 Whenever we are conducting research and especially correlational research, most of the time, we are using PSN product movement correlation method, which we covered in our last lecture. But there are other types of correlation as well, depending upon the type of data, type of scale, situation, or the type of variables. So I will briefly go over with a few important types of other correlational methods. I'm not going to solve them, but just want to give you an overview of that. We can easily calculate that in SPSS by changing the option from PSN product moment to other methods. So the first one I'll talk about is a partial correlation. Partial correlation, there are many situations when we are trying to find relationship between the two, but that relationship is distorted by any other third variable. For instance, in the last example, we covered that relationship between number of churches and number of crimes, that if there are fewer churches, fewer crime, but actually we saw that the relationship was explained by or affected by the third variable, and that was the size of the town. It was not the number of churches, rather small towns have fewer churches. That's why there's a lesser crime as compared to the big cities where there are a lot of population. So the third variable was the size of the town. So whenever there's a situation like this, that the third variable is actually distorting and giving a wrong impression of that very relationship, we use partial correlation. So partial correlation simply calculate the relationship between x and y by partialing out the effect of the third variable. Partialing out means that after controlling the effect, it purely finds out the relationship in x and y. So when we calculate partial correlation, the philosophy behind it is that we are calculating bi-stereally, we calculate the relationship between x and y, y and z, and x and z, and then we look at the third variable and then we control it. The statistical significance of partial correlation is determined using the same procedure. How do we find out the statistical significance of it? As we used to do before, we will see it in table value and if our p value is smaller than the table value, then we say that it's a significant test, so we will be using the same table that is B6 in the Gravator book that we used for the PSN product movement correlation. So for partial correlation, there's one difference that we have two variables in the arm bi-serial correlation. So our degrees of freedom is n minus 2. But in partial correlation, because we have a third variable inside, so we calculate the degrees of freedom of n minus 3. And significant correlation means that your relationship between two variables is significant by partialing out the effect of the third variable. The second type is Spareman correlation. When we have data in rank orders, that is, we have the ordinal data, and then for ordinal data, correlation is a better method. Spareman rank order correlation, in which we give each points of data in ranks, that is, we give them in an order, and then we take out X and Y correlation in the same way. For this, simply go to SPSS and check the Spareman instead of the PSN product, and it will give you the correlation coefficient and then it will calculate the p-value. The symbol of this is written as RS, whereas for the PSN product moment, we use the symbol of R. So Spareman correlation is used to measure the relationship between X and Y when both variables are measured on ordinal scale. Additionally, it can be used as a valuable alternative to the PSN correlation, even when the original raw scores are on the interval or ratio scale. Sometimes we have continuous data and the ratio is on the interval scale, but by giving it ranks, we can calculate the correlation on the ordinal scale. But mostly, Spareman rank order correlation is used on the ordinal data, like the variable socioeconomic status and your academic achievement, then you can get the correlation between the ordinal data and then you can get the correlation. In Spareman correlation, there is consistency rather than the POM. So mainly, they see that between X and Y, because we see both on the ordinal scale, we measure consistency in it. When two variables are consistently related, their ranks are linearly related. If X is ranked 3 on the variable, then Y is ranked 3 on the variable, then it checks your consistency and then you get the correlation. For example, a perfectly consistent positive relationship means that every time X variable increases, the Y variable would also increase. The ranks of both X and Y will have perfect consistency to find a perfect relationship on Spareman rank order. When there is a consistency, one directional relationship between two variables, the relationship said to be monotonic. Between both X and Y, there is consistency. If it is higher than one, then it is higher than the other. It is called a monotonic relationship. Thus, in the Spareman correlation, this is the degree of monotonic relationship between two variables. It measures the consistency of both the ordinal scales and how your ranks are going. But you can easily calculate it in SPSS by just using the option from Pearson to Spareman.