The degree or level of correlation is measured with the help of the correlation coefficient or coefficient of correlation. For population data, the correlation coefficient is denoted by . The joint variation of and is measured by the covariance of and . The covariance of and denoted by is defined as:
The may be positive, negative or zero. The covariance has the same units in which and are measured. When is divided by and, we get the correlation coefficient . Thus , is free of the units of measurement.
It is a pure number and lies between and . If , it is called a perfect correlation. If , it is called perfect negative correlation. If there is no correlation between and , then and are independent and . For sample data, the correlation coefficient denoted by “” is a measure of strength of the linear relation between and variables, where “” is a pure number and lies between and . On the other hand Karl Pearson’s coefficient of correlation is: