As mentioned earlier, correlation analysis is a statistical tool, which should be properly used so that correct results can be obtained. Sometimes, it is indiscriminately used by management, resulting in misleading conclusions. We give below some errors frequently made in the use of correlation analysis:
Correlation analysis cannot determine cause-and-effect relationship. One should not assume that a change in Y variable is caused by a change in X variable unless one is reasonably sure that one variable is the cause while the other is the effect. Let us take an .
Suppose that we study the performance of students in their graduate examination and their earnings after, say, three years of their graduation. We may find that these two variables are highly and positively related. At the same time, we must not forget that both the variables might have been influenced by some other factors such as quality of teachers, economic and social status of parents, effectiveness of the interviewing process and so forth. If the data on these factors are available, then it is worthwhile to use multiple correlation analysis instead of bivariate one.
Another mistake that occurs frequently is on account of misinterpretation of the coefficient of Suppose in one case r = 0.7, it will be wrong to interpret that correlation explains 70 percent of the total variation in Y. The error can be seen easily when we calculate the coefficient of determination. Here, the coefficient of determination r2 will be 0.49. This means that only 49 percent of the total variation in Y is explained..
Similarly, the coefficient of determination is misinterpreted if it is also used to indicate causal relationship, that is, the percentage of the change in one variable is due to the change in another variable.
Another mistake in the interpretation of the coefficient of correlation occurs when one concludes a positive or negative relationship even though the two variables are actually unrelated. For example, the age of students and their score in the examination have no relation with each other. The two variables may show similar movements but there does not seem to be a common link between
To sum up, one has to be extremely careful while interpreting coefficient of correlation. Be- fore one concludes a causal relationship, one has to consider other relevant factors that might have any influence on the dependent variable or on both the variables. Such an approach will avoid many of the pitfalls in the interpretation of the coefficient of correlation. It has been rightly said that the coefficient of correlation is not only one of the most widely used, but also one of the widely abused statistical measures.