 Hello, welcome you all to my channel and the topic of today's discussion is raw scores, standard scores and normalized score. Okay, join my telegram group, explore education and I am Dr. Rashmi Singh, Assistant Professor Department of Education, S.S. Khanna Gulstrivi College. It is a constituent college of University of Allahabad. This is my email ID and this video will be useful for certain types of teaching examinations and subscribe my channel. So, let's start the topic. First of all, we are going to talk about raw score, standard score and normalized standard score or normalized score. So, first of all, we have to know where the topic of the discussion will start, that when we do psychological testing, right, when we do some test, then if we have the score that comes out, we cannot interpret it as it is, because it is raw score. So, first we have to put it on a scale, then we can interpret it as it is, if we are doing intelligence testing, then how can we know who has the better intelligence or you can consider it as in general, in simple words, we have given two tests, we are talking about the class test, we are not talking about standardized tests, then if we have scored 80 in one issue and 90 in the other issue, then how can we say that we have scored better in one issue than in the other issue, we will be able to tell only when we know that the rest of the students who were our competitors were performing like that. We will get to know if they performed well or not. So, let's say we get 60 in Hindi and 80 in maths, so we can't say that we didn't perform well in Hindi and maths was good, because in maths, the rest of the students were around the 90s, so that means we gave below performance from average. And in Hindi, it can be that the rest of the classes were similar to the rest of the 50-50 students, and if we got 60, that means we gave good performance from average. So, we are not able to interpret from raw score, that's why we need standardization. So, first of all, let's know what raw score is, and raw score is a number, it's an ink that summarizes and captures some aspect of a person's performance in the carefully selected and observed behavior sample that make up psychology tests, that is, if we perform psychology tests on someone, on a student, on a person, then we get some ink that is raw score, or we can say simply that it is the score which the individual got on his performance, the time of administration of the test, that is, if we did a test on a student, then the performance that he got was raw score. Then by itself, raw score does not convey any meaning, that is, there is no meaning of raw score, we can't get any meaning from it, we can't interpret it, we can't do anything, we can't do our performance, then what is the need for it? We need standard score, why do we need it? What is it called? It is called scaling. Why is it called scaling? Because we get a lot of raw scores, if we get a lot of raw scores, we get them on a single scale, so it is the same scaling or the same standardization. To convey the meaning of test scores, if we want to convey the meaning of test score, relative to a normative or reference group, if we have a norm or a reference group, then we want to perform the results of the results, then what do we have to do? Transform, sorry, is to transform raw scores into scales. What will we do? We will change the raw score to such a scale that express the position of scores relative to mean in standard deviation units. That is, we will get to know how far the rank is from the middle, that is, how close we are, how much distance we are showing from the middle. We have to know that we are performing average or below average performance or higher above average performance. So, the mean, that is, the performance of the maximum is standard deviation, that is, how far we are deviating from the mean. This conversion process is called standardizing. This process is called standardizing. And this can be accomplished by means of simple linear transformation. If you study more, then you will know that we can change the raw score to standard score in two ways. One is linear transformation and the other is non-linear transformation. So, first, we are talking about linear transformation. Linear transformation means we are changing the rank. So, what is the characteristic of the change in the rank? That the variables in this are their basic nature. A linear transformation changes the units in which scores are expressed while leaving the inter-relationships among them unaltered. That is, the inter-relationship between them does not change. It only changes the rank. Then there is linear transformation. So then, what is the advantage of the standard score? A great advantage of this procedure is that the normally distributed scores of tests with different means, standard deviations and score ranges can be meaningfully compared and averaged. So, we can know that we know a lot of scores, we know standard deviation, we know mean. So, we will bring them on a single scale, on any single scale and then we can divide them. Once they have been linearly transformed into a common scale as long as the same reference group is used. That is, the reference group is the same we are using. And with linear transformation, we have changed the raw score to a standard score. So, when all the raw scores will come to a standard score and one guest will come to a standard score, then we will be able to tell that yes, we performed better, we performed worse, we performed better. Okay, then this standard score is where the mean and standard deviation are the same for a set of scores. That is, what is the standard score? Where one set of scores that we know, what are the mean and standard deviation? They are the same. Making it easy to compare them. That is why we can easily compare them. That is why we can tell that we know the standard deviation and we can tell that how deviated the mean is. That is when we can interpret it. What is all this? Interpretation. So that we can provide the raw score to a certain level. That is why we have changed the raw score to a standard score. So, when a standard score is asked to us, it is taught to us. So, the most common standard score is z score. It is so common that sometimes z score is called standard score whereas standard score is a type of z score. So, what is z score? z score is also known as standard score. Look, it is also known as standard score. This is a statistic. This is a kind of statistic that tells us where a score lies. It tells us where our score lies. It means where it is. In relation to the population mean. According to the population, where is our human being? It tells us z score. A positive z score means if our human being comes to us, it means that we are performing above mean. While a negative z score means that the score is below the means. And if we have a negative z score, it means that we have given a bad performance to the human being. Our performance is less. Then, in addition, the z score also tells us how far the score is from the mean. In addition, z score also tells us how far away we are from the mean. When you make an NPC, you will be able to understand it in the next slide. You can imagine the NPC in your mind that how much standard deviation we are in which run. The more we are, we will be able to know how far the mean is from the mean. It is a very useful statistic because it allows us to compare two scores coming from two different distributions. That is, this is a very important statistic. Why? Because it gives us the permission that we cannot compare two scores when they are coming from different distributions. Then, what are the other z scores? They are transformations. We have changed the raw score in which standard score. And when we should know two things, we should know the mean, the sample, and the standard deviation. The formula is to change the raw score to z score. z is equal to x minus m upon sd. What is x here? What is raw score? What is mean? And what is sd? It is standard deviation. And the standard score we make, the transformation from raw score to standard score, we will read all the standard scores. We have set the arbitrary mean and sd. The statisticians who have made all these scores, who have worked on them, they have set the standard deviation and all the computations are done accordingly. Similarly, the mean of z score is zero. It is set. And the standard deviation is set to one. So, if you know the mean and standard deviation from this formula, then you can convert raw score to z score. And in this formula, it is x minus m. If the mean and raw score is more, then z score will be minus. Because if the standard deviation is more, then the standard deviation from x score will be zero. And the standard deviation from x score will be minus. If x is greater, then it will be positive. That is, z score is minus plus two. Only then we can tell whether we are taking the performance above or below the performance. Okay. Sorry. Then it can be used to compare across distributions unless the mean and this Sd are identical in each distribution. Or if the raw scores come from the same distribution, that is, when can we compare them when we know that mean and Sd are identical, that is, they are the same thing. Or from where we have taken raw score, they are coming from the same distribution. The distribution should be similar. That is why we can compare. Or what are its characteristics? Another characteristic is that larger standards score means larger deviations. That is, the more the standards score, the more we will understand that we are showing deviations more than mean. And what can be this? It can be positive or negative. I have told you. And where does z score be used? Most intelligence test, most intelligence test, and many intelligence test also use standard score or z score. Let's tell you in our interpretation how many Sd plus 1, plus 1 Sd, plus 2 Sd, plus minus 2 Sd, plus minus 1 Sd. We have performed a standard of 1 mana, which is good or 1 mana, which is bad. Then let's talk about C score. C score, z score and C score are often broken. Z score is the most popular. T is less popular than that. And C score is less popular. But you should know what is C score. The scale of this is 0 to 10. That is, from where do we start? From Shunia. And how far do we go? From 11 to 10. And from 1 to 10. Plus there is an additional. So it is 11. We have 11 scores in C score. And these scores are ordered. That is, all these scores are in order. That is, Shunia is the least. 1 is more than that. Then 2 is 3. And 10 is the lowest. Then raw scores can be converted into C score. That is, C score is also a kind of standard score. We can change this raw score to C score. How? With the help of percentile rank. We can change it from percentile rank to percentile rank. Or we can get C score from z score. What is the formula? C is equal to 5 plus 2z. That is, what is 5 here? It is mean. How? Look, there are 11 scores. So we will start from Shunia. So the fifth will come in the middle. And the fifth will go up and the fifth will go down. So C is equal to 5 plus 2z. This is the formula. And this is the C score. It is asked a lot. But it is still in your course. So you should know. Normalized score. We talked about raw score. We talked about raw score. It has no meaning itself. We will have to standardize it to create its meaning. We will have to bring it to a scale. So we have brought it to a scale. And we have taken the standardized score. Then why did we need normalized score? Look, normalized standard scores have the same meaning. As linearly derived standard scores, in terms of the position of the original raw scores, they represent relative to their distributions. What are we talking about? What is linear transformation? It does not change the earth. The interrelationship between variables does not change. What is special? The population from which you are taking it should be the same distribution. So when does the standardized score apply? When the distribution is different. One, it will be a normal distribution. The other, it will not be a normal distribution. So how will we compare both? So what will we have to do when the normal distribution is not distributed? We will have to make a normal distribution. Only then we will be able to divide both. So in this condition, what will be the standardized score? What is it saying? Conceptually, normalizing a distribution involves stretching the skewed curve into a shape of a normal curve. Many of you may not know NPC. If you know the skewed curve, you will understand it in the next slide. What we have to do? One is a normal curve. But the other is skewed. So what will we stretch and make the skewed curve normal? And then we will create a corresponding scale of standard scales. A scale corresponding scale of standard scores. A scale that is technically referred to as a normalized standard score scale. So when we stretch and make the skewed curve normal, what will be the standardized standard score? What will be the standardized standard score scale? Look at this. For example, distribution A was normal. This is normal. Think of the NPC. These are the three mediums. 1, 2, 3, 4, 3, 4, 3, 4, 6, 8, 9, 10, 12, 6. This is coming between plus minus 1 sigma. But our diagram B, which is our population B. Distribution B is skewed. It means this is a negative skewed and this is a positive skewed. This is more than this. So this is not normal. So what do we have to do? We have to stretch and make it normal. Only then we will be able to divide between the two. What will happen? Respective distribution was represented. Different amounts of area subsumed under the curve. Another area is coming in this curve. Another area is coming in this curve. When the area is not the same, how can we do comparison? That is why this is called normalized score. When the population is different. This is normal and this is skewed. So skewed is called normal. That is why it is called normalized score. Lastly, T score. This is also very popular. Who has devised the T score? Mac call. He made it in 1932. And named it T score. Why is it called T score? Why is it called T score in the name of Professor Thorndike? There is a term in the name of Thorndike. He named it T score in the name of Thorndike. Then what is the mean and SD set for this? The mean set is 50 and the SD is 810. That is, the mean set is 50 and the SD is 10. Used when the distribution is normal. When the distribution is normal, then we use it. What is better than Z in this case? What was Z? Positive was also negative. But its mean is only positive and not in the fraction. Enjoys advantage over standard scores. As in it, the negative and fractional standard scores can be avoided. Because here there is no negative. There is no fraction. That is why it is better than Z. And in T scale, it is assumed that the distribution is normal. This is why T score is called a normalized standard score. Like Z is called a standard score. Similarly, T score is a normalized standard score. Why? Because the distribution here is normal. But T score can also be changed to Z score. Or Z score can also be changed to T score. What is the formula? T score is equal to 50 plus 10 Z. What is always going on? What is being connected in the mean? Z is made up of its standard deviation. 50 plus 10 Z. 50 is equal to mean and standard deviation is equal to 10. So, the mean is always the same. And it will never come to the full mark. So, this is a normalized standard score. This is a non-linear transformation. Whereas Z score is a standard score. And that is a linear transformation. What is its formula? X minus M of 1 is D. What is its formula? 50 plus 10 Z. What is the formula of C score? 5 plus 2 Z. So, remember, it is easy. And we often ask short notes. When an objective question comes on paper, when it comes theoretical, we ask short notes. Write short notes on standardized score. Write short notes on normalized score. Write short notes on T, Z and C score. We will ask like this. And when an objective question comes, then there are a lot of questions. We will ask the formula. Or we will give you the meaning of T score. And the mean S D is equal to Z score. Or the mean score is equal to your raw score is equal to the standard deviation is equal to Z score. Or Z is equal to T score. Or T score is equal to C score. We should know all the formulas. If we know the formula, then numerical is not easy. It is difficult. Our numerical is not there. The problem is that we should know the formula. If we know the formula, then we will not get it. Okay. So, finished. In the educational measurement and evaluation paper, or in some part of psychological testing, or in some part of educational research, in some portion, we have this psychological testing portion where we have to read the standardised score. So, I hope you have cleared it. So, thank you all. And don't forget to like and subscribe my channel. And join my daily gram group too. That's name is Explore Education. Okay. Done from my side.