 Hello, I welcome you all once again to my channel Explore Education, I am Dr. Reshmi Singh, Assistant Professor Department of Education, Assistant Khanna Girls Rugi College, University of Palahapad and we are nowadays we are discussing over various types of correlation, correlation coefficient in which I have already discussed with you the spearmen's rank correlation coefficient and product moment correlation coefficient and this time I am going to discuss bi-serial and point bi-serial correlation okay and the lecture will be in bilingual mode and it must be useful for all of us hmm I have already told you that this name, this technical name, this terminology, do not worry for its Hindi, you are bi-serial correlation, point bi-serial correlation, product moment correlation coefficient, spearmen's rank correlation coefficient as it is, you can understand the concept in Hindi, you can use the whole language in Hindi but you can use it in terminology in English because their Hindi name is difficult to take, it is easier to read in English, okay, the first thing, the second thing is that we are talking about correlation and all of them are completely crumbly, it is not that you will be discussed before the correlation, then variability, then position and then results of central tendency, all of them and who are all these, who are all these and who are describing it, it is a part of descriptive statistics, what is descriptive statistics that help in the description of the eyes, and the second thing is inferential which helps in prediction, descriptive statistics do not help in prediction or inferrence, it is just telling us how the eyes are, what is their body, what is their physical condition, what is their body, and how much deviation is there from their body, they have two variables, so if they are correlated or not, then you will have to study the prediction and regression. So there is correlation in that, it just tells you that they are both connected to each other or they are getting closer to each other or they are getting closer to each other and getting closer to each other, but it does not tell you who is causing and who is effect, it means who is the reason how, which one is better, you don't know from the correlation. Then we will read one more step, prediction and regression. Regression and prediction, we will get to know who is the cause, which variable is responsible for its cause, and which variable is it, it is dependent and independent variable. So, everything is exactly the same. If you understand it in this way, if you are connected to each other, then you will understand things better. So, we will tell you one more special thing, that the numerical in your course, MEM edge, comes up to the product-moment correlation. That is, if you ask the correlation, then either you will have to remove the rank-correlation coefficient or you will have to remove the product-moment. Bi-serial, point-bi-serial, tetra-corrigan-phia, which are 4 children, theoretical questions are not asked from them, what is the relationship between them, what is the difference between them, or right-shot notes on bi-serial and point-bi-serial correlation, or what is the difference between point-bi-serial and bi-serial correlation, or what is the difference between tetra-corrigan-phia, what is the relationship between tetra-corrigan-phia, in this way. So, the question is not asked based on this. So, do not worry about numerical. Just understand the concept. If you are asked, then you will be asked. And if not, then you will not be asked. Because there are many questions to be asked, whether it is mean or median, whether it is a quartile deviation or standard deviation. Okay. Now, your t-test is over and your non-parametric test is left. In which there is chi-square, median test and sine test. Okay. So, let's start by what bi-serial correlation is. In educational or psychological studies, we often come across situations where both the variables correlated are continuously miserable, while one of them is artificially reduced to dichotomy. Now, see what are the words, artificially reduced to dichotomy, continuously miserable. So, when you do not know what the variable is, who is the continuous variable, who is the dichotomy, who is the artificially reduced dichotomy, then you will not be able to understand. So, the concept is to be understood. So, the concept is to be understood. It is said that there are many times that we get very different variables. That is, both the charges are continuously miserable. That is, we will go to the level, right? And one of them will be artificially reduced to dichotomy. Dichotomy means die, that is, two, right? That is, we have reduced it. That is, it is not natural dichotomy. Natural dichotomy means natural nature. It is divided into two parts in two ways. But we have divided it artificially according to ourselves. We have divided it into two parts. How? In such a situation, when we try to compute correlation between a continuous variable and a variable reduced to artificial dichotomy, we always compute the coefficient of bi-serial correlation. See, your question of competitive examination will be asked to you very simply. When one variable is a continuous variable and the other variable is artificially reduced to two, then which coefficient of correlation will be removed? Tetra, Coret 5, bi-serial, point bi-serial. So, you will take the bi-serial correlation there. So, you should know that this bi-serial correlation is a special thing that one variable should be continuous and the other should be artificially dichotomy. Now, let's talk about artificial dichotomy. What is it? At this point, the artificial one is from the Krithrim root. Dichotomy means we have divided it into two parts. Seriously. At this point, the question arises to what do we mean by a dichotomy and also by an artificial and a natural dichotomy? He is saying that now we have to understand what is dichotomy and what is artificial and natural dichotomy? So, he is saying that the term dichotomy means cut into two parts or divided into two categories. Dichotomy means that we have divided any part into two parts or divided into two categories. This reduction into two categories may be the consequence of the nature of the data obtained. And whose result is divided into two parts? The nature of the data is divided into two parts. How? For example, in a study to find out whether or not a student passes or fails, look, there is no space between A and student, spaces, passes, and others. Whether or not a student passes or fails a certain standard, we place the crucial point dividing pass and fail students anywhere we please. He is saying that in a quiz study, we have to decide whether a student has passed or failed an exam. Let's put a criteria somewhere. This is not a natural criteria. We have set it artificially that if a 100 is 34, then it is 5 and if it is 33, then it is a fail. We divided all the data into two parts. Pass students, fail students, and divided into two parts, we have made this dichotomy according to our knowledge. This is not natural. This is an artificial dichotomy. Hence, measurement in the variable is reduced to two categories. So, whatever we got, it was divided into two parts. In two categories, pass categories and fail categories. This reduction into two categories, however, is not natural. Why is it not natural? Because we have applied it from our knowledge. If there is a second exam, we will not be able to say, if there is a 50, then it is a fail. So, this is artificial. We set this point according to our knowledge that from where we will divide it into two categories. So, if there are two steps like this, in which there is one structure and we have divided the other step in two categories, then we always have to apply bi-serial correlation. Okay. In conclusion, we made term a dichotomy in the region of a variable into two categories, an artificial dichotomy when we do not have any clear-cut crucial point or criteria for such a division. That is, we did not know any clear-cut point. We fixed the dividing point according to our own convenience. According to our own convenience, we divided it into two categories. Hence, the basic assumption in using bi-serial correlation as an estimate of the relationship between a continuous variable and a dichotomous variable is that the variable underlying the dichotomies is continuous and normal. He is saying that the basic assumption that the main ghost believes in is that the correlation as an estimate of the relationship between one variable is continuous and the other is dichotomous and that too such a dichotomous which we have to divide artificially in two categories. This implies that it should be an artificial dichotomous variable rather than a natural dichotomous variable. Hence, you will always have to see that the dichotomy is applied according to our own convenience. This is not a natural dichotomy. It is not a natural dichotomy like a male-female, isn't it? Like this. Okay. The question is not that simple but you can still see its formula. Computation of bi-serial coefficient of correlation formula. This is the general formula of bi-serial coefficient of correlation, R-bis. But what is the bi-serial of bis? And what is R? It is for the coefficient, it is for the correlation. So, R-bis is equal to M-capital M, which is P-capital MQ upon sigma 1 into small p into small q upon small y. Now, let us see what is small p? Proportion of cases in one of the categories of dichotomous variables. That is, how many variables and how many factors have become two categories. Then, Q-proportion of cases in the lower group 1-p, M-p mean of the values of the higher group. We will have to form two groups. We will have to form two groups as soon as you have dichotomy. So, it is said that the higher group's mean is how much, the lower group's mean is how much, the standard deviation of the whole group is how much, and y is equal to the height of the ordinate of the normal curve separating the portion p and q. When we talk about x-axis, y-axis, when we talk about graphs, it is about the ordinates. So, yes, that was it. The question will not be asked. But still, since the bi-serial coefficient of correlation is talked about, the formula is at least the formula is better than the formula in front of you. You will not remember it. Okay. Now, let's talk about the point bi-serial. Oh, one line has gone down. It's okay. Now, let's talk about the point bi-serial correlation. It is a little higher. Okay, no problem. What is the point bi-serial correlation? Everyone has to see the difference between bi-serial and point bi-serial. What is bi-serial? When one variable is continuous and the other variable is artificially dichotomous. In this, it is also said that some variables are dichotomous. Some are dichotomous. The dichotomous variable is the one that can be divided into sharply distinguished and mutually exclusive categories. He is saying that you will call that variable dichotomous out of which two of you are looking at different ways. Like, male-female. I told you, this is natural dichotomy. Male-female. You didn't artificially do anything about it. Then what else could be dichotomous? Rural, urban, Indian, American, diagnosed with illness and not diagnosed with illness. I mean, those who have that disease and those who don't have it. Two categories like this. Two categories of the city, the city, the state, or two categories of America. These are the truly dichotomous variables for which no underlying continuous distribution can be assumed. He is saying that these examples are naturally dichotomous. Now if we want to correlate these variables, then applying Pearson's formula has problems because of lack of continuity. He is saying that you can understand that point-by-serial-by-serial-period product-moment-correlation-coefficient So why? Because Pearson's correlation requires continuous variable, that is why we are correlating gender and male will be given a score of 0 and females will be given a score of 1 or vice versa. Indeed you can give a score of 5 to me and score of 11 to female and it won't make any difference for the correlation coefficient. So it says that if we are talking about product moment correlation coefficient, it needs continuous variable, i.e. if there is a natural dichotomy, then male, female, rural, urban, Indian, American, these are not continuous variables. So, which no underlying continuous distribution can be assumed, that is why you can't put a Pearson formula in it. So what formula will you put in it? You will put point-by-serial. So what happened? And what does it mean here? It means that your natural dichotomy is male-female. So it doesn't matter if you give a zero number to a male, i.e. you give a score of 5 to a female, it doesn't make any difference to a female. So what is point-by-serial correlation? This is also a kind of Pearson product moment correlation in which there is between one truly dichotomous variable. One variable is truly dichotomous, natural dichotomy. And the other variable is continuous. I.e. when both the variables are continuous, what will you think? Pearson product. When one variable is continuous and the other will be natural dichotomous, what will you think? Point-by-serial. When one variable is continuous and the other will be artificially dichotomous, what will you think? By-serial. Remember this. And what is point-by-serial? It is Pearson's product moment correlation between one truly dichotomous and another continuous variable. The same thing happened yesterday. Algebraically, i.e. in the term of algebras, so rpb is equal to r. i.e. in the term of beads, you can say that point-by-serial correlation coefficient is only product moment correlation coefficient. In this, there are four factors. In Pearson product, what happens in point-by-serial? One is truly dichotomous. i.e. in the form of truth, it is also involved in two-four factors. And when do we apply by-serial? When one is continuous and the other is artificially dichotomous. Okay. We resort to the computation of point-by-serial coefficient for estimating the relationship between two variables when one variable is in a continuous state and another is in a state of a natural or genuine dichotomy. i.e. actually it is also involved in two variables. If we are sure that the dichotomized variable does not belong to the category of artificial dichotomy, then we should try to compute point-by-serial correlation coefficient. When we feel that it is really natural dichotomy, not artificial, then you should apply point-by-serial. And if it is artificial dichotomy, then you should apply by-serial. Look at its formula as well. Its formula is that rp-bis. P-bis means point-by-serial. If it was just bis, then it was by-serial. mp-mq upon sigma1 is equal to into under root pq. And this is all its formula. Similarly, mp means mq, mt, q, th is for this one. Okay. So, if you don't want to ask this question, then you just know its formula. Okay. So, what do you think is the main concept? Conceptual understanding. Conceptual understanding is that Pearson product moment correlation coefficient is applied. When we are discussing two steps, and both are by-serial. Then, it is no problem for you to use a Pearson product. But, as soon as the second step is not by-serial, then we need to apply by-serial or point-by-serial. When will we apply by-serial when there is artificial dichotomy? When will we apply by-serial when there is natural dichotomy? What happens in artificial dichotomy? Where we also run, depending on our own, how many children are there, how many are there. But naturally, it is genuine. I think you must have understood something, if the statistical background of people is not educational or numerical, they are a little afraid or there is no such science background, they will understand it again and again, and when they understand it, they will remember it for a long time. This is also special, mathematical equations, numericals, and when they start to come, when they start to solve the question, they are very happy. And most importantly, if you have opted for numericals and you have done the whole number, you have done the whole formula, the answer, then you will get no number, you will not get the whole number in any theoretical question, no matter how good you will be. So, this is plus point for this, right? So, you just have to discuss tetra, corig, and phi in correlation with you, I have spearmanned you, pierced you, bi-serialed you, point-by-serialed you, okay? So, thank you and don't forget to like and subscribe to my channel, Explore Education, I have done from my side.