 Hello. I welcome you all once again to my channel Explore Education. I am Dr. Rashmi Singh, Assistant Professor, Department of Education, Assistant Kanna Girls' Relief College, University of Alhaka. And in the series of discussing various types of ways, concepts under educational statistics, we are discussing now product moment correlation coefficient. Prior to this I have already discussed with you all the spearmen ranks, spearmen's rank correlation coefficient. And this time I am going to discuss product moment correlation coefficient. Okay. So, the lecture will be in bilingual mode as usual and it must be useful for all of you. First of all, we will take a recap of what we have studied in statistics. We have started with the results of statistics, then the statistical series is discussed in terms of time, space, continuous, discrete, then the characteristics are discussed with you. Then we talked to you about Measles of Central Lendency, which is the map of the secondary probability in which we have discussed the concept of the mean, median and mode. Then how do we calculate it? Similarly, the Measles of Periability. The Measles of Central Lendency tells us that the data is on the one side, on the other side, on the mean side, on the mean side, its tendency is in the middle. But we do not know how its dimension is in the whole data. So, for this we have to see the Measles of Periability, where it is more, we have studied the standard deviation, quartile deviation, we have talked about the range. Then it happened that the dimension of the data is understood, but it is also understood that if there are two variables, we are comparing, then the data is so correlated. So, what is the relationship? So, we have discussed the Spearman's Rank, the formula of the Spearman's Rank and how it will be taken out and now we are going to discuss the product-moment-correlation coefficient and the questions are also asked on this. So, again, what is the correlation? Correlation is a measure of association between two variables. Oh, it is T w or 2. It means that the relationship is the basis of the association between two fours. How much is the relationship between them? Typically, one variable is denoted as x and the other variable is denoted as y. Generally, we give one four as x and the other as y. The relationship between these variables is assessed by correlation coefficient and we measure the relationship between these two fours. Following statements are an example of correlation. So, he is saying that we are sharing this example with you. It is a statement related to that. As the intelligence increases, the marks obtain increases. He is saying that as the intelligence increases, our numbers increase. Generally, there is a correlation. As the introversion increases, number of friends decreases. As we get introvert, if we are very introvert, what will our friends do? Why? We don't want to meet anyone, we don't like to go to school, we don't like to live alone. So, we won't get friends. Then, more the anxiety or personal experiences, weaker the adjustment with the stress. He is saying that as one person's stress increases, the stress increases. The stress, the stress, the stress decreases. This is a correlation. If one is increasing, the other is increasing or decreasing. Positive, negative and zero correlations have been discussed. As the score on openness to experience increases, scores on creativity test also increases. What creativity is? He is saying that as the score increases on openness to experience, the creativity increases. Similarly, the more the income more the expenditure. So, these are all correlated. On a reasoning task, as the accuracy increases, the speed decreases. As the accuracy increases, the speed decreases. As the cost increases, the sales decreases. These are all the examples of this kind of correlation. To explain to you how one-step, another-step is required. Then there can be two types of correlation. Linear and non-linear. The relationship between two variables can be of various types. He is saying that there can be some kind of relationship between two pairs. But you have to break it from the point of view. And you have to break it from the point of view. So, what will be the linear relationship? One of the basic forms of a relationship is linear relationship. The linear relationship can be expressed as a relationship between two variables that can be plotted as a straight line. which can be plotted as a straight line. And what is a non-linear relationship? So, this also means that if one is increasing, the other is increasing. That is why both the two variables are coming. Then the non-linear is saying that the York's Dotson law, Stevens's power law in psychophysics, etc. are good examples of non-linear relationship. What does this mean? This means that if one is increasing, the other is increasing. The relationship between stress and performance is popularly known as York's Dotson Law. It suggests that the performance is poor when the stress is too little or too much. It improves when the stress is moderate. When stress is so nominal and moderate, then our performance is better. This is an example of non-linear relationship and you cannot plot it straight. Why? Because performance is poor at extremes. The minimum performance is the highest and the moderate performance is the highest. This cannot be a straight line. This is called non-linear, curve-linear, curve-linear. Non-linear means linear. This is an example of non-linear relationship. This is the strength of the relationship. How will the strength be known? How powerful is the co-efficiency of the relationship? Obviously, the relationship between intelligence and reasoning as well as the relationship between intelligence and creativity are positive. The more intelligent you are, the more reasoning questions you will get. Similarly, if you are intelligent and creative, then both relationships are positive. But at the same time the co-relationship coefficient is higher for intelligence and reasoning than for intelligence and creativity. But if you look at it closely, To find out whose strength is more in this relationship. You will find that intelligence is more in reasoning and co-relationship coefficient. It is more in terms of intelligence and creativity. Both are also positive. But you will learn from the co-relationship coefficient of its strength. The strength of relationship between two variables is an important information to interpret the relationship. When you get to know the relationship between two variables, you will be able to get to know the relationship between two variables. The correlation between two variables is expressed in terms of a number, usually called as correlation between two variables. The correlation coefficient is denoted by various symbols depending on the type of correlation. Indicating the Pearson's product moment correlation coefficient. There is no need to find everything in Hindi. The representation of correlation between x and y is rxy. The correlation coefficient is x and y. The correlation between x and y is less than or equal to r. The range of the correlation coefficient is from minus 1 to plus 1. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. The correlation between x and y is less than or equal to r. correlation coefficient can be calculated by various ways. The correlation coefficient is a description of association between two variables in the sample. So, it is a descriptive statistics, so it is a descriptive statistics. Various ways to compute correlation simply indicate the degree of association between two variables in the sample. The distributional assumptions are not required to compute correlation as a descriptive statistic, so it is not a parametric or non-parametric statistics. We have already discussed parametric and non-parametric statistics, which are based on normal distribution. It is not necessary to be distributed normally for non-parametric. So, we are saying that this is not a parametric or non-parametric statistic, but a descriptive statistic. Why? Because we are only telling that the variable in the sample is the association between them. Then the calculated sample correlation coefficient can be used to estimate population correlation coefficient. If we have chosen the sample well, it is representative of our sample population, then we can estimate the correlation coefficient of the sample from the correlation coefficient of the population. Similarly, we can denote it as generally small r, then we denote the population correlation coefficient as n, then we denote the spare man, which we have talked about as rho. Generally, this is how it is done, rho. Now, let us talk about Pearson product moment of correlation. What is the peer correlation? The Pearson correlation coefficient was developed by Carl Pearson in 1986. Pearson was an editor of Biometrica, which is a leading journal in statistics. Pearson was the editor of the leading journal Biometrica. He was a close associate of psychologist, Sir Francis Galton. You must have heard of Galton. He was a statistician. He was a psychologist in psychology. He was a psychologist. The Pearson correlation coefficient is usually calculated for two continuous variables. Look, it is very important to pay attention to what kind of correlation is put in the variable. So, when there are seventy four, then the Pearson correlation coefficient is generally put in it. If either or both the variables are not continuous, then other statistical procedures are to be used. Some of them are equivalent to Pearson's correlation coefficient. Now, we will talk about variance and covariance. What are the needs of the Pearson product moment correlation? One, you will need the mean, one, you will need the variance and one, you will need the covariance. We have read about the standard deviation many times, but this may not be the case. The standard deviation coefficient is the same. We have read about the standard deviation many times, but this may not be the case. The square of the standard deviation is called the variance. And what is the covariance? Look, you know the mean. The mean of variable X is the sum of scores divided by the number of observations. That is, all the scores are connected. The number of scores that are given to us will be the mean. Do you know the variance? Do you know how to get the deviation? The variance of a variable X is symbolized as SX square. What do we call it? The square of the standard deviation. SX square is the sum of squares of the deviations of each score from the mean of X divided by the number of observations. What will you do? We will get all the deviations. Then we will square all the deviations. And if we connect them, we will get variance. We would get the same under root, so we would get the standard deviation. Simply, when we square the standard deviation, we get variance. Simple. What is covariance? It is a number that indicates the association between two variables. To compute covariance, the deviation of each score on X from its mean and deviation of each score on Y from its mean is initially calculated. What will we do? We will get two squares. The correlation will always be between two squares. First, you get the deviation of X from its mean. X can be one square. You get the deviation of Y. And multiply those two. Then products of these deviations are obtained. Product means that the result is good. And then you connect them. And what will you do? This sum gives us the numerator for covariance. It means that each and every number is equal to that. And then the numerator will come up. That means the covariance will be the sum of the covariance. And if you divide this by the number of observations, then covariance will come up. That means that variance is the square of deviations. And covariance is the good and bad of both the squares. And then you have to combine them and divide them by the number of observations. This is the formula. Equation for Pearson product moment coefficient of correlation. What is R? Pearson product moment correlation. Covariance. What is C-O-V? For covariance. And the covariance between the two is X into Y. X is one square and Y is one square. We have to divide it by SX into SY. What is SX? What is S? It is for standard deviation. So, for the standard deviation of X, you will get R if you divide it by the standard deviation of Y. So, covariance XY is covariance between X and Y. SX is standard deviation of X. SY is standard deviation of Y. Since it can be shown that covariance is always smaller than or equal to SX into SY. So, it is said that covariance will always be equal to SX and SY. Or it will be smaller. Because the maximum value cannot be more than one. Sine of Pearson's R depends on the sine of covariance XY. And the sine of the covariance XY depends on the sine of Pearson's correlation coefficient. So, our formula is R is equal to summation of X minus X bar. Look, I want to put X bar over X. Because I couldn't put it on X. So, I have to put X bar over X. X minus X bar. X bar means a small circle over X. Similarly, Y minus Y bar is a small circle over Y. That is not possible. Upon N into SX into SY. Now, if you put it in the formula, you will understand how it is put. Look, we will be given only one subject. We will give X and Y. You will get this much data. And it will be told to you that its product moment correlation coefficient has been removed. So, what should we do? This is the number of observation. There are 10. X is Y. Remove the mean of both. So, it is 110. It has been removed from 10. It has been removed from 11. It has been removed from 120. It has been removed from 10. It has been removed from 12. It has been removed from 12. Now, if we want to get all the deviation from the abstract, then this balance is 11 out of 11. It has been removed from 3 out of 11. it has been removed from 2. It has been removed from 6. It has been removed from 5 in this way. That is X minus X bar. In the same way, output Y minus Y bar. Imagine here, how is the mean over 12. We have to eliminate 12 out of 12. it has been removed from 3. It has been removed from 1. It was removed 16. There are 4 in this way. Now, what we have to do? For calculation, cast the code above B and Y minus B. Cast the code above B and perform with X minus X bar. S x is equal to x is equal to 4.16, S y is equal to 3.33, so r is equal to 116. This is given as x minus x bar into y minus y bar which is your formula. This is r is equal to summation of x minus x bar into y minus y bar. In this, S x is equal to 4.16, S y is equal to 3.33, which you saw in that formula. What does this mean? What is the correlation between the two fours? Because 937 means 137% correlation. The coefficient has come out. It's over. The formula is small but you have to remember that first you have to remove the mean in x and y, then you have to remove the deviation, then you have to remove the square of the deviation, then you have to remove the variance. Look, here we don't have to remove the under root. We don't have to remove the standard deviation, then you have to remove the under root, then the covariance will come out. And the covariance, after removing the number of observations, if we remove it from both the variance, then it will come out. What? Product moment correlation coefficient. Did you remove sx? Did you remove sy? So it's 4, 10, 9, 6, 3, 10, 3, 3, and then you have to remove these two and then you have to remove them from 117, 10, 10. This is the sign of the problem. Look at this. This is the sign of the problem. You have to run away. It was a little difficult to do all these types. It was very difficult to apply all these symbols. So this is the product moment correlation coefficient. And it is also asked a lot from you. First you have to know the concept. Always try to understand the statistics like maths. Try to understand that this is a kind of work. It's not just calculation. First you have to understand the concept of correlation. Why? Why is it necessary? Now this concept will be clear. Then you will be able to understand that between minus 1 and plus 1 it can be considered as correlation coefficient. It is not that you have given the answer of the question of correlation coefficient. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It can be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 2.5. It cannot be 3.5. If I can see that it is a test term. It is not. But the body language is even different. I think some people are surprised by such facts as there is this topic today.