Interpreting the Coefficient of Correlation

The coefficient of correlation measures the degree of relationship between two sets of figures. As the reliability of estimates depends upon the closeness of the relationship it is imperative that utmost care be taken while interpreting the values of coefficient of correlation, otherwise fallacious conclusions can be drawn.

Unfortunately, the interpretation of the coefficient of correlation depends very much on experience. The full significance of r will only be grasped after working out a number of correlation problems and seeing the kinds of data that give rise to various values of r. The investigator must know his data thoroughly in order to avoid errors of interpretation and emphasis. He must be familiar, or become familiar, with all the relationships and theory which bear upon the data and should reach a conclusion based on logical reasoning and intelligent investigation on significantly related matters. However, the following general rules are given which would help in interpreting the value of r:

1. When r = +1, it means there is perfect positive relationship between the variables.

2. When r = - 1, it means there is perfect negative relationship between the variables.

3. When r =   0, it means that there is no relationship between the variables, i.e., the variables are uncorrelated.

4.  The closer r is to + 1 or – 1, the closer the relationship between the variables and the closer r is to 0, the less close the relationship. Beyond this it is not safe to go. The full interpretation of r depends upon circumstances one of which is the size of the sample. All that can really be said that when estimating the value of one variable from another, the higher the value of r the better the estimate.

5. The closeness of the relationship is not proportional to r. If the value of r is 0.8 it does not indicate a relationship twice as close as one of 0.4. It is in fact very much closer. 

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