Algebraic Properties of Pearson’s Co-efficient of Correlation

Prof. Karl Pearson’s co-efficient of correlation thus discussed above has the following algebraic properties:

• Its value must lie between +1 and -1 i.e. -1 ≤ r ≤ + 1. This property providers us with a yardstick of checking the accuracy of the calculations.
• It is independent of the changes of origin and scale as well. By change of origin we mean subtraction or addition of some constant value from/to each value of a variable. Such constants may be the same or different for the two variables X and Y. Further, by change of scale we mean dividing or multiplying each value of variable by some constant figure and such constant figures may also be the some or different for the two variables of X and Y. This property implies that the value of the co-efficient of correlation will remain the same, eve if, there occurs a change of origin or a change of scale. This property helps us in simplifying the process of calculations.
• It is independent of the units of measurement. This implies that even if the two variables are expressed in two different units of measurement viz. rain fall in inches, and yield of crops in quintals, the value of the coefficient of correlation comes out with a pure number. Thus, it does not require that the units of measurement of both the variables should be the same.
• It is independent of the order of comparison of the two variables. Symbolically, r_xy = r_yx. This is because,