Association vs Correlation
Association and correlation are two methods of explaining a relationship between two statistical variables. Association refers to a more generalized term and correlation can be considered as a special case of association, where the relationship between the variables is linear in nature.
What is Association?
The statistical term association is defined as a relationship between two random variables which makes them statistically dependent. It refers to rather a general relationship without specifics of the relationship being mentioned, and it is not necessary to be a causal relationship.
Many statistical methods are used to establish the association between two variables. Pearson’s correlation coefficient, odds ratio, distance correlation, Goodman’s and Kruskal’s Lambda and Spearman’s rho (ρ) are a few examples.
What is Correlation?
Correlation is a measure of the strength of the relationship between two variables. The correlation coefficient quantifies the degree of change of one variable based on the change of the other variable. In statistics, correlation is connected to the concept of dependence, which is the statistical relationship between two variables
The Pearson’s correlation coefficient or just the correlation coefficient r is a value between -1 and 1 (-1≤r≤+1). It is the most commonly used correlation coefficient and valid only for a linear relationship between the variables. If r=0, no relationship exist, and if r≥0, the relation is directly proportional; the value of one variable increases with the increase in the other. If r≤0, the relationship is inversely proportional; one variable decreases as the other increases.
Because of the linearity condition, correlation coefficient r can also be used to establish the presence of a linear relationship between the variables.
Spearman’s rank correlation coefficient and Kendrall’s rank correlation coefficient measure the strength of the relationship, excluding the linear factor. They consider the extent one variable increases or decreases with the other. If both variables increase together the coefficient is going to be positive and if one variable increases while the other decreases the coefficient value is going to be negative.
The rank correlation coefficients are used just to establish the type of the relationship, but not to investigate in detail like the Pearson’s correlation coefficient. They are also used to reduce the calculations and make the results more independent of the non-normality of the distributions considered.
What is the difference between Association and Correlation?
• Association refers to the general relationship between two random variables while the correlation refers to a more or less a linear relationship between the random variables.
• Association is a concept, but correlation is a measure of association and mathematical tools are provided to measure the magnitude of the correlation.
• Pearson’s product moment correlation coefficient establishes the presence of a linear relationship and determines the nature of the relationship (whether they are proportional or inversely proportional).
• Rank correlation coefficients are used to determine the nature of the relationship only, excluding the linearity of the relation (it may or may not be linear, but it will tell whether the variables increase together, decrease together or one increases while the other decreases or vice versa).