WEBVTT 00:01.220 --> 00:08.660 High in this session, we will discuss about the next set of tests, which is Guy Square Test. 00:09.440 --> 00:12.260 So we have two types of test undercut. 00:12.560 --> 00:20.750 Square one is the test for goodness of fit and the other one is the best for independent. 00:21.620 --> 00:29.380 And these two tests are non parametric hypothesis tests using these type of sticks. 00:30.200 --> 00:37.460 So we will learn about what guys of statistics is and how we can perform these duties and when are we 00:37.460 --> 00:39.530 actually going to perform these tests. 00:42.580 --> 00:45.980 So first of all, let us talk about non parametric. 00:46.240 --> 00:51.130 What do we mean when we say these are known parametric hypothesis testing? 00:53.170 --> 01:00.310 So the total non parametric refers to the fact that these guys squared this do not require assumptions 01:00.310 --> 01:07.050 about population barometer's, nor do they test hypotheses about population barometer's. 01:09.100 --> 01:19.720 Now, the tests which we have conducted, that is the Z test and the deepest both of these tests was 01:19.720 --> 01:23.340 revolving around the population barometers. 01:24.250 --> 01:31.180 We were trying to find out either what the population barometer should be or we were trying to compare 01:31.180 --> 01:38.500 a particular sample of the population to find out if this sample actually belonged to the population 01:38.500 --> 01:39.120 or not. 01:40.640 --> 01:48.980 But in this case, we are not comparing with the population, we are not trying to find out something 01:48.980 --> 01:53.520 about the population, we are just analyzing about the data at its. 01:55.620 --> 02:04.980 So previous examples of hypothesis tests such as the fetus are barometric test, and they include assumptions 02:04.980 --> 02:12.690 about barometers and hypotheses about the parameters that is the mean of the population should be of 02:12.690 --> 02:18.840 one population, should be greater than something or not or mean of the populations are equal or not, 02:19.050 --> 02:25.030 or we know one population is greater than the other population of a particular treatment. 02:25.350 --> 02:27.420 So these kind of problems were there. 02:28.430 --> 02:36.860 For example, we would come betting that if there is a kid who has some disease, then he will have 02:36.870 --> 02:39.890 little number of or more number of broken. 02:40.790 --> 02:44.570 So that is one assumption which we are making here. 02:45.020 --> 02:54.830 We wanted to compare if a kid who is 80 is different from the population of the kids who are not in 02:55.010 --> 02:59.500 and comparing the population mean for the number of broken beat. 02:59.750 --> 03:01.220 So that was what we were doing. 03:01.220 --> 03:04.550 We were comparing to two samples of children. 03:04.820 --> 03:12.290 One sample had kids who have a particular disease, and another sample was of the kids who did not have 03:12.290 --> 03:13.040 any disease. 03:13.220 --> 03:16.860 And we were comparing the mean value of the broken between them. 03:17.750 --> 03:25.280 So there we were considering these two to analyze about the whole population, that we have all those 03:25.280 --> 03:32.360 children in the world and we take samples and we find out the mean of all the children who are ill and 03:32.360 --> 03:39.700 all the children who are naughty, then is the mean number of their broken needs would be equal or not. 03:39.740 --> 03:42.380 That is what we were trying to find out to that. 03:42.800 --> 03:45.950 But here we are trying to find out a different thing. 03:45.970 --> 03:46.850 Now, what does this. 03:47.890 --> 03:54.580 The most obvious difference between Chi Square test and the details hypotheses we have considered is 03:54.580 --> 03:56.230 the nature of data. 03:56.350 --> 03:59.380 So in the desert we had a different type of data. 03:59.380 --> 04:01.990 And in Geisler, we will have a different type of data. 04:02.200 --> 04:05.090 What type of data would be then we will seen something. 04:05.380 --> 04:10.840 Now, in case of Chi Square, the data are frequencies rather than numerical scores. 04:12.510 --> 04:17.460 So in case of deepest, what did we have in case of a. 04:18.060 --> 04:25.790 We had different children and a different data about children and for each children, each child, we 04:25.800 --> 04:27.780 had the number of broken teeth. 04:27.780 --> 04:32.560 He will have another child, the number of broken bones she will have and so on. 04:33.210 --> 04:39.400 Now, here we have a particular new medical school or we can see a particular marks and an exam that 04:39.400 --> 04:40.500 the child would not be. 04:40.740 --> 04:45.060 So these are different things which we were comparing earlier and gives of the best and safest. 04:45.540 --> 04:53.580 But now, in case of Chi Square, we are not comparing the numerical value, but we are actually comparing 04:53.580 --> 05:01.110 the frequency of the data that for a particular thing, there are 20 children available or there are 05:01.110 --> 05:02.580 20 children who are the. 05:03.750 --> 05:10.530 So we are talking about frequency here instead of the data related to them, not about the height of 05:10.530 --> 05:15.300 the children, but actually the number of the children who would represent this kind of data would be 05:15.300 --> 05:15.560 that. 05:15.660 --> 05:18.900 And to clarify more, we will take some examples of that. 05:18.930 --> 05:21.780 You'll have a better understanding of this. 05:24.110 --> 05:30.810 So let's get further, and the first test, which we will be talking about is the guy is quirkiest of 05:30.810 --> 05:31.980 goodness of. 05:33.410 --> 05:41.750 Now, the guy's got this for himself, it uses the frequency data from a sample to test the hypothesis. 05:43.120 --> 05:49.780 And what does this hypothesis here, what is the hypothesis in case of Woodenness offered, the hypothesis 05:49.930 --> 05:54.440 is about the shape or proportions of the population. 05:54.640 --> 06:04.660 So here we are trying to find out if a particular sample which we have is having a particular shape 06:04.660 --> 06:05.230 or not. 06:06.360 --> 06:12.990 That is, if the population will follow a particular type of distribution or not, that is what we are 06:12.990 --> 06:16.590 trying to find out here and we are trying to find out. 06:17.010 --> 06:22.080 Let's see, we have a sample X and we have the entire population. 06:22.440 --> 06:24.660 So we want to find out that the. 06:25.870 --> 06:32.610 Distribution that we are gaining from this particular sample would fit into a particular distribution 06:32.610 --> 06:32.910 or not. 06:33.180 --> 06:35.130 That is why it is known as woodenness of. 06:36.320 --> 06:43.220 We are trying to find out if we have this particular sample with 10 or 20 values, then willing to fit 06:43.220 --> 06:46.950 a normal distribution or it will fit any other type of distribution. 06:47.270 --> 06:49.540 So that is what we are trying to find, OK. 06:50.090 --> 06:56.860 Now, here, the guy square test is used to test it for a sample of data came from a population with 06:56.870 --> 06:58.160 a specific distribution. 06:58.160 --> 07:02.270 That is, it is belonging to a specific distribution or not. 07:03.390 --> 07:09.820 Now, every individual in the sample is classified into one category on the scale of measurement. 07:10.110 --> 07:15.270 So we will have different categories in case of this particular test. 07:15.780 --> 07:21.720 Earlier, we had just some numerical values, but here we will have certain categories. 07:21.870 --> 07:29.130 And based on those categories, we will have a number of people being allocated to that particular category, 07:29.400 --> 07:31.860 maybe 20 male and 30 female. 07:32.910 --> 07:35.020 So this kind of data would be available. 07:36.310 --> 07:44.980 Now, the data called absorbed frequencies simply count how many individuals from the sample are in 07:44.980 --> 07:45.790 each category. 07:45.820 --> 07:52.660 So basically we get to know that how many people are belonging to the category or category B and C and 07:52.660 --> 07:53.010 so on. 07:53.920 --> 07:54.430 So. 07:55.970 --> 07:58.760 What does the guy square this, what would this fit for? 07:59.510 --> 08:09.210 The null hypothesis specifies the proportion of the population that the bag should be in each category. 08:09.230 --> 08:14.370 That is how much of a particular population should belong to each category. 08:14.510 --> 08:20.960 If each category should have equal number of people in them, or there should be more number of people 08:20.960 --> 08:24.500 in one category and less number of people in the category. 08:24.680 --> 08:27.710 So this is what the null hypothesis would be about. 08:29.230 --> 08:37.690 And the proportions from the null hypothesis are used to compute the expected frequencies that describe 08:37.690 --> 08:43.240 how the sample will appear if it were in a perfect agreement with the null hypothesis. 08:43.420 --> 08:49.840 So basically, we create a null hypothesis, which will imply that latency there should be equal number 08:49.840 --> 08:57.790 of male and female for a particular service and B, on having those equal number of male and female. 08:57.790 --> 09:04.130 But we have this is what null hypothesis would suggest, that we should have 20 million, 25 million 09:04.130 --> 09:07.210 in this particular survey giving a particular opinion. 09:08.340 --> 09:17.190 Now we want to find out if the actual data, which we have, because what we have now is a sample of 09:17.190 --> 09:17.640 the data. 09:18.500 --> 09:23.010 And a sample might have less number of middle and high number of female. 09:23.600 --> 09:24.860 That is a possibility. 09:25.250 --> 09:31.820 But because this is a sample we cannot see straight away about the number of people in the population, 09:32.000 --> 09:36.170 because maybe when I took a sample, there were nine being male. 09:36.170 --> 09:37.610 I'm twenty one female. 09:37.820 --> 09:43.740 But in the population actually there were four hundred million four hundred females, which is an equal 09:43.740 --> 09:43.920 number. 09:44.720 --> 09:51.290 So here we want to find out if the distribution, which the sample is showing, is putting into the 09:51.290 --> 09:53.540 distribution, which the population would do. 09:53.930 --> 09:58.700 So we want to find out what the distribution of the population, which it will be giving up. 10:02.910 --> 10:04.280 So let us see here. 10:05.810 --> 10:10.280 So here we have a frequency data of different eye colors. 10:11.820 --> 10:19.080 And it says that there are 12 people with blue eyes, 21 people with brown eyes, three people with 10:19.080 --> 10:22.770 green eyes and four people with other eye color. 10:23.820 --> 10:31.340 Now we want to find out if let us say all people will be there will be all colors are equally present. 10:31.350 --> 10:35.520 And so we are comparing the people in the entire world. 10:35.700 --> 10:38.130 And this is the sample which we have. 10:38.130 --> 10:46.650 And based on the sample we want to derive, if all the people in the world will have same color I same 10:46.740 --> 10:53.420 quantity of eye color or not, or the same proportion of white colors or not, that is, let us see. 10:53.940 --> 10:56.700 Twenty five percent people will have blue eyes next. 10:56.700 --> 10:59.460 Twenty five percent people will have brown eyes next. 10:59.730 --> 11:03.150 Twenty five percent will have green eyes and the rest. 11:03.180 --> 11:05.510 Twenty five percent will have other colors. 11:06.810 --> 11:08.660 So this is what we want to prove here. 11:08.700 --> 11:11.020 This is worth something which we are trying to do here. 11:11.310 --> 11:15.720 So this is what the null hypothesis would be, that all the people we have seen, Michael. 11:16.730 --> 11:20.600 Now, this is what we would try to accept or reject or find notable. 11:21.900 --> 11:28.650 So this is the main objective here to find out about the guy that is. 11:29.710 --> 11:32.620 Using the frequency of data which we have. 11:33.900 --> 11:39.670 So this is what Gry Square test provides us and helps us in finding. 11:41.850 --> 11:50.140 Now, let us have a look at an example so considered a standard bag of milk chocolate Eminem's and there 11:50.160 --> 11:52.820 are six different colors in an eight. 11:53.070 --> 11:54.390 So what are different colors? 11:54.420 --> 11:57.910 We have red, orange, yellow, green, blue and brown. 11:58.320 --> 12:01.470 So these are the six colors which we have now. 12:01.470 --> 12:09.690 Suppose that we are curious about the distribution of these colors and we like the the production of 12:09.690 --> 12:10.440 the Eminem's. 12:10.710 --> 12:18.060 Does it happen in equal quantity or they are there creating a particular color would incorporate into 12:18.060 --> 12:18.840 some of the color. 12:19.140 --> 12:25.290 So we are trying to compare these categories, these colors as a category and we are trying to find 12:25.290 --> 12:31.650 out if they're if the categories are equally uplifting in the same proportion or that is a particular 12:31.650 --> 12:37.890 category see orange or green, which are being produced and the rest of being produced less. 12:37.950 --> 12:40.100 So that is something which we are trying to compare here. 12:41.760 --> 12:45.700 So do all the six colors in the equal proportion. 12:46.170 --> 12:51.490 Now, this is the type of question that can be asked with a witness list. 12:52.440 --> 12:59.760 That is what is the proportion of the values which are being created out of all the different colors 13:00.120 --> 13:04.760 or what are the proportion of different eye colors present in the wood? 13:05.960 --> 13:12.280 All right, so let us see what is the proportion of the transportation people are using, comparing 13:12.390 --> 13:17.720 what we learned or four wheeler that is a car or maybe a bus or train. 13:17.900 --> 13:20.140 So how are people actually commuting? 13:20.150 --> 13:21.200 What is the proportion? 13:21.890 --> 13:24.440 So these are different kind of questions which could be asked. 13:26.660 --> 13:30.740 Now, let us ask a question that why do we need guys Squit? 13:32.160 --> 13:41.190 So we begin by noting that the setting and why the goodness of this is appropriate, so we will find 13:41.190 --> 13:44.560 out that what is the need of this? 13:45.150 --> 13:52.440 So here we have a variable, which is categorical now because this is a categorical data and there are 13:52.440 --> 13:56.280 different levels of data presence in this particular case. 13:57.330 --> 13:59.690 That is why we will be using squarest. 14:00.600 --> 14:06.690 OK, so whenever we have categorically done, we have certain levels then we can use Guisewite. 14:08.100 --> 14:15.780 Now, we assume that the Eminem's recount will be simple, random sample from the population of all 14:15.780 --> 14:20.720 Eminem's, that is, we will assume that all the counts will be same. 14:20.730 --> 14:25.390 That is all of these Eminem's will be appearing in same proportion. 14:25.740 --> 14:27.570 So that is what we are assuming. 14:29.570 --> 14:37.010 So once we have the made the assumption that all the six colors are present in the same proportion, 14:37.340 --> 14:38.930 then we will. 14:41.280 --> 14:43.190 Creating an alternate type. 14:44.570 --> 14:49.100 Now, what are the Nalin alternate hypotheses these will be? 14:50.230 --> 14:57.670 Reflecting the assumption that we are making about the population, so we are testing whether the colors 14:57.670 --> 15:05.200 will occur in equal proportions or not, so this will be all null hypothesis that all the colors, all 15:05.200 --> 15:09.070 the colors of this a.m. are occurring in the same proportion. 15:09.070 --> 15:16.060 That is when the company is actually producing these product, they are producing these in equal quantities 15:16.060 --> 15:18.640 and randomly pushing them into different packages. 15:18.880 --> 15:22.110 That is why the numbers are coming out to be different. 15:22.600 --> 15:26.740 But actually the Eminem's which are being produced are same. 15:26.830 --> 15:28.020 No, OK. 15:29.420 --> 15:35.630 So what is the null hypothesis, the null hypothesis is if the one is the population proportion of red 15:35.630 --> 15:44.510 candies, then BIDU is the population of orange candies and so on, then the value of the would be equal 15:44.520 --> 15:49.250 to BIDU is equal to be three is equal to four is equal to be five is equal to be six. 15:49.250 --> 15:55.040 That is all the proportion, all the number of candies being created are seen. 15:56.120 --> 16:00.850 The production is same for all the six colors. 16:01.010 --> 16:02.720 This is a null hypothesis. 16:04.080 --> 16:11.040 What is the alternate hypothesis, the alternate hypothesis is that at least one of these colors. 16:12.950 --> 16:21.260 Is not equal to the others, that is at least one of the population proportion is not equal to one sixth 16:21.500 --> 16:23.030 of the entire population. 16:24.170 --> 16:29.120 So this is what our null hypothesis, an alternate hypothesis will. 16:31.560 --> 16:36.820 Now we've got to find out the actual and the expected outcomes. 16:37.230 --> 16:38.730 So what are the actual count? 16:39.030 --> 16:44.590 The actual count will be the count of the Eminem's, which we find out in a particular. 16:46.650 --> 16:51.810 And the expected count will be the sum of all the values divided by six. 16:53.260 --> 17:00.700 That is the exact expected count, so the actual count as the number of Gandy's, what each of the six 17:00.700 --> 17:07.870 colors which we find out in the frequency and the expected count refers to the what we would expect 17:07.870 --> 17:10.110 if the null hypothesis, what's true. 17:10.810 --> 17:18.070 So we will check be the size of our sample and the expected number of red candies will be in by six. 17:18.070 --> 17:23.530 If the entire sample is in, then the number of red candies will be in BASIX. 17:23.530 --> 17:26.980 Number of orange candies will be in by six and so on. 17:28.210 --> 17:28.540 Right. 17:28.900 --> 17:35.920 So for this example, the expected number of Gandy's for each of the six colors will simply be in Times 17:35.930 --> 17:41.500 VI or in BASIX, that is the the number of the entire sample divided by six. 17:42.440 --> 17:43.650 So let us go further. 17:43.850 --> 17:48.110 Now, let us apply the guys to find out the squad statistics. 17:49.390 --> 17:56.110 So if the null hypothesis were true, then the expected count for each of these colors would be one 17:56.110 --> 18:03.570 by six in six hundred, where the total number of Gandy's is six hundred. 18:03.790 --> 18:09.220 So let's say the total number of cammies for this particular date, the sample data, which we have 18:09.400 --> 18:10.460 is six hundred. 18:10.690 --> 18:18.520 So for this entire six hundred, we expect that there should be one by six hundred that this. 18:20.680 --> 18:23.490 Hundred counties of each and every color. 18:24.880 --> 18:30.580 But what is the actual value which is coming out, actual value shows that blue is two hundred and twelve 18:30.580 --> 18:36.820 oranges, one for the seven, green is one hundred and three, red is 50, yellow is forty six and brown 18:36.820 --> 18:37.750 is 42. 18:38.800 --> 18:47.890 So this is the frequency and we were expecting a hundred of each actually now, so we will now use this 18:47.890 --> 18:51.580 in calculation for the statistics of how we will find that out. 18:52.000 --> 18:57.310 We will find that out by subtracting the expected value from the observed value. 18:58.740 --> 19:03.190 Taking a square of that divided by the expected value. 19:03.810 --> 19:05.700 So what is the value here? 19:05.730 --> 19:11.900 It is one, two hundred and well, the expected is one hundred, so two hundred and twelve minus hundred 19:12.360 --> 19:14.110 who is square divided by one hundred? 19:14.490 --> 19:18.730 Similarly, we will calculate the value for all the different categories. 19:18.750 --> 19:21.090 That is all the different colors which we have. 19:22.660 --> 19:24.700 And then we will take some of these. 19:25.790 --> 19:29.480 So the sun comes out the week to thirty five point four to. 19:32.960 --> 19:39.330 This to thirty five point four is the guys square statistics. 19:39.350 --> 19:41.300 It is, these guys are sarcastic one. 19:43.340 --> 19:48.190 So this is the value which we have found for these guys sticks. 19:49.550 --> 19:53.820 Now we will find out the degree of freedom now what is the degree of freedom? 19:53.930 --> 19:56.180 This is the table which we will be having. 19:56.180 --> 20:02.110 This is the table which we will be having and the people will have the degree of freedom on the left 20:02.120 --> 20:05.960 inside the vertical column on the. 20:09.160 --> 20:18.250 The fee value will be present in the role here in the top role here, so we will be comparing it to 20:18.250 --> 20:19.480 zero point zero five. 20:20.340 --> 20:26.430 For this particular scenario, now, if you see what will be the degree of freedom we have in those 20:26.430 --> 20:27.780 six values here. 20:28.940 --> 20:35.510 So we have six values, then we can freely select five values out of this and one value would have to 20:35.510 --> 20:36.110 be fixed. 20:37.360 --> 20:43.180 Or any of the one value will have to be fixed and we will have to begin randomly select any. 20:44.290 --> 20:45.130 Five values. 20:46.420 --> 20:48.760 So here, the degree of freedom will be fine. 20:49.570 --> 20:53.710 That is six minus one, the number of degrees, minus one. 20:55.140 --> 21:02.790 So the degree of freedom is five and we are looking at the P value to zero point zero five. 21:03.850 --> 21:09.640 So four degrees of freedom value for zero point zero five is eleven point zero seven, and what is the 21:09.850 --> 21:10.840 square value which we have? 21:10.840 --> 21:12.130 We have 235. 21:13.200 --> 21:18.330 Now, if we look further forward for the smallest, we value the. 21:19.590 --> 21:23.220 Value is a stylistic value is zero point zero zero one. 21:24.370 --> 21:31.810 This gives us twenty point five one five, which is still lead to less in comparison to the guys square 21:31.870 --> 21:33.070 statistics, which we got. 21:33.790 --> 21:35.620 So what does this imply? 21:36.040 --> 21:42.910 This implies that we have a very small p value and hence we will be able to reject the null hypothesis. 21:43.180 --> 21:49.990 Even if the value would have been anything greater than eleven point zero seven zero, we would have 21:49.990 --> 21:55.660 rejected the null hypothesis, considering the P value to be zero point zero five, which is a standard 21:55.660 --> 21:56.290 P value. 21:57.550 --> 22:05.170 OK, so this is the reason why we are rejecting the null hypothesis and we are saying we are clearly 22:05.170 --> 22:15.250 able to see that the different colors of Eminem are not acting in same proportion, but actually have 22:15.250 --> 22:17.460 some different proportions associated. 22:17.740 --> 22:20.660 So they are not producing these colors equally. 22:20.920 --> 22:25.760 They are creating a few colors, more in number and a few colors. 22:25.760 --> 22:28.920 And they said no, the reason could be anything. 22:29.320 --> 22:36.520 Maybe the production cost is impacting or maybe the popularity of those colors, but they are creating 22:36.520 --> 22:37.990 them in different proportions. 22:38.800 --> 22:43.600 You see, this is something which we have gained from this guy's school statistics test and we were 22:43.600 --> 22:45.380 able to derive something from this. 22:46.150 --> 22:51.820 So this is how you will apply Chi Square statistics for goodness of fit for any example. 22:54.820 --> 23:03.430 So this is for the first example, we will discuss about this second example now, so what is this example? 23:03.550 --> 23:05.660 So here we have another problem. 23:05.950 --> 23:12.220 So earlier we were curious about the number of Eminem's that if they are producing them in the same 23:12.220 --> 23:18.160 number, the next problem which we have is that we have a casino game which involves rolling off three 23:18.160 --> 23:18.730 doses. 23:19.780 --> 23:24.420 And the winners are basically proportional to the total number of sixes ruled. 23:25.710 --> 23:27.720 So if someone has. 23:28.970 --> 23:35.210 So how would be finding out the winners we are finding out the winners based on the number of success 23:35.210 --> 23:38.130 they will be rolling in the hours of these three. 23:39.680 --> 23:45.830 Right now, suppose a gambler plays the game a hundred times with a given of the phone. 23:45.860 --> 23:51.050 So this is the observed count for a particular gambler that he had zero sixes. 23:51.320 --> 23:59.310 That is 40 times one six thirty five times double sixes, 15 times, and three sixes to the ace. 24:00.140 --> 24:07.320 So we want to find out if this gambler is playing with a good conscious or not. 24:07.640 --> 24:10.250 So is there something wrong with the dice or not? 24:11.410 --> 24:19.360 They saw the casino become suspicious of the gambler and wishes to find out if the dice up there or 24:19.360 --> 24:19.600 not. 24:19.930 --> 24:21.970 So how do they conclude that? 24:22.060 --> 24:24.820 What do they find out by these observations? 24:26.200 --> 24:28.370 So, again, what do we want to find out here? 24:28.750 --> 24:31.150 Here we have these four categories. 24:33.050 --> 24:40.580 We have these four categories and we have these expected gowns and the absolved gowns now out of these 24:40.580 --> 24:47.420 observed gowns, we want to find out if this is actually a good fit to the normal distribution, which 24:47.420 --> 24:49.100 we have for Dice's or not. 24:49.760 --> 24:53.300 Now, this is the expected gown which has been generated from the probability. 24:54.600 --> 25:02.010 Now, how do we find out the value, guys, good value for value will again be calculated by Absol value, 25:02.400 --> 25:06.180 minus expected value, whole square of this. 25:07.070 --> 25:13.500 Calculation divided by the observed value and the summation of this calculation for all the food, that 25:13.530 --> 25:14.960 is right. 25:15.080 --> 25:21.860 So how do we find that out for the minus fifty it square divided by fifty eight plus or minus thirty 25:21.860 --> 25:26.180 four point five, square divided by fifty eight and so on. 25:29.640 --> 25:30.150 Now. 25:31.610 --> 25:33.680 What do we do for them now? 25:33.700 --> 25:40.040 This is equal to one point seven to zero point zero zero seven plus nine point one four one four plus 25:40.040 --> 25:44.440 twelve point five plus twenty three point is equal to twenty three point three six seven. 25:44.450 --> 25:47.720 So the value which we get is twenty three point three six seven. 25:48.980 --> 25:55.760 Now, the degree of freedom will be four minus one, so the degree of freedom is three. 25:57.690 --> 25:59.880 So, Jake, what degree of freedom, three. 26:00.860 --> 26:03.110 And the value of zero point zero five. 26:04.480 --> 26:09.220 For this, the value has to be greater than seven point eight one to be rejected. 26:10.170 --> 26:17.880 Now, because twenty three point three, six seven is greater than seven point eight one five, so we 26:17.880 --> 26:19.600 can reject the null hypothesis. 26:19.950 --> 26:26.300 This means that the biases are not felt right. 26:26.340 --> 26:29.470 The null hypothesis was that the biases are bad. 26:29.490 --> 26:32.180 That is why it will be a part of the distribution. 26:32.490 --> 26:36.260 But because the it is of the significance level. 26:36.270 --> 26:44.490 So we can easily see that the dice is not fed and we can let go of the gambler and give him back his 26:44.490 --> 26:46.590 Dice's and have a good thing. 26:46.830 --> 26:47.190 Right. 26:47.310 --> 26:49.210 So this is what we will be doing here. 26:49.380 --> 26:54.660 So we are able to find out if there is something wrong with a particular distribution using the goodness 26:54.750 --> 26:55.260 of the. 26:56.920 --> 27:03.970 So this is how we use the goodness of the test, the next what we will be checking about is the. 27:05.300 --> 27:07.050 Best for these guys, quietist. 27:07.560 --> 27:12.830 OK, so let us have a look at this one more example which we have. 27:13.770 --> 27:23.190 OK, so this example contains two fifty six visual artists were surveyed to find out that Zodiac sign. 27:23.700 --> 27:30.150 So we want to find out if the visual artists have even distribution across a particularly or across 27:30.150 --> 27:30.810 these objects. 27:31.410 --> 27:36.450 That is, there is no particular Zodiac sign which makes a good visual artist. 27:36.750 --> 27:37.040 Right. 27:37.230 --> 27:42.150 If there would be difference in the distribution, it would simply mean that a particular zodiac sign, 27:42.150 --> 27:44.460 people will make good visual artists. 27:44.460 --> 27:47.400 So we might really high in the particular Zodiac sign. 27:48.450 --> 27:55.110 So what we do here is, again, we will have the categories as those 12 Zodiac signs, which we have, 27:55.650 --> 27:57.300 what will be the degrees of freedom? 27:57.300 --> 28:00.090 The degree of freedom will be 12 minus one. 28:01.300 --> 28:07.360 These are the words of values, these are the expected values, the expected value is one hundred by 28:07.360 --> 28:10.090 twelve, which is the expected value. 28:11.150 --> 28:17.870 So how do we find out that the residual value we find all of those value minus expected value? 28:17.900 --> 28:24.140 We take a whole square of this value and then divide it by the expected value, the desired, which 28:24.140 --> 28:28.790 we get me some more of these and we get five point zero nine for. 28:31.860 --> 28:39.030 Now, we can consider it a very small P value, if the P value is very small, then we will reject the 28:39.030 --> 28:41.070 null hypothesis like this. 28:41.070 --> 28:48.720 All the Zodiac signs are equal, and if the P value is very large, then the null hypothesis should 28:48.720 --> 28:49.800 not be rejected. 28:49.810 --> 28:50.140 Right. 28:50.610 --> 28:51.570 So what do we have? 28:51.570 --> 28:57.060 We have degrees of freedom 11 and the values five point zero nine. 28:59.360 --> 29:01.100 Degree of Freedom 11. 29:02.830 --> 29:05.140 And the value was five point. 29:06.310 --> 29:07.150 Zero nine. 29:07.420 --> 29:11.430 So here you can see that five point zero nine something here. 29:13.260 --> 29:20.310 Right between zero point nine five zero nine zero point nine, which means that we cannot reject the 29:20.310 --> 29:21.340 null hypothesis. 29:22.170 --> 29:22.650 So. 29:24.110 --> 29:31.730 We can easily see that all the Zodiac signs have equal possibility of having a talented visual artist 29:31.730 --> 29:36.590 that is no particular Zodiac sign, which will create a better visual artist. 29:37.820 --> 29:40.920 So this is what we gain from the goodness of the test. 29:41.120 --> 29:45.320 The next thing which we will be learning about is these guys with this sort of independence, which 29:45.320 --> 29:47.720 will be taken up in the next session. 29:48.170 --> 29:48.710 Thank you.