Methods of Studying Correlation : The Scatter Diagram Method, Karl Pearson's & Spearman's Rank Correlation Coefficient.

 

Methods of Studying Correlation ©

1. Scatter Diagram:

 It is the simplest method of studying the correlation between the two variables. Scatter diagram is a diagrammatic representation of bivariate data. To draw a scatter diagram, consider two co-ordinate axes, one for variable X and other for Y. Then each pair (Xi, Yi), i = 1, 2, ...n of values of variables X and Y is plotted as a point on graph paper.

Scatter diagram gives us a visual idea whether the variables are correlated or not. The way in which (i.e. the trend of points) the points are scattered indicate the degree and direction of relationship. The degree of correlation depends upon the width of trend of points. The narrowness of width of trend suggests high degree correlation. If the points are close to each other we infer that the variables are correlated. If they are spread away from each other, we infer that the variables are not correlated. Moreover, if the points lie in a narrow strip rising from left hand bottom to right hand top, we say that there is positive correlation of high order. If the points lie in a narrow strip falling from left hand top to right hand bottom, we say that there is negative correlation of high order.

The typical examples of scatter diagrams:

Merits : 

It is simplest method. 

It can be understood easily. 

It gives the rough idea about the  existence of correlation.

Demerits:

 It is not a mathematical method; therefore we can not measure the degree of correlation.

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Covariance

Definition:

Let (xi, yi), i = 1, 2,.....n be a set of n paired observations on two related  variables X and Y. The covariance between X and Y is defined as,

It also represent first order central moment µ11, of a bivariate data and so known as product moment of X and Y.


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