 Hello, I welcome you all once again to my channel explore education. I am Dr. Rashmi Singh assistant professor Department of Education assistant girls really college University of Allahabad and This is the last video related to correlation coefficient Tetra core can pi coefficient of correlation. I have already discussed the concept of correlation the concept of correlation coefficient the Method of spearman's rank correlation coefficient Pearson's product moment correlation coefficient partial and multiple correlation and Bicereal and point bicereal correlation. I have already discussed and this is the last topic in this in this Context okay, so the lecture will be in bilingual mode and it must be useful for all of you Corric correlation we have read the relationship we know that the relationship is between the four In the middle, this positive negative can also be zero then we have to know that the relationship is good Ang will tell us strength that how much how much strength this relationship is then if the wealth is Atman then it means that one is increasing from one step to another is increasing from one step to another is decreasing and Its amount can be between minus one to plus one it cannot be in this you should know Now in this just a tetra core core pi is left It will not be asked to you numerically because it has cost theta There is a little trigonometry involved in its formula, so you will not be able to put it, it will only ask you for conceptual Questions that what is the difference between tetra core again pi correlation In in what condition you can use tetra core correlation and all So what does a tetra core correlation coefficient RT ET The point by serial is used when both variables are Dicotomous like the five, but we need also to be able to assume both ways really are continuous and normally distributed. Till the time you don't know what a continuous variable is, what a normal distribution is, what a dichotomy is, if you don't know what a dichotomy is, then you can just write it down and when you write it down, your knowledge won't be with you when you need it. You will have to understand that if you are normally distributed, that means they are following the NPC. They are following the NPC, that means they are following the normal probability curve. Luckily, the maximum area is in the middle and the extreme cases are less. And what are the continuous variables? What are the discrete variables? Then when we divide a corner into two categories, that is dichotomy. We have also talked about natural dichotomy, such as male, female, gender wise or artificial dichotomy. For example, we have divided something into two parts. For example, we have told you how many students have passed, they have failed, this is artificial dichotomy. So, tetrachoric is said to be used only when both the variables are dichotomy, just like phi, but in this, the variables should be continuously distributed. So, tetrachoric correlation is a correlation between two dichotomous variables with underlying continuous distribution. That is, when we put tetrachoric correlation, when the correlation between the variables is between the dichotomous and continuous distribution, that is, we follow the normal distribution. If the two variables are measured in a more refined way, then the continuous distribution will result. For example, attitude to females and attitude towards liberalization are two variables to be correlated. They are saying that women and liberalization are related to each other. If we want to create a correlation then you can put tetrachoric. Why? Because both the variables are dichotomous. We have divided the two, attitude towards liberalization, attitude towards females, that is, they are both dichotomous. Now, we measure them as having positive or negative attitude. So, we will measure whether it is positive or negative. Suppose we are giving negative attitude as zero and positive attitude as one on both the variables. Then the correlation between these two variables can be computed using tetrachoric correlation. So, we have to remember this ten by serial, point by serial, tetrachoric and phi. What is the relation between the ten when both the variables are dichotomous and they are normally distributed, if there is a continuous variable, then tetrachoric. For example, they have given this example that the variables are actually continuous in nature, but measured as nominal set and dichotomous. You should also remember scales of measurement. I have already discussed that in the ordinal interval ratio, these are four scales. The lowest one is called nominal. Nominal means name. We don't know their rank, order, or anything else. These continuous variables, if measured exactly, would lead to a normal distribution. These are two points for tetrachoric. The variable which should be continuous and should be in the nominal set and should follow the normal distribution. For example, female and male. This is dichotomous. It is not about natural and artificial dichotomy. It is just that both the variables should be dichotomous. So, female and male are natural dichotomy. And non-smokers and smokers are artificial dichotomy. Right? Or it can be natural dichotomy. Genuine dichotomy. These are both dichotomous. So, these female and non-smokers are 23. Smokers are 21. Male and 27 are for the formula. The formula will not be asked. So, the total is 34. The total is 54. And it will be said. For example, tell us the tetrachoric correlation coefficient. The formula is this. That is why it will not be asked. Because cos theta is in it. Trignometry is in it. So, you will not be able to apply it. So, RTET is equal to cos 180 degree into under root BC. Under root AD plus under root BC. So, you will know the name of BC AD-BC. And 180 degree. So, you will have to see this table. So, its value will be 10, 10, 1, 4, 5. So, what is the thing to pay attention to? The thing to pay attention to is that continuous in nature should be variable and nominal set should be measured and this should follow normal distribution. Now, what is phi? Phi is saying that if phi coefficient is calculated as non-parametric measure of association when the data is genuinely dichotomous in nature. That is, the data here the variable should be in natural dichotomy. That was not in tetrachoric. Second thing, this is non-parametric measure. Now, pay attention to what is parametric and non-parametric. Parametric is what follows normal distribution. What is non-parametric? This means it will not follow normal distribution. This means what is the main difference between tetrachoric and phi? Dichotomy is happening in both places. But tetrachoric is a parametric measure. That is, it should follow normal distribution of its data. Whereas, phi coefficient is non-parametric. This means it will not follow normal distribution. As the variables are not exactly continuous so they cannot fall into normal distribution. The data of phi coefficient does not follow the normal distribution of the variable. And this sets phi coefficient different from tetrachoric correlation. And this is the difference between phi coefficient and tetrachoric correlation. What is the difference between tetrachoric and phi? We take out the correlation when we have a dichotomous variable. But we take out the tetrachoric coefficient when that variable is parametric. That is, it follows the normal distribution and does not follow the phi coefficient. Sorry. The phi coefficient is very useful in item analysis. The calculation of item to item correlation is to be calculated. The tetrachoric and phi coefficient share the same relationship among themselves and the point-by-serial correlation coefficients have among themselves. So, in this way, tetrachoric and phi also share the same type of relationship. So, we have to pay attention to what we will put in this condition. And what is the formula for this? It is said that Pearson's correlation between one dichotomous variable and another continuous variable is called as point-by-serial correlation. We have read that Pearson has a special form. In Pearson, when one dichotomous variable and another continuous variable is called as point-by-serial. When both the variables are dichotomous, what will we put in the file? We have to understand that when one dichotomous variable is called as point-by-serial. Now, we have to see what is dichotomy. Is it natural or artificial? It is not natural or artificial. Is it normal or distributed? It is not. When one dichotomous variable is called as point-by-serial, you can put in the file. For example, let us say that you have to compute correlation between gender and ownership of the property. What is gender? It becomes two categories, male and female. And ownership of property, what is the property? It will be divided into two categories. Some people will have it, some will not. So, both the variables are dichotomous. Now, we can put in the file coefficient. Why? Because this data does not follow the normal distribution. If it follows the normal distribution, then you can put in the data formula. This is its formula. We have to pay attention to these three things. Variables are truly discrete in nature with no underlying continuity. Variables are not continuous. They are discrete. Variable can be measured in only mutually exclusive categories. It will be equal to AD minus BC under root A plus B into C plus D into B plus D into A plus C. This will be equal to 10,000, 9, 1. Okay? You have to pay attention to all the types of correlation coefficient. And all the Pearson's products are in a refined way. When one dichotomous happened, you put in the point-by-serial by looking at the dichotomy that is natural or artificial. If you are a dichotomous, you will put in the point-by-serial by looking at the data whether the normal distribution is following or not. If the normal distribution is following, then you will put in the data formula. For all these, you will need variable, nominal, ordinal, ordinal, ordinal, interval, ratio, scales of measurement, continuous, discrete, normal distribution, dichotomy, variable. That is why you have to look at the basics first, then see how easy the statistics look. You won't be able to ask questions in this. You will be able to ask questions from the product moment or from the partial or multiple correlation. So in this way, finally I have completed the whole topic of correlation and correlation coefficient. So thank you and don't forget to like and subscribe to my channel, Explore Education. See you in the next video.