Partial correlation is defined as the measure of the association that occurs between two variables after keeping the control or adjusting the effects of one or more additional variables.
The process of partial correlation is used by researchers to answer many things. The process of partial correlation can be used in order to understand whether or not sales and advertising expenditure are strongly related when the effect of the price is kept under control.
The process of partial correlation can be used in order to understand whether or not there exists any association between the market share and the size of the sales force when the effect of the sales promotion is adjusted.
In order to solve such cases, the researcher would first remove the effect of the additional variable from the first variable. In order to perform this, the prediction of the values of the first variable is done on the basis of the knowledge obtained from the additional variable. This is obtained with the help of the product moment correlation between the first variable and the additional variable. The predicted value of the first variable is then subtracted from the actual value of the first variable for the purpose of constructing the adjusted value of the first variable.
Along similar lines, the values of the second variable are adjusted for the purpose of removing the effects of the additional variable. Finally, the product moment correlation between the adjusted values of the first variable and the adjusted values of the second variable is basically the partial correlation between them after the removal of the effects of the additional variable.
Statistically, since the process of simple correlation between the two variables completely describes the linear relationship between the two variables, the partial correlation coefficient is calculated with the knowledge of the simple correlation coefficient alone, without the use of any individual observations.
The partial correlation between the variable ‘X’ and ‘Y’ when the effects of the additional variable ‘Z’ is kept under control is given by the following formula:
rxy.z= rxy – (rxz)(ryz)/1-rxz2 1-ryz2
The process of partial correlation consists of an order which is associated with them. The order in partial correlation indicates the number of the variables that are adjusted or are controlled. Therefore, the first order partial correlation coefficient controls the effect of one additional variable and simultaneously the second order partial correlation coefficient controls the effects of two additional variables. Similarly, the third partial correlation coefficient controls the effects of three variables and so on.
The process of partial correlation is helpful for the purpose of detecting spurious relationships in the following manner:
Partial correlation shows that the relationship between the variable ‘X’ (for example) and variable ‘Y’ (for example) is of the spurious type if and only if the variable ‘X’ is associated with the variable ‘Z,’ which is the true predictor of the variable ‘Y.’ As a result, the correlation between the variable ‘X’ and the variable ‘Y’ disappears when the variable ‘Z’ is controlled. Thus, the relationship became spurious.
