WEBVTT 00:00.950 --> 00:04.780 In this session, we will discuss about Zinnanti this so for. 00:04.820 --> 00:07.930 First of all, let us understand about some important films. 00:08.360 --> 00:16.590 So the P value, p value is the value of probability, which is obtained from the Z value or B value. 00:16.820 --> 00:26.210 When we look these values on the Z or B, B, but now this probability is the probability of obtaining 00:26.210 --> 00:35.000 a particular sample mean is less than the alpha value, then it is going to be falling in the B or also 00:35.000 --> 00:36.590 known as a critical region. 00:38.400 --> 00:41.370 So let us have a look at the DiGRA. 00:43.250 --> 00:44.690 So this is their dytham. 00:46.430 --> 00:50.690 And we are checking that we have a particular mean value. 00:51.860 --> 00:58.550 And we want to compare a different mean and we want to check if the machine is actually falling in the 00:58.550 --> 01:08.240 same distribution or not, that is let us see the example of the beat so the children would have the 01:08.240 --> 01:09.080 mean value. 01:09.240 --> 01:13.350 The population mean value for the children's teeth was one point four. 01:13.580 --> 01:17.330 So one point four beats, one missing for the children. 01:17.330 --> 01:19.790 The average value missing was one point for. 01:20.900 --> 01:30.080 Now, we want to check that if the average value of the missing teeth is one point, which is somewhat 01:30.080 --> 01:36.950 higher, then is this value significantly different from this one point four or not? 01:37.990 --> 01:46.240 So if the value is not significantly different, if the value is not significantly different, then 01:46.240 --> 01:51.880 it will fall in this region, only then it will be the part of the distributionally. 01:53.440 --> 02:01.990 But if the value was not one point two, but the value was actually us is zero point five. 02:02.940 --> 02:07.440 If the value was zero point five, then maybe the value would have fallen here. 02:08.690 --> 02:15.400 Then what would happen is that the value is actually falling into the value or elfatih Jim. 02:17.870 --> 02:24.380 So when the value is falling in this region, which is the region, this is the Lord and this is the 02:24.380 --> 02:29.780 Upworthy, if the value is, let's say, zero point five zero point zero, then it will fall in the 02:29.780 --> 02:30.380 Lordi. 02:30.620 --> 02:34.940 If the value is three or four, then the value will lie in the Upworthy. 02:35.720 --> 02:43.430 So if the value is falling in that region, then we will see that the meaning of the new new scenario, 02:43.670 --> 02:47.870 then we have some kind of illness in the children. 02:47.870 --> 02:52.010 And because of the illness, the number of falling teeth is actually changed. 02:52.280 --> 02:55.940 The usually the children have one point four missing teeth. 02:56.180 --> 03:03.200 But now in this scenario, because the children are ill, they are having less number of these or they 03:03.200 --> 03:04.660 have more number of falling. 03:06.110 --> 03:14.000 So now the population has entirely changed, so in this case, the mean of the population of nine of 03:14.000 --> 03:19.610 the children, all of the children, the deed is actually different from this one point. 03:19.630 --> 03:22.790 For now, the mean is some other value. 03:23.810 --> 03:30.230 So if the value is significantly different, then it should fall in the regions. 03:31.040 --> 03:38.150 So this is what we are taking in the case of the best or the best, basically, in case of hypothesis 03:38.150 --> 03:46.070 testing, if the value which we are checking, if the hypothesis which we are checking is significantly 03:46.070 --> 03:53.060 different from this data or it is just by chance, if the value is significantly different, this means 03:53.060 --> 03:58.910 that it is not by chance what actually there is something which is different in the scenarios or in 03:59.170 --> 04:03.380 the samples, which is the reason why these means are coming out with different. 04:04.570 --> 04:11.090 If the means are not coming out to be significantly different, that will mean that it is just by chance. 04:11.110 --> 04:17.680 The value comes out to be something here or something new and not something very not exactly the mean 04:17.680 --> 04:18.040 value. 04:22.350 --> 04:29.700 So if the Z score or this school is greater than the critical level, that is when the P value is less 04:29.700 --> 04:38.010 than the critical alpha value, then it is said that the mean is significantly different than the population 04:38.010 --> 04:42.040 mean, hence pointing out that the population is entirely different. 04:42.270 --> 04:49.620 That is what we just said, that if the value of the value of the new machine is significantly different 04:50.070 --> 04:52.320 and is lying in this region. 04:53.710 --> 05:01.750 This critical region, then it means that these two samples are belonging to the different population, 05:02.080 --> 05:04.220 one population is one healthy kids. 05:04.480 --> 05:09.720 For them, the missing teeth number is one point for and for the unhealthy. 05:09.720 --> 05:16.980 They the missing teeth value is either four or five, which means that this is belonging to a local 05:17.090 --> 05:21.390 population, which has a completely different number of missing deep. 05:22.270 --> 05:30.340 So this means that the illness has actually changed the population with illness, thus children have 05:30.340 --> 05:33.730 different demographic and without illness, the children have different. 05:35.540 --> 05:39.420 So this is what we can prove using the speed that this. 05:43.410 --> 05:49.680 So this means that there was no impact from the treatment on the existing population, does the null 05:49.680 --> 05:51.370 hypothesis is rejected. 05:51.680 --> 05:58.590 Now, if there is no significant difference between the populations, that means and the population 05:58.590 --> 05:59.520 are completely. 06:01.430 --> 06:07.640 And there is no difference, there is no impact of the treatment on the existing population. 06:07.820 --> 06:13.580 The population is just laid back and the null hypothesis can be rejected. 06:15.220 --> 06:16.120 And also. 06:17.090 --> 06:19.740 We cannot accept the null hypothesis. 06:20.060 --> 06:25.680 We can only reject the null hypothesis on the basis of the evidence. 06:26.540 --> 06:29.280 We cannot say that the null hypothesis is correct. 06:29.600 --> 06:33.010 We can only say that the null hypothesis is incorrect. 06:36.040 --> 06:38.800 Now, let us have a look at one example. 06:39.430 --> 06:47.230 So on the twenty five point five, the scheme men and women differed by about five points. 06:48.070 --> 06:53.370 The means for men and women were eighteen point seventy five belonging to men. 06:53.770 --> 06:58.090 I'm twenty three point five belonging to women now. 06:58.090 --> 07:03.160 They were not identical, but how likely is five point difference to occur just by chance? 07:03.520 --> 07:10.120 So here what we are trying to say is that there was a sort of scaling system and there was a satisfaction 07:10.120 --> 07:17.620 scale which was set up and men said that they were satisfied eighteen point seven, five times out of 07:17.620 --> 07:22.750 twenty five points, they give eighteen point seven five and women give twenty three point five. 07:24.010 --> 07:31.960 Now, again, these two values are two different means, belonging to two different datasets. 07:32.990 --> 07:40.820 Now, out of these two different data sets, we want to find out that are these two belonging to the 07:40.820 --> 07:45.380 same population or it is actually different for men and women? 07:45.650 --> 07:48.930 Is the satisfaction criteria different for men and women? 07:49.550 --> 07:51.800 So we will check. 07:52.160 --> 07:56.720 So we will find out if these populations are similar or different. 07:58.400 --> 08:06.280 So an analysis was conducted, I'm the P-value value for the gender comparison was found out to be point 08:06.290 --> 08:06.750 one one. 08:07.980 --> 08:13.210 Which means that the probability was find out to be 11 percent. 08:13.590 --> 08:20.110 Thus there was about 11 percent chance that this data, the five point difference would occur by chance. 08:20.370 --> 08:23.790 So there was an 11 percent chance that this would occur by chance. 08:24.510 --> 08:27.140 Now the P value is greater than point five. 08:27.360 --> 08:29.420 So we would fail to reject the null. 08:29.640 --> 08:30.900 That is the. 08:32.040 --> 08:39.660 That is this is not a significant difference, thus there is no evidence that the male and female differ 08:39.660 --> 08:46.050 in their satisfaction if the probability was lower than zero point five. 08:47.160 --> 08:55.050 If the probability was lower than zero point five or zero point five, that is, there was about five 08:55.050 --> 09:02.010 percent chance that this would occur by a chance that this is occurring by chance, then we would have 09:02.010 --> 09:05.670 rejected the null hypothesis that these populations are safe. 09:05.880 --> 09:11.980 We would see that these populations are actually different and they have different satisfaction levels. 09:14.960 --> 09:16.860 Let us look at another example. 09:17.030 --> 09:23.780 So we are comparing how means and females differ with respect to how likely they would be recommended 09:23.780 --> 09:25.080 on an online course. 09:25.520 --> 09:26.540 OK, so. 09:28.570 --> 09:34.130 Measurement is on a five point gain, so the measurement is five point scale. 09:34.450 --> 09:42.000 The men have given four point one and the men have given three point one here. 09:42.040 --> 09:47.110 Men have given four point to the rating and women have given three point one rating. 09:48.510 --> 09:50.490 Now, the null hypothesis states. 09:51.710 --> 09:57.470 Then there is no difference between men and women in the recommendation of an online course, which 09:57.470 --> 10:05.150 is men and women will equally recommend an online course, it is not like if we are target men, then 10:05.150 --> 10:10.490 they will recommend more of online courses and women will not recommend online courses. 10:10.700 --> 10:13.570 So we just want to check if this is a scenario or not. 10:13.880 --> 10:18.410 So the hypothesis is that they are saying they are no different. 10:20.060 --> 10:27.290 Now, on a five point satisfaction scale, they differ by one point, men give four point three and 10:27.290 --> 10:31.160 women give three point one recommendation of value. 10:31.760 --> 10:38.750 Now, these values are not identical, but we want to find out how much is the chance that this one 10:38.750 --> 10:41.090 point differences by chance. 10:41.750 --> 10:48.620 We want to find out if these two populations are actually different, if men and women will give different 10:48.890 --> 10:55.820 amount of recommendations, or that it is just by chance that the samples which we were taking and the 10:55.820 --> 10:58.340 people which we were targeting, they give different answers. 11:00.650 --> 11:08.090 So for this analysis was conducted and the P-value for the gender comparison, give point three point 11:08.090 --> 11:12.980 zero three, this means that this was a three percent chance that this would occur by chance. 11:13.310 --> 11:18.960 This means that the value is less than zero point five, the P value zero point five. 11:19.160 --> 11:24.970 So we will reject the null hypothesis that the results are actually significant. 11:24.990 --> 11:28.660 There is a significant difference between four point three and three point one. 11:29.060 --> 11:35.060 That is why we are rejecting this hypothesis that both had equal goodwill equally. 11:35.690 --> 11:40.460 So now what we will do, we will target men for recommending our course. 11:41.770 --> 11:45.760 Thus, there is evidence that male and female differ in their recommendations. 11:47.380 --> 11:54.280 So now you can understand how we are doing this, we will be basically having to type of data sets and 11:54.370 --> 12:00.160 based on these two mean values, we are just trying to find out the difference between these values. 12:00.160 --> 12:02.380 Is it actually significant or not? 12:02.680 --> 12:09.910 So if the difference is significant enough, if it is significant enough, then we will see that they 12:09.910 --> 12:15.500 are belonging to the two different population and that is it is not occurring by chance. 12:15.700 --> 12:23.470 And if it is not different enough, then we will see that this is just Biogen's and this is calculated 12:23.470 --> 12:25.570 on the basis of this probability value. 12:25.750 --> 12:28.060 And this is something which we will have to decide. 12:29.290 --> 12:34.690 So this is different significance level, so we decide on different significance level, there is a 12:34.690 --> 12:40.300 zero point zero one zero point zero five and zero point one as significance level. 12:40.510 --> 12:46.080 So this are these are the Z school values which define the significance levels. 12:46.360 --> 12:52.090 Ideally, the significance level, which is chosen is zero point zero five. 12:54.400 --> 13:01.030 So these Xcode value is one point ninety six, if the Z value is greater than one point ninety six, 13:01.060 --> 13:04.600 then it is significantly different. 13:04.870 --> 13:09.180 If it is not greater than one point ninety six, then it does not significantly different. 13:09.190 --> 13:11.100 That is what we define here. 13:11.680 --> 13:13.090 And these are the values. 13:14.300 --> 13:18.860 So we can directly calculate this on the basis of the Z values or. 13:20.890 --> 13:22.240 So let us get back. 13:25.510 --> 13:33.160 So this is what we have for now and we will discuss about the different types of errors and what is 13:33.160 --> 13:40.140 the meaning of significance and discuss about this in the next session.