SCATTER DIAGRAM METHOD

The simplest device for ascertaining whether two variables are related is to prepare a dot chart called scatter diagram. When this method is used the given data are plotted on a graph paper in the form of dots, i.e., for each pair of X and Y values we put a dot and thus obtain as many points as the number of observations. By looking to the scatter of the various points we can form an idea as to whether the variables are related or not. The greater the scatter of the plotted points on the charts, the lesser is the relationship between the two variables. The more closely the points come to a straight line, the higher the degree of relationship. If all the points lie on a straight line falling from the lower left-hand corner to the upper right- hand corner, correlation is said to be perfectly positive (i.e., r = +1) (diagram I). On the other hand, if all the points are lying on a straight line rising from the upper left-hand corner to the lower right- hand (i.e., r = -1) (diagram II).


If the plotted points fall in a narrow band there would be a high degree of correlation between the variables – correlation shall be positive if the points show a rising tendency from the lower left-hand corner to the upper right-hand corner (diagram III ) and negative if the points show a declining tendency from the upper left-hand corner to the lower right – hand corner (diagram IV).

 

                              III                                                               IV

On the other hand, if the points are widely scattered over the diagram it is the indication of  every little relationship between the variables --- correlation shall be positive if the points are rising from the lower left – hand corner to the upper right – hand corner (diagram V) and negative if the points are declining from the upper left – hand side to the lower right – hand side of the diagram (diagram VI).
 



If the plotted points lie on a straight line parallel to the x-axis or in a haphazard manner, it shows absence of any relationship between the variables (i.e., r = 0) as shown by diagram VII.



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