Question

What are the two limitations of correlation when interpreting the data?

Answer 1

Solution :

Two limitations of correlations when interpreting the data are :

1st Limitation : One of the limitations of the Pearson's Correlation Coefficient is it is the measure of linear association between two variables. Let us consider the following example!

x	-2	-1	0	+1	+2
y	4	1	0	1	4

Let X and Y be two random variables having 'n' sample values each.

The formula for calculating the Correlation Coefficient (r) between X and Y is given as ,

Here, after calculating the Pearson's Correlation Coefficient for the above data, we get, r = 0, which implies that there is no association between x and y.

But actually, we can manually observe that, x² = y. So, we can say that the Pearson's Correlation Coefficient is a measure of linear association between x and y. Thus, this measure is not applicable for Non - Linear type of data. Thus, it can be considered as a limitation.

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2nd Limitation : Another limitation of the Pearson's Correlation Coefficient is that in some cases there might appear a situation which is known as Non - Sense Correlation or Spurious Correlation where the two variables are not related casually among each other. Let us consider the following example !

There might appear a situation, where we can find the Correlation Coefficient between the variables (say) Height of sample of a students and Marks of those students and it may come out to be r = 0.85 which does not make any sense. This does not necessarily mean that the Heights of the Students influence the Marks of those Students. Thus, here appears a situation where Non - Sense Correlation or Spurious Correlation occurs. Thus, it can be considered as another limitation.

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