements should be contradicting in nature and null hypothesis is something which we want to 12:45.340 --> 12:49.090 actually evaluate and we want to prove wrong. 12:51.080 --> 12:59.780 So we want to reject the null hypothesis, which is why we want to create this null hypothesis as something 12:59.780 --> 13:06.200 which we want to prove wrong, an alternate hypothesis will always be opposite to the null hypothesis. 13:08.880 --> 13:17.340 So now check for so let us see notice clearly the null hypothesis, so we have a question that is only 13:17.370 --> 13:25.230 certain things that if knee surgery patients go to a physical therapy twice a week instead of three 13:25.230 --> 13:28.580 times, their recovery period will be longer. 13:29.310 --> 13:33.970 Average recovery time for a knee surgery patient is eight point two weeks. 13:34.620 --> 13:36.750 So this is what a researcher thinks. 13:36.960 --> 13:44.040 A researcher thinks that if someone will go for the therapy for twice a week instead of three times, 13:44.190 --> 13:46.170 then the recovery period will be longer. 13:47.180 --> 13:50.270 So they want to prove this wrong. 13:50.480 --> 13:58.130 So if the researcher is wrong, then the recovery time is less than or equal to eight point two weeks. 13:59.730 --> 14:08.610 So the researcher wants to say that the surgery period and the physical therapy should be reduced to 14:08.610 --> 14:15.450 two weeks, if the therapy period is two weeks, then that if the repeated would be longer. 14:15.840 --> 14:22.120 So what we want to say here is we will create a null hypothesis and we will try to prove the research 14:22.120 --> 14:28.290 done wrong here to actually evaluate in the world the researcher thinks is correct or not solve the 14:28.290 --> 14:32.520 evil that I do oppose this statement by the researchers. 14:32.910 --> 14:40.320 So the researchers say that if knee surgery patients go for physical therapy twice a week, then the 14:40.320 --> 14:41.890 recovery period will be longer. 14:41.910 --> 14:49.790 So the opposite of this will be that the recovery period will be less than or equal to eight one two 14:49.800 --> 14:50.130 weeks. 14:50.670 --> 14:53.190 So this is what the null hypothesis will be. 14:54.420 --> 15:01.560 A null hypothesis will state the opposite of what that is such a thing so that we can actually reject 15:01.980 --> 15:03.370 the hypothesis. 15:03.630 --> 15:09.390 So we are seeing that the recovery time is less than or equal to the eight point two weeks. 15:10.360 --> 15:16.180 And the alternative would be completely opposite to the state doing so opposite of this statement would 15:16.180 --> 15:17.040 be here. 15:17.140 --> 15:20.490 The statement is new is less than equal to eight point two weeks. 15:20.740 --> 15:24.840 So the opposite of this will be new, will be greater than eight point two weeks. 15:25.120 --> 15:28.460 So the average recovery time is more than eight point two weeks. 15:29.230 --> 15:34.780 So this is what the null hypothesis and alternate hypothesis looks like. 15:36.770 --> 15:44.560 So what we want to do here is we want to check if the researcher is right or wrong. 15:45.590 --> 15:54.620 So using hypothesis testing, we can only prove if the researcher is wrong or not, we cannot see that 15:54.650 --> 15:58.830 the decision is correct, but we can only say that the decision is wrong. 15:59.690 --> 16:03.320 So for that, we evaluate this null hypothesis. 16:03.650 --> 16:06.750 We see that the researcher is actually wrong. 16:06.770 --> 16:10.000 So we created this statement that research is wrong. 16:10.520 --> 16:15.230 So we can either reject this or accept this. 16:16.660 --> 16:19.330 So this is what null hypothesis will allow us to. 16:19.840 --> 16:29.470 Now let us look further and create more statements so we have another study of the status of critically 16:29.470 --> 16:37.150 ill children in a pediatric intensive care unit and then examine 16 children. 16:37.390 --> 16:40.170 So the number of children examined are 16 here. 16:40.780 --> 16:48.100 And these children are with a woman and B and they were found that the number of missing 132 was one 16:48.100 --> 16:52.000 point and the standard deviation was of one point nine. 16:53.950 --> 17:01.270 Now, the extensive analysis has established that the number of such teeth is wider population of children 17:01.570 --> 17:03.910 is one point four, so. 17:05.220 --> 17:14.550 For example, we have the mean Value 1.0 and the standard deviation of one point nine and the. 17:15.550 --> 17:24.280 Actual value is one point four, so we want to check if the mean value for the critically ill children 17:24.280 --> 17:27.410 is different from the actual population or not. 17:27.880 --> 17:35.560 So this is the actual population and we want to check if this mean value, which we have found out is 17:35.680 --> 17:37.310 different from this one or not. 17:38.260 --> 17:45.550 So we want to prove here that this these both of these belong to two different population instead of 17:45.560 --> 17:46.540 same population. 17:48.570 --> 17:56.070 So for that, we will actually have to prove that this one point two is significantly different from 17:56.070 --> 18:01.750 this one point for so let us see the null hypothesis which we will be creating. 18:02.520 --> 18:08.850 So the statement about the population barometer, we would have to prove this wrong if possible. 18:08.860 --> 18:10.930 So something which we want to prove wrong. 18:11.650 --> 18:14.910 OK, and we want to check here is that. 18:16.320 --> 18:19.470 The meaning of critical children is different from the. 18:21.710 --> 18:25.520 Actual mean of the number of feet. 18:26.580 --> 18:31.410 So our hypothesis will be that the meme is one point for. 18:35.520 --> 18:37.920 And the alternate hypotheses will be. 18:41.010 --> 18:44.850 That this is not equal to one point for. 18:46.290 --> 18:53.060 OK, so the null hypothesis will be that both of these are actually steam and the children are not different, 18:54.150 --> 18:59.400 the mean for both the population is seen and we want to put all this wrong. 18:59.910 --> 19:02.790 So we will see that both of these have same mean. 19:02.790 --> 19:09.570 It is one point for only, and the alternate hypothesis will be that all the populations are different. 19:09.990 --> 19:16.200 And the mean of these 16 students is not equal to one point for. 19:18.830 --> 19:26.480 Now, what is probability theory now, probability theory allows us to calculate the exact probability 19:26.720 --> 19:30.260 that chance was the real reason for the relationship. 19:32.670 --> 19:41.400 That is this what the data which has happened, that is the number of children had missing the as one 19:41.400 --> 19:44.580 point two had the standard deviation of one point five. 19:44.620 --> 19:49.380 So here the mean which came out will be one point two, is actually dealable johns. 19:49.590 --> 19:52.530 And actually the mean is one point for me. 19:52.740 --> 19:54.630 But this is just the Biogen's. 19:54.640 --> 19:56.190 It came to be one point. 19:59.680 --> 20:07.420 So probability theory allows us to produce death statistics and the death statistics is a number that 20:07.420 --> 20:12.170 is used to decide whether to accept or reject the null hypothesis. 20:12.940 --> 20:17.670 So probability theory allows us to accept or reject the null hypothesis. 20:17.950 --> 20:23.170 So we will be able to either accept this or we will be able to reject this hypothesis. 20:23.560 --> 20:27.300 So this is the only thing which we can prove, correct or wrong. 20:29.440 --> 20:35.890 We cannot say anything about this one, so we will be either accepting the null hypothesis or rejecting 20:35.890 --> 20:37.090 the null hypothesis. 20:41.620 --> 20:47.680 So we will learn about the test and the test and how these are conducted in the next session.