WEBVTT 00:00.870 --> 00:01.690 Hello, everybody. 00:02.010 --> 00:10.050 In this particular session, we will be discussing about a new law, which is yet another model of another 00:10.440 --> 00:13.720 testing method used in statistics. 00:14.580 --> 00:22.560 Now know what is similar to other testing methods, but the only difference is that there the other 00:22.560 --> 00:24.060 testing methods like. 00:24.870 --> 00:33.900 Guys, where they help us compare one or two variables, ANOVA helps us in deal with multiple values, 00:34.440 --> 00:36.510 that there's multiple variables. 00:36.840 --> 00:48.420 Now, what is an over and over is analysis obedience, which is taking the in from analysis and or from 00:48.450 --> 00:52.260 all the wrong variance analysis of variance. 00:53.540 --> 01:00.170 Now, it is a technique from statistical inference that allows us to deal with several populations. 01:00.560 --> 01:07.340 So as I said, in the case of other tests, we used to have either one or two population and we were 01:07.340 --> 01:10.580 trying to find out if these populations are similar or not. 01:11.680 --> 01:19.030 Now, in case I have to compare not just two populations, but if I have to compare five, six or hundred 01:19.030 --> 01:19.930 populations. 01:21.060 --> 01:30.600 In that scenario, I will have to conduct a lot of this to come to a conclusion, but I know what helps 01:30.600 --> 01:34.970 me to reduce the problem and do just one thing the best. 01:35.250 --> 01:38.390 So instead of conducting hundred faced. 01:39.480 --> 01:45.060 I can find out the conclusion by conducting just one single test, which is unknowable. 01:45.510 --> 01:51.300 That is why I know what is extensively used when we have a large number of populations, when we have 01:51.300 --> 01:54.350 to conduct this for multiple populations. 01:55.780 --> 01:57.380 So let us get further about it. 01:57.850 --> 02:03.850 So what do we have for that is so let us say we have a similar example. 02:03.880 --> 02:09.910 OK, now we have the same data set where we have a lot of Eminem's. 02:11.170 --> 02:18.640 So we want to connect the world with them now for this, when we want to know what. 02:19.270 --> 02:21.660 We will test a different null hypothesis. 02:21.670 --> 02:26.560 So usually what the null hypothesis used to be was that is one is equal to. 02:27.940 --> 02:34.480 For another test, it will be Mutu equal to military, for another test, it will be military will do 02:34.690 --> 02:37.120 food and there will be more number of tests. 02:37.270 --> 02:42.310 So if I was conducting would be test, I will have to create so many null hypothesis. 02:45.880 --> 02:54.550 But in case of a Nova, I have just one null hypothesis, and the null hypothesis will be it's not that 02:54.550 --> 02:58.500 this new one is equal to the military is equal to Muifa. 02:58.900 --> 03:05.380 So I am combining all the formal hypothesis into just one null hypothesis here. 03:06.360 --> 03:12.300 So this state that there is no difference between the mean waves of red, blue and green Eminem's, 03:12.480 --> 03:15.390 there is no difference between these four populations. 03:16.080 --> 03:20.960 And the alternate hypothesis will be that there is at least one population, which is different. 03:21.510 --> 03:21.780 Right. 03:22.050 --> 03:26.490 That is at least one population which is having a different date. 03:27.330 --> 03:30.120 It could be either red, the blue, green or orange. 03:30.600 --> 03:38.040 And any one of these, if they have a different way, then it will be an alternate hypothesis. 03:39.010 --> 03:46.090 Now, how this is a combination of those several hypotheses, so let's say I was doing this, then these 03:46.090 --> 03:48.560 would be the different hypotheses which I will have. 03:48.790 --> 03:49.520 What are these? 03:49.870 --> 03:55.540 One is that the mean little population of Red Gandy's is not equal to the mean weight of the population 03:55.540 --> 03:55.990 of the blue. 03:55.990 --> 03:57.150 Gandy's right. 03:57.190 --> 03:59.240 This is one alternate hypothesis. 03:59.470 --> 04:04.990 What is the one that the mean weight of the population of blue candies is not equal to the weight of 04:04.990 --> 04:13.780 the green can be similarly green compared with orange and the green compared with red and blue, compared 04:13.780 --> 04:16.280 with orange and blue compared with red. 04:16.420 --> 04:18.640 So all the combinations which we have. 04:18.850 --> 04:21.310 So we are combining all of those. 04:21.310 --> 04:23.290 I'm creating just one list here. 04:24.430 --> 04:32.470 So instead of conducting so many tests, we are combining all of those details in just one single test. 04:33.160 --> 04:35.330 This is what I know, what helps says in achieving. 04:36.070 --> 04:43.620 So now the P value, which we will be using in probability distribution for ANOVA is known as if that's 04:44.480 --> 04:51.210 OK, as we know that for every test we have a different P value rate based on the problem than the solution. 04:51.220 --> 04:53.420 The distribution is different. 04:53.620 --> 04:56.410 Hence, we have a different P value for each and every test. 04:56.560 --> 05:01.350 The bewailing for the test is calculated differently, the distance differently. 05:01.660 --> 05:02.140 So. 05:03.150 --> 05:09.000 Guys, when four guys split again, the statistics this guy did differently, so similarly, in case 05:09.000 --> 05:12.300 of another, we have the P-value as if distribution. 05:15.490 --> 05:22.960 Now, the calculation which we will be doing in case of ANOVA is a little more complex in comparison 05:22.960 --> 05:27.940 to the other calculations which we have done because again, solving a very difficult problem. 05:28.330 --> 05:34.900 So that is why we won't usually conduct this using by home. 05:35.170 --> 05:38.470 So we will be using some computer to solve this problem. 05:39.280 --> 05:47.140 OK, similarly for other guests, also, usually what we do is we solve these problems by using a system 05:47.500 --> 05:48.330 I'm not by. 05:48.970 --> 05:55.840 So all the examples which I have shown you now, we have solved the problems by hand so that you actually 05:55.840 --> 05:57.640 know what is happening behind. 05:58.640 --> 06:07.010 But in actual life, you will be solving those problems using a system, using a computer. 06:07.460 --> 06:10.260 OK, so I'll show you how you would be doing that. 06:10.490 --> 06:14.180 But now let us again try to solve this by hand. 06:14.670 --> 06:15.080 OK? 06:16.410 --> 06:24.600 So what are the steps which are involved in the ANOVA test, so let us go through these steps once and 06:24.600 --> 06:27.060 then we will go through each step one by one. 06:28.450 --> 06:34.810 So the first thing that we do is we calculate the sample mean for each of these sample as well as we 06:34.810 --> 06:40.000 mean for all the same for OK, so we will be calculating through means. 06:40.420 --> 06:48.180 One thing will be for each and every population, for each and every sample and another we would be 06:48.190 --> 06:53.530 for the all of the samples which we have from the data, all of these. 06:54.280 --> 06:58.240 OK, the next is calculating the sum of squared error. 06:58.850 --> 07:05.160 OK, now with each sample we square the division of each do the data value from the sample. 07:05.170 --> 07:11.500 We and the sum of all the squared deviation is the sum of the square in an abbreviated sample sweater. 07:11.530 --> 07:17.890 So basically what we are doing is we are just finding out the mean and we are comparing the mean with 07:17.890 --> 07:21.340 each and every value in the sample and finding out the. 07:22.920 --> 07:28.930 It is from that submissives attracting the expected value from the actual value, the value which we 07:28.930 --> 07:34.720 have in hand, that the mean which we have and the values in the sample, and then we square those and 07:35.050 --> 07:40.010 we square those what each and every sample we add those values and see how we do that. 07:40.030 --> 07:41.820 But for now, this is just somebody offered. 07:42.490 --> 07:45.930 Next, we calculate the sum of squares of three twin. 07:46.450 --> 07:52.750 OK, so what does a Mosquera Friedman Square division of each sample mean from the overall mean? 07:52.990 --> 07:59.230 So here what we were doing is initially we were finding out the sample squared error for each and every 07:59.230 --> 07:59.680 sample. 08:00.910 --> 08:08.710 OK, so the squared was a sample specific thing, but now we are finding out the sum of squared error 08:08.950 --> 08:15.410 specific to all the data, so we will be calculating an overall sum of spread error here. 08:16.220 --> 08:16.620 OK. 08:17.780 --> 08:24.200 Then we find out the degree of freedom again, there will be two types of degrees of freedom, one degree 08:24.200 --> 08:30.380 of freedom will be the respective to the Sam Phillips in, for example, we will be calculating the 08:30.380 --> 08:36.440 degree of freedom and another degree of freedom will be for the entire treatment for the entire removalist. 08:36.620 --> 08:39.680 So we will be calculating for all the samples which we have. 08:39.680 --> 08:43.450 So based on all the samples, we will be calculating the other degree of freedom. 08:43.940 --> 08:49.280 OK, then we will be calculating the mean squared of error and mean squared off frequent. 08:50.480 --> 08:54.620 And later, we will get the stylistics, which is equal to the. 08:55.800 --> 09:03.300 Mean squared, we mean squared off treatment, divided by the mean squared off at this particular value, 09:03.300 --> 09:04.950 divided by this particular value. 09:06.160 --> 09:09.560 OK, so let's go ahead and lay this out. 09:10.390 --> 09:15.400 It will be a little difficult for you to understand because it is a very complex process, but once 09:15.400 --> 09:18.250 you see the example, it will be a little easier to understand. 09:20.170 --> 09:23.450 So for us, we will find out the date in time for me. 09:23.810 --> 09:25.780 OK, so what do we have? 09:25.780 --> 09:27.940 We have four independent population. 09:28.600 --> 09:35.590 OK, so for those four independent population, the null hypothesis will be No one is equal to me is 09:35.590 --> 09:36.670 equal to Mutiny's equal. 09:37.630 --> 09:39.910 And what will be the alternate hypothesis? 09:39.940 --> 09:43.930 The alternate hypothesis will be that either one of these. 09:44.940 --> 09:52.020 Is not equal to the others, so it will be like at least one of these population mean is different from 09:52.020 --> 09:52.720 other samples. 09:53.410 --> 09:53.780 OK. 09:54.980 --> 10:01.430 Now, for this example, we will be using a sample size of three so that it is simply not the way to 10:01.430 --> 10:02.280 solve this problem. 10:02.720 --> 10:05.230 You will be having a large dataset. 10:05.450 --> 10:08.170 So it will be a little complex in nature. 10:08.180 --> 10:14.480 But for example, I'm thinking small number of samples, so then it is easier to this time. 10:15.900 --> 10:19.250 So what we do here is so this is my first population. 10:20.130 --> 10:27.270 Plus, population contains three values, 12, nine and 12, second population contains seven then and 10:27.270 --> 10:31.290 for the third population contains five, eight and 11. 10:32.160 --> 10:34.320 Next we have five, eight and eight. 10:35.960 --> 10:41.960 Now, what is the sample mean, the sample mean will be the meaning of these three values for the first 10:41.960 --> 10:44.180 population, it comes out to be 11. 10:45.120 --> 10:49.080 For the second population, the mean of these three values comes out to weepin. 10:50.060 --> 10:56.480 For the third population, the meaning of these sea values come out to be eight, and for the population, 10:56.480 --> 10:59.450 the mean of these three values turns out to be seven. 11:00.990 --> 11:02.280 So now what we have done. 11:04.090 --> 11:10.780 We have calculated the sample mean for each of our sample as well as the mean for all of this. 11:11.110 --> 11:14.780 So this is the mean for these samples. 11:15.310 --> 11:16.720 Now we need to find out. 11:16.720 --> 11:20.500 The mean for all of the details will mean of all of the data we can give. 11:20.500 --> 11:22.660 You mean of all these four values? 11:24.630 --> 11:28.560 OK, so it comes out to be nine, so we have two types of means. 11:28.560 --> 11:28.860 No. 11:29.160 --> 11:32.700 One is the entire sample means no. 11:32.790 --> 11:37.470 I mean, of all the samples and these are means specific to each and every sample. 11:38.790 --> 11:41.400 OK, next, what we are doing here, this. 11:43.300 --> 11:48.180 Next, we will include the sum of squared deviation from each sample mean. 11:48.710 --> 11:50.610 OK, so what do we have here? 11:51.280 --> 11:57.160 The meaning of the first sample sample from the first population is 11. 11:59.080 --> 12:01.310 And these are the values 12, nine and 12. 12:01.810 --> 12:07.120 So what I do is I subtribe this mean value from each of these values in the sample. 12:07.980 --> 12:09.570 I where those values. 12:10.990 --> 12:11.950 So I get the. 12:13.130 --> 12:18.960 So a sum of squared off error for each population like this, so this is what the population does, 12:18.980 --> 12:21.960 what the second population, third population and fourth population. 12:22.430 --> 12:24.860 Again, how did you how did I do it? 12:26.020 --> 12:30.220 The values are 17 and 13 for the second population, minus 10. 12:30.580 --> 12:37.720 So what will be the values the most, whether it will be seven, minus 10 will square plus 10, minus 12:37.720 --> 12:42.510 10 will squared plus 13, minus 10, Woodsworth, what is it, seven, minus 10. 12:42.520 --> 12:44.260 Will 20 plus then minus 10. 12:44.260 --> 12:46.090 Looks with plus 13 minus. 12:46.090 --> 12:46.900 Then we'll square. 12:46.900 --> 12:48.400 It is equal to 80. 12:49.210 --> 12:49.510 Right. 12:49.810 --> 12:53.590 So this is the sum of squarer for this population. 12:53.920 --> 12:59.800 Similarly here, the menas e so I subtract these values from each of the population values. 13:00.010 --> 13:05.740 I'm square those values to get the sample mean some squared header here. 13:06.980 --> 13:10.220 Right now, this is the sum of squared it up for. 13:11.390 --> 13:17.830 Each and every population, and now we want to find out the summer of sweat and for the entire population, 13:17.840 --> 13:24.550 for all the values which we have so that we will get by adding six plus 18 plus 18 plus six. 13:24.740 --> 13:26.680 So it comes out to be forty eight. 13:27.290 --> 13:28.870 OK, what have we done? 13:29.050 --> 13:35.320 Now we have calculated the sample mean for sample and the mean of all the samples. 13:35.630 --> 13:39.670 Then we calculated the sum of sweat and what each and every population. 13:40.160 --> 13:45.320 Then we calculated the sum of squared error for each and every value in the. 13:46.670 --> 13:49.600 Some of all the squared deviation, right? 13:49.850 --> 13:52.100 So this is the sum of squared, Ayda. 13:53.710 --> 13:57.520 Next, we want to find out the sum of square off treatment of gay. 13:58.680 --> 14:01.660 So now we want to find out the sum of squared off three minutes. 14:01.720 --> 14:02.900 How do we find that out? 14:04.430 --> 14:11.720 So we square the division of the sample mean from the overall sample, me and the sum of all of these 14:11.720 --> 14:15.110 is multiplied by one less than the number of samples. 14:15.410 --> 14:16.850 So what we do here is. 14:18.280 --> 14:19.090 We have the. 14:20.280 --> 14:24.330 Value here, what is the sum of squared error in this 40? 14:24.930 --> 14:27.690 Now we want to find out the sample mean. 14:27.690 --> 14:31.740 What is the sample mean of all data comes out to be nine. 14:34.040 --> 14:39.340 I mean, for example, 11, then eight and seven. 14:42.510 --> 14:51.020 So we have 11, ten, eight, seven, and this is the mean for all the data for the oil. 14:51.750 --> 14:59.460 So how do we find out the population mean for the first sample, minus the mean for all? 14:59.480 --> 15:09.720 The whole square plus population mean for the second sample, minus the mean for all the data is with. 15:11.330 --> 15:20.030 Plus, I mean, for example, minus all the mean for all the double squared plus I mean for the fourth 15:20.030 --> 15:30.290 sample minus the overall, you mean both with like and multiplying this with what, B and multiplying 15:30.290 --> 15:35.030 this with the number of samples minus one. 15:35.060 --> 15:39.770 So what is the number of samples that are one, two, three, four samples. 15:40.160 --> 15:41.780 So we multiply that with. 15:45.060 --> 15:47.290 So this is multiplied by three. 15:47.460 --> 15:49.230 So this is the sum of squared off. 15:50.310 --> 15:53.670 So that is how we calculate the sum of squared off treatment, right. 15:54.150 --> 15:54.990 So what have we done? 15:55.200 --> 15:59.880 Now, we found out the sample means we found out the overall mean. 16:01.280 --> 16:04.340 We found this of squared of some of square Edda. 16:05.800 --> 16:12.520 For so basically, it's almost better for each and every population and and all of these. 16:13.410 --> 16:15.600 For all the populations. 16:17.770 --> 16:24.220 Then we find this of squared off treatment by multiplying by the number of population minus one and 16:24.520 --> 16:31.370 finding out the sum of squared off error with respect to each and every population, me with the entire 16:31.390 --> 16:32.830 mean of the all the data. 16:32.950 --> 16:34.550 So this is what we have until. 16:36.040 --> 16:40.670 Now, what do we have done, we have done this particular save, this is all you've done, this is also 16:40.690 --> 16:41.590 done now. 16:41.590 --> 16:43.870 We want to find out the degree of freedom. 16:50.590 --> 16:58.930 Now, what are the degrees of freedom, the degrees of freedom are now there are two big data values. 16:58.960 --> 17:00.070 One for Sampas. 17:01.400 --> 17:08.120 So the dignity of freedom for the treatment will be number of samples, minus one, that is number of 17:08.120 --> 17:09.630 populations, minus one. 17:09.980 --> 17:11.950 So there are the whole population. 17:11.960 --> 17:16.300 So the degree of freedom of the treatment will be four minus one. 17:16.550 --> 17:17.310 That is three. 17:17.990 --> 17:18.950 You can say this. 17:19.340 --> 17:22.000 What is the treatment, which I have been talking about? 17:22.670 --> 17:26.080 Maybe you are confused about the treatment ward, which I have been using. 17:26.270 --> 17:29.480 So this treatment is nothing but legacy. 17:29.480 --> 17:38.900 I'm talking about say there are different types of of that and that these doctors are being fed by different 17:38.900 --> 17:40.310 types of food. 17:40.490 --> 17:42.630 They're being fed by different types of food. 17:42.920 --> 17:47.700 So these are four different food items which I am feeding to the characters. 17:47.930 --> 17:54.470 And I'm comparing these four food items and finding out if they have if these four are equivalent oil 17:54.470 --> 18:03.710 for food works well on these this or there is one or there is any specific food which works extremely. 18:03.720 --> 18:12.050 But then all of the food in the way of the causes war for any one particular specific item of what, 18:12.050 --> 18:13.290 a specific food item. 18:13.640 --> 18:18.740 So this treatment is nothing but what I am doing to make these populations different. 18:18.950 --> 18:20.130 That is one of the treatment. 18:20.130 --> 18:24.320 This makes a number of degrees of freedom of the industry. 18:24.710 --> 18:27.200 That is, instead of having the full food items. 18:27.200 --> 18:30.860 I am so out the food food items when they are there. 18:30.870 --> 18:33.830 So the of freedom of choosing the food item will be three. 18:34.610 --> 18:41.600 Right now, the degree of freedom of error is basically the degree of freedom of what we can select 18:41.600 --> 18:42.820 from the populations. 18:43.010 --> 18:45.290 So there are potential values. 18:46.510 --> 18:53.080 There are two, three values, so from this sample, I can pick up randomly the values from each sample, 18:53.080 --> 18:55.270 I can go through values randomly. 18:55.510 --> 18:57.680 So gross food comes out to the EP. 19:00.550 --> 19:03.220 So this is the big deal, freedom. 19:04.380 --> 19:05.190 Of Ed. 19:09.700 --> 19:17.050 Now, the means squared off treatment and means squared off of it has to be found so mean squared off 19:17.050 --> 19:24.340 treatment will be cut by three and means word of error of will be fourteen by eight. 19:24.670 --> 19:25.520 What is this the. 19:25.670 --> 19:26.680 And what is this for? 19:26.680 --> 19:27.070 Be it. 19:30.570 --> 19:32.820 This is some sort of treatment. 19:34.040 --> 19:38.060 So some of square of reedman divided by the degree of freedom of treatment. 19:39.100 --> 19:43.040 Gives the means where it gives the means of treatment. 19:44.290 --> 19:45.490 And when we divide. 19:46.770 --> 19:47.220 The. 19:48.630 --> 19:57.480 Sum of squared off error by the degree of error of a degree of any degree of freedom of error, because 19:57.570 --> 20:03.140 if so, this is the mean squared off error means we're afforded, OK? 20:03.180 --> 20:05.280 So these are the values that we have will be. 20:07.380 --> 20:08.610 Then on six. 20:09.750 --> 20:17.790 Now I can simply find out the statistics by dividing them by six, so it comes out one point six six. 20:19.120 --> 20:24.800 OK, so you can go to this again in case you want to let me take you through this again. 20:24.820 --> 20:26.590 OK, now what do we have? 20:26.600 --> 20:28.050 We have these samples. 20:29.570 --> 20:36.080 So out of these samples, we calculate the means for each and every population and we find out the mean 20:36.080 --> 20:39.540 of all these populations, which comes out to be nine. 20:40.350 --> 20:40.660 OK. 20:40.700 --> 20:43.470 This is the mean with respect to each and every population. 20:43.490 --> 20:45.950 This is the mean with respect to the entire population. 20:47.620 --> 20:52.780 Then we find out the mean minus something mean minus sample mean, which is. 20:53.690 --> 20:54.350 11. 20:57.880 --> 20:58.990 So what is this? 20:59.020 --> 20:59.700 This is night. 21:00.040 --> 21:07.210 So we are subtracting 11, minus nine, then minus nine, eight minus nine and seven minus nine, which 21:07.210 --> 21:09.540 comes out of the four one one four. 21:09.940 --> 21:11.330 And we are thinking of this. 21:11.350 --> 21:12.070 Some of these. 21:14.350 --> 21:19.570 Now we are finding out the sum of squared error, so what is the sum of squared error in this? 21:21.010 --> 21:28.810 Twelve minus 11 will squared plus nine, minus 11 squared, plus 12, minus 11 was when it comes out 21:28.810 --> 21:29.530 to be six. 21:30.460 --> 21:33.500 This is some of square and what, each and every population. 21:33.850 --> 21:40.660 So what are we doing again, seven minus 10 or 12 and minus 10 squared, 13 minus then will square and 21:40.660 --> 21:42.250 the sum of all of these comes out. 21:42.280 --> 21:44.860 We begin with just one more square in a row population. 21:45.340 --> 21:49.630 So similarly, we calculate this what each and every population, some of square. 21:50.260 --> 21:56.980 And when we add these some of squared with respect to each and every population together, we get some 21:56.980 --> 21:59.290 of the complete some of squared added. 22:00.860 --> 22:05.450 Right, and what is the sum of squared of treatment, the sum of squared off? 22:06.010 --> 22:11.140 This is the value which we call the 48 value, which we got, and this is the sum of squared of treatment. 22:12.270 --> 22:17.370 So what is the most frequent examples where treatment is in the sample mean? 22:18.540 --> 22:21.750 So what does mean mine sample mean, so this is the mean. 22:23.020 --> 22:24.340 Minus sample mean. 22:25.640 --> 22:26.450 This value. 22:27.560 --> 22:29.120 I mean, minus sample mean. 22:31.810 --> 22:38.110 These values, so what is the sum of these values, these some of these values is then. 22:39.180 --> 22:42.510 Multiplied by the 320 degree of freedom. 22:42.540 --> 22:47.910 So what is the degree of freedom when degree of freedom is the number of populations minus one? 22:47.940 --> 22:49.320 So this comes out to be three. 22:49.560 --> 22:52.680 So three then comes out with 30. 22:53.910 --> 22:57.760 Now, this is the sum of squared off treatment. 22:57.800 --> 23:01.410 This is the sum of squared error, what else we need to find? 23:01.410 --> 23:08.070 We need to find the degree of freedom for each degree of freedom for tourism industry, which we have 23:08.070 --> 23:14.340 already found no degree of freedom for the entire population comes out to be to. 23:16.320 --> 23:22.140 Plus two, plus two plus two, which comes out to be eight. 23:24.450 --> 23:26.050 How do we find this out? 23:26.110 --> 23:33.090 We find this out by the sum of all of these values, the total number of values which we have in the 23:33.090 --> 23:34.710 population minus. 23:35.740 --> 23:41.770 The number of populations, so it will be 12, minus four comes out to be. 23:44.500 --> 23:50.680 So this is what we calculated, and lastly, what we do is we find out the means of treatment, that 23:50.680 --> 23:56.830 means of means of treatment will be 30 by three and means we're available before the break. 23:58.400 --> 24:04.790 Thirty by three and fourteen by eight, which is dividing by their own degree of freedom, basically 24:04.820 --> 24:09.070 a degree of the sum of squared off divided by the degree of freedom of religion. 24:10.170 --> 24:15.000 And some of squared off and divided by any degree of freedom of ÉDITH. 24:16.000 --> 24:24.520 And we simply divide the sum of squared of treatment divided by degrees of divided by this square of 24:24.520 --> 24:25.910 error, divided by negative. 24:26.390 --> 24:30.110 And so we get down by six with just one point six and seven. 24:30.130 --> 24:31.830 So this is the statistics value. 24:32.140 --> 24:37.830 Now, next thing is to find out what is the meaning of this F statistic value, which we have just found 24:37.840 --> 24:38.060 out. 24:38.380 --> 24:41.200 So we go to the distribution table. 24:42.580 --> 24:46.420 And in this distribution, they will compare different degrees of freedom. 24:46.720 --> 24:48.830 So what is the degree of freedom that we have? 24:49.120 --> 24:52.890 We have the first degree of freedom as eighth and the second degree of freedom. 24:53.590 --> 24:57.490 So the value corresponding to this would point zero six six. 24:58.120 --> 25:03.450 Now, four point zero success is with respect to the Alpha zero point zero fight. 25:03.790 --> 25:09.370 Make sure that you check the alpha value related papers and distribution will have different deals for 25:09.370 --> 25:10.650 different values. 25:10.870 --> 25:16.840 And because Alpha zero point zero five is of a particular value, which is. 25:18.430 --> 25:24.880 Considered to be a standard, so we will consider this if value for now, so it comes out to be four 25:24.880 --> 25:26.360 point zero six six. 25:27.050 --> 25:30.160 Now, what do we do on this zero four point zero six six? 25:32.760 --> 25:35.610 The actual value is one point six, six, seven. 25:36.270 --> 25:43.590 Now, the statistical value is really less than the value which we have got from the distribution deal, 25:43.980 --> 25:50.700 which means that this there is no significant difference between these populations. 25:50.700 --> 25:53.340 These populations are similar to each other. 25:53.340 --> 25:57.900 That is, there is no impact of these. 25:59.640 --> 26:00.710 The men on the. 26:02.030 --> 26:05.480 So this is what we find out from this particular test.