WEBVTT 00:01.050 --> 00:02.380 Hello, dear. 00:02.430 --> 00:06.300 Now, we have discussed about descriptive statistics. 00:07.340 --> 00:15.320 And descriptive statistics, we have learned about the measures of central tendency like mean median 00:15.500 --> 00:25.280 mode, we have talked about the different type of distributions that we have and how the distributions 00:25.280 --> 00:31.160 vary, the respect of the dosis which is present in those. 00:32.270 --> 00:35.300 Lord, or with respect to the Skewness. 00:36.850 --> 00:45.580 Apart from that, we have discussed about the measures of offspring, which is ratings on standard deviation. 00:46.630 --> 00:54.910 Now, all of these are part of descriptive statistics, which basically provide a summary of the data. 00:56.730 --> 01:05.220 But usually what we will be working with is not the descriptive statistics, but with the inferential 01:05.220 --> 01:06.040 statistics. 01:06.900 --> 01:10.190 So let us look at what inferential statistics it's. 01:14.890 --> 01:25.120 So influential statistics consists of making inferences from samples to populations, hypothesis testing, 01:25.300 --> 01:31.900 data mining, relationship among variables and making predictions, which is based on the probability 01:31.900 --> 01:32.320 theory. 01:34.010 --> 01:40.640 In case of descriptive statistics, we organize the data and we summarize the data. 01:41.990 --> 01:50.900 In case of inferential statistics, we will be taking up a sample and based on the sample, we will 01:50.900 --> 02:00.590 make different inferences regarding the population data because usually we will not be able to find 02:00.590 --> 02:03.770 out everything about the population. 02:04.550 --> 02:11.870 Finding out the measures regarding the population is a very tedious task. 02:13.020 --> 02:18.570 For example, we are talking about salaries of all the people in the world. 02:19.790 --> 02:26.180 Now, calculating the salaries for all the people in the world will take a lot of pain. 02:27.250 --> 02:35.110 So instead of calculating and summing up the salaries of all people of the world, what we do is we 02:35.110 --> 02:39.250 take small samples of people from all over the world. 02:39.430 --> 02:47.980 And then based on these samples, the light of day, we try to find out these salaries, which would 02:47.980 --> 02:50.660 be belonging to the all the people of the world. 02:51.220 --> 02:53.680 So this is what inferential statistics is. 02:54.250 --> 03:00.790 We will have some sample data and based on the sample that we will try to find out about the population. 03:01.880 --> 03:09.440 Again, we will try to compare different samples and find out if they belong to the population or not 03:09.620 --> 03:14.010 or if there is some relationship between these two samples or not. 03:14.180 --> 03:18.920 So these kind of things, which when we do those are called inferential statistics. 03:21.610 --> 03:30.400 So why do we need this so descriptive statistics describes the data, why the influential statistics 03:30.400 --> 03:38.440 allows us to make predictions, that is inferences from this data which we have now with inferential 03:38.440 --> 03:39.250 statistics. 03:39.400 --> 03:46.690 You can dig the data from samples and generalize about the population, which is we can the mean of 03:46.690 --> 03:51.830 the sample and then try to find out what would be the mean of the population itself. 03:52.090 --> 03:56.410 For example, I have a bit of a sample of people who are diabetic. 03:56.770 --> 04:05.590 So from their diabetes level, I can find out about the diabetes level of people all around the population. 04:08.150 --> 04:09.650 So why do we need this? 04:11.130 --> 04:19.680 Inferential statistics provides a view of going from a sample to a population, inflating the barometer's 04:19.680 --> 04:23.410 of a population from the data on the statistics of the sample. 04:23.700 --> 04:30.630 So based on the statistics which are belonging to sample, we are trying to find out the bottom of the 04:30.630 --> 04:31.880 entire population. 04:34.200 --> 04:41.960 Now, it is usually necessary for a researcher to work with samples rather than the whole population, 04:42.750 --> 04:50.910 but one difficulty is that a sample is generally not identical to the population which it comes from. 04:51.690 --> 04:59.280 So it is difficult to find out that the population sample has to be a part of the population completely. 04:59.580 --> 05:04.950 We need to make sure that the sample is identical to the population and. 05:06.050 --> 05:09.050 The sample actually represents the population. 05:09.800 --> 05:14.030 Now, another difficulty is that no samples are the same. 05:14.300 --> 05:19.840 When we are taking some random values from a population, the values tend to differ. 05:20.180 --> 05:23.850 We cannot always get the same sample from the population. 05:24.470 --> 05:28.460 So how can we know which is the best described sample? 05:28.460 --> 05:31.320 Which sample will actually describe the population? 05:31.880 --> 05:38.750 So this is why we need rules which will actually be able to relate the samples to the population. 05:41.630 --> 05:48.560 Now, what a different estimation techniques, how do we actually estimate these values, so there are 05:48.560 --> 05:57.230 two different approaches for estimating, one being the point destination and another being the interval 05:57.230 --> 05:57.920 estimation. 05:59.720 --> 06:07.580 The point dimension, we give one value for a characteristic which is hopefully to lose to the unknown 06:07.580 --> 06:07.990 value. 06:08.660 --> 06:15.830 So in case of point destination, what happens is it will try to provide a value for me or it will try 06:15.830 --> 06:18.920 to provide a value of a standard deviation. 06:19.640 --> 06:25.610 And based on the standard deviation, we are not really sure if the standard deviation of the sample 06:25.790 --> 06:32.180 will actually be the standard deviation of the population or the mean which we have calculated for the 06:32.180 --> 06:40.700 sample will actually be the mean of the population because the samples are generated randomly and because 06:40.700 --> 06:44.750 these samples are generated randomly, the values in the samples would differ. 06:44.990 --> 06:47.370 So the mean will each and every day. 06:48.110 --> 06:55.940 So we need to find out a value which would be exactly similar to the population or which is as close 06:55.940 --> 06:57.500 as possible to the population. 06:59.110 --> 07:07.090 So we cannot actually expect to find the precise value describing the population then only using date 07:07.100 --> 07:07.850 of the sample. 07:08.230 --> 07:15.820 So when we are finding out some point estimations from the sample, we can not be completely sure that 07:16.090 --> 07:21.460 the sample mean, which we have calculated will always be equal to the population. 07:22.210 --> 07:27.970 This is something which we can very easily see because we are not sure how the sample has been generated 07:27.970 --> 07:31.700 and if this sample actually represent the population. 07:31.840 --> 07:35.770 So we need to calculate and find out several samples. 07:35.950 --> 07:43.780 And from those several samples, we will have to find out the mean which will actually justify the population. 07:43.790 --> 07:44.020 We. 07:45.170 --> 07:50.210 So we cannot see about a population from just one single sample. 07:50.900 --> 07:52.170 So what do we do now? 07:53.310 --> 08:00.220 The other method which we have is interval estimation now, what does interval estimation, though, 08:00.300 --> 08:00.630 do? 08:01.080 --> 08:04.360 It gives an interval of likely values. 08:04.530 --> 08:12.750 So instead of seeing that the mean is 20, it will see that the mean value for the population lies between 08:12.960 --> 08:16.120 18 and 22. 08:16.410 --> 08:25.180 And I am 90 percent sure that it will be correct on I am 95 percent sure that this value is always good. 08:25.770 --> 08:32.820 So what will happen is what I'm trying to say here is that when I say 95 percent confident that I'm 08:32.820 --> 08:41.360 95 percent confident that the population mean is 20 or or the meanness between 18 and 22. 08:42.240 --> 08:52.800 So this means that if we do these sampling hundred times, then out of those hundred samples, 95 percent 08:52.800 --> 08:57.580 of the times, the mean value will lie between 18 and 22. 08:58.580 --> 09:03.850 This is what this in Doel estimation will actually allow us to. 09:05.830 --> 09:15.250 So it will give you an interval of likely values where the width of the interval, which is from 18 09:15.250 --> 09:15.890 to 20. 09:15.910 --> 09:18.160 So here the word this four. 09:19.550 --> 09:26.000 So the width of the interval will depend on the confidence to be required to have in this in the. 09:26.690 --> 09:30.020 So this will be basically dependent on how much confidence. 09:30.890 --> 09:34.350 So what will happen if I am very, very, very confident? 09:35.060 --> 09:44.090 So if I am saying that I'm 99 percent confident, so I will have to have a larger window to be 99 percent 09:44.090 --> 09:44.630 confident. 09:44.630 --> 09:52.440 I will have to have something like I'm 99 percent sure of the values line between fifteen to twenty 09:52.490 --> 09:52.810 five. 09:53.420 --> 10:01.850 So in that case, I can be 99 percent sure now for being 95 percent sure the window will be because 10:01.850 --> 10:04.690 I am decreasing the window now. 10:04.910 --> 10:13.670 So by decreasing the window of the estimation, I will be a little less sure because I have to be very 10:13.670 --> 10:14.470 precise here. 10:14.900 --> 10:22.370 So if I have something like 18 to 22, so now I can be only 95 percent sure. 10:23.790 --> 10:32.280 And then when I'm seeing my mean value is between 19 and 21, so in that case, I am only 90 percent 10:32.280 --> 10:33.200 sure about this. 10:33.600 --> 10:36.600 So this is what in the world estimation will provide us. 10:36.780 --> 10:41.530 The smaller the window we are trying to get, the less of the confidence we. 10:42.880 --> 10:49.570 So that is what usually happens, but we will actually see how we will derive this confidence, how 10:49.570 --> 10:55.750 we will be driving the values and the intervals, so all these things are what we will be learning in 10:55.750 --> 10:59.230 these estimation techniques and information statistics. 11:03.190 --> 11:09.250 So one thing to remember is that statistics never proves anything. 11:10.260 --> 11:23.270 So with statistics, I can see that of all the people who are drinking coffee will actually have insomnia, 11:24.060 --> 11:26.030 so I cannot say something like that. 11:26.370 --> 11:31.180 So it will not give me a causal relationship relationship. 11:31.380 --> 11:32.780 It will not prove anything. 11:32.790 --> 11:35.910 It will just indicate a relationship that increases. 11:36.180 --> 11:38.760 The intake of coffee is high. 11:38.910 --> 11:41.280 Then the chances of insomnia is also high. 11:41.430 --> 11:49.130 But it will not to I cannot see that likely that insomnia is caused by Heigl's. 11:50.470 --> 11:51.620 High amount of coffee. 11:52.890 --> 11:59.850 So you see the difference between this, when I see it will never prove prove anything. 12:00.000 --> 12:03.420 So here I am saying that it will not give a causal relationship. 12:03.870 --> 12:09.640 So an association does not necessarily negate US shortfalls, effect relationship. 12:09.900 --> 12:17.100 So this means that I'm trying to say I cannot see that golf will cause insomnia, but I can only say 12:17.100 --> 12:21.780 using statistics that coffee and insomnia go hand in hand. 12:22.620 --> 12:24.000 So that is something which I consider. 12:25.570 --> 12:34.090 Now, statistics can always be wrong, however, there are things that researchers can do to improve 12:34.090 --> 12:40.090 the likelihood that the statistical analysis is correctly identifying a relationship between the lead. 12:40.450 --> 12:47.680 So here, what we will be doing is we will be trying to find out and trying to make as correct predictions 12:47.680 --> 12:48.570 as possible. 12:48.760 --> 12:50.930 But we are not really sure about that. 12:50.950 --> 12:56.580 We cannot be 100 percent sure about what we will try to be as precise as possible. 13:00.040 --> 13:03.190 So we will learn about video tapes in the next session.