ABSTRACT
The magnitude of the covariance is a function of the scales used to measure X and Y (i.e., their standard deviations). Hence, the covariance is not appropriate to measure the strength of the relationship between two variables. An absolute covariance of a given size may reflect either a weak relationship, if the standard deviations of the two variables investigated are large, or a strong relationship if the standard deviations of the two variables are small. To avoid this problem we need an index of the strength of the linear relationship between two variables which is independent of the scales used to measure them. To obtain this index the covariance is divided by the product of the standard deviations of the variables. The standardised covariance between two variables is called the Pearson product-moment correlation coefficient r and is defined as:
In the case of the relationship between degree mark and monthly salary, the correlation coefficient r is:
where sx is the standard deviation of the degree marks and sy is the standard deviation of the salaries. Table 11.3 provides, in detail, all the data and the computational steps required to calculate Pearson’s r.
