 Hello, I welcome you all once again to my channel Explore Education. I am Dr. Rashmi Singh, Assistant Professor, Department of Education at Suskanna Girls degree college, University of Allahabad and nowadays we are discussing about the concepts of educational statistics or the use of statistics in education. So in this series, now I am going to discuss the concept of correlation and how to compute correlation coefficient, okay. So, the lecture will be in my little more, so let's learn correlation, see the name of the relationship between the dose of insulin and the blood sugar, there may be n number of variables that may affect each other and the relationship might exist among all of them, for example, there are three variables x, y and z, x may be related to z and y both and z may relate to y and hence we can state that the correlation is a statistic tool to find out the relationship between two or more variables, you know. So, if we look at its definition, the definition says that the total defined correlation as an analysis of the co-variation of two or more variables is usually called correlation, it is a process to determine the amount of relationship between variables with the help of tools and techniques provided by statistics. And this is a way to determine the relationship between the four or more variables, I am telling you here that correlation, you may have understood that there are three ways, positive, negative and zero. Positive correlation means that if one thing is increasing, then the other is also increasing, that is, if the height is increasing, then the weight is also increasing, if the earning is increasing, then the expenditure on the luxurious item is also increasing, then these are all examples of positive correlation. Negative correlation can be that if your age is increasing, then your physical strength is less. So, how is this a correlation? Negative, because if one is increasing, then the other is decreasing. And this can also be the case with two variables that are not related to each other that your physical appearance and your intellectual ability are not related to each other. So, this will be an example of zero correlation. So, this is the relationship. Now, what are the characteristics of this? What are its characteristics? Although correlation analysis establishes the degree of relationship between variables, it fails to throw light on the cause effect relationship. Yaddiyapi tells us the degree of relationship that is related to each other. It tells us about the limit of the relationship. But it does not tell us the cause effect. It does not tell us who is the cause and who is the effect. It does not tell us who is the cause and who is the effect. So, this is one of these characteristics. And the existence of a correlation between the variables may be due to chance, especially when the sample is taken in a small number. And sometimes it can be that the relationship you are showing is by chance. But actually, it is not necessary. And this is especially the case when you have taken a small sample. So, this is your definition of correlation. What is correlation? Now, what we have to take out from you is the formula. The question will be asked. Spierman's rank method helps to take out the correlation coefficient. Generally, in two subjects, the students' marks are given. It is said that you take out the correlation coefficient. So, in case it is not possible to measure the variables quantitatively but can be arranged in serial order, then Karl Pearson's coefficient of correlation is not applicable. Because Karl Pearson's product moment correlation is very important. It is asked a lot, but here we are reading the Spierman's rank. They are saying that these were British psychologists, Charles Edward Spierman. He said that in this method, the individuals in the group are arranged in order. He said that first arrange the individuals in a crumb. They are by obtaining for each individual a number indicating its rank in the group. So, as soon as you arrange it in a serial, you rank it up to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This type of correlation is often called a non-metric correlation as it is a measure of correlation for two non-metric variables that rely on ranking to compute the correlation. This is your definition. What are merits and demerits? The method is quite simple and is comparatively an easier way to establish a relationship between variables. It is an easy way. You can get a connection between the two values. And easily in the case of non-quantitative or qualitative variables, you can get a connection between the two values. Through this method, ordinal ranks can be given easily to establish a relationship between two qualitative variables. It is assumed that both variables are normally distributed that may not always be true. It is assumed that both are following the normal distribution but it may not be true. It only describes the linear relationship between the variables and does not interpret anything about the non-linear relationship. For example, if we say that a rank tells us that it is increasing, it is decreasing, it is decreasing, it is increasing. But it does not give any information about the non-linear relationship. In the case of large data, giving ranks is a bit cumbersome. In the case of large data, giving ranks is a bit cumbersome. They are saying that if there is a very large rank, then it will be difficult for you to rank. When group data is available, this method cannot be applied. And if you get a large rank, then you cannot apply this method. So, these are the numbers. Now, look at the formula. This is an easy formula. R is equal to rank correlation coefficient. That is why R is the rank correlation coefficient. R correlation coefficient is equal to 1 minus 6 sigma d square. We have learned again and again that this is called sigma, the summation sign. So, 1 minus 6 sigma d square. What is d? Difference of rank between paired and them in two series. If we are given two, then we will be given two variables. Then we will divide them. So, we will rearrange both of them. We will give them ranking. So, if we remove the second rank from one rank, then d will come. And n is always the total number of observations. So, this is the formula. 1 minus 6 sigma d square upon n into n square minus 1. That means n is outside. If we take it inside, then what will happen? n cube minus n. The bracket outside, then everyone is counted, right? So, n is n. So, if we take it inside, then n cube n square into n. That is n cube minus n. Okay. So, look. The number of children in two series is Marks of Subject A and Marks of Subject B. This is the method. Okay. Now, what do you call it? Put it in a series. Marks of Subject A is the ranking. See, from where it will be ranked? From here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Okay. Marks of Subject B. Now, to rank it, you will have to pay great attention. You will have to rank it many times. See, the smallest angle is 7. 7 is the number 1. Where does it come from? 7. Then, 2 is the number 2. 7 is the number 3. 6 is the number 4. 7 is the number 5. 8 is the number 6. 8 is the number 6. 10 is the number 6. You have given it in this. Okay. This is easy. Sometimes, it happens that the number 2 is number 1. Like, say, 60, 60. So, you have given 60, 60. But, if 60, 60, 60 is twice, then how will you give number? Who will give number? Who will give 5? Then, you will give 4. That is, 4 plus 5 is 2. 4, 4, 4, 4 is 4. So, you have used both the angles. You have used the 4th rank. You have used the 5th rank. You can use it. So, after that, the number will be 6. So, many times, it is called tie. It is called tie. So, we will combine the rank of the previous rank and skip the rank of the previous rank. So, this is the method. Okay. So, you have r1, r2. Now, r1 minus r2. That is, d square. Do it. It is 9 out of 10. It is 9 out of 10. It is 2 out of 9. It is 1 square. So, it is 1 square. It is 2 square. It is 2 square. So, by doing it like this, you have got the whole d square. That is it. That is it. You have got d square. You have combined it. The summation of d square is equal to 44. Now, there is nothing left in the formula. There is nothing left. n is equal to 10. What is n? Number of observations here. Number of scores. It will come into the formula. r is equal to 1 minus 6 sigma d square upon n into n square minus 1. 1 minus 6 sigma d square. How much was it? 44. How much was n? 10. So, if you take n inside, what happened? n cube minus n. So, 10 cube minus 10. What does 10 cube mean? 10 into 10 into 10. That is, what will happen? 1000. So, it will be 1 minus 6 into 44. That is 264. And this is 1000. It has become 1000. What is 10 out of 1000? 990. Now, solve this whole thing first. This is not a lot of math. I mean, it will start decreasing in one month. No. What will happen in one month? Bring this angle first. So, 264 by 990. So, whatever will happen, 10 times 2 something will happen. So, if it will happen in one month, then 10 times 3 will not happen. Then, it is also possible that this angle will be more than 1. If it is more than 1, then it will be minus sign. 10 into inne. So, 10 into inne does not happen. What number does it meet? 11 which is the last number. I have already drawn it. So, the last number has solved. So, it is號 means equals 250. Then, it is hoswer so, what cannot be set. I have polled it. This is no problem. I have also drew it. Let me start explaining it. So, 10 row at 2 feet. 10, hoswer comes up to and positive sign means that it is related to the dhanaatma group. Ok, so it is done, it is very easy. The spearman rank formula is a small formula, 1 minus 6 sigma d square upon n into n square minus 1. You have to do the ranking, put the order, rank both of them, remove the second rank from one rank, put the order, rank both of them, and put the order, rank both of them, and skip the rank and move on. This is very easy. There are so many small calculations in R1, R1 is R2, R1 is R1, put the order, put the square of R1, put the order of R1, sigma d square is known, and there is nothing else in this formula. It will come out. Ok, so it was easy, I think you understood. So thank you and don't forget to like and subscribe my channel Explore Education. See you soon from my site.