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Pearson Product-Moment Correlation is one of the measures of correlation which quantifies the strength as well as direction of such relationship. It is usually denoted by Greek letter ρ.
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In the study of relationships, two variables are said to be correlated if change in one variable is accompanied by change in the other - either in the same or reverse direction.
This coefficient is used if two conditions are satisfied
- the variables are in the interval or ratio scale of measurement a linear relationship between them is suspected
Positive and Negative Correlation
The coefficient (ρ) is computed as the ratio of covariance between the variables
to the product of their standard deviations. This formulation is advantageous.
First, it tells us the direction of relationship. Once the coefficient is computed, ρ > 0 will indicate positive relationship, ρ < 0 will indicate negative relationship while ρ = 0 indicates non existence of any relationship.
Second, it ensures (mathematically) that the numerical value of ρ range from -1.0 to +1.0. This enables us to get an idea of the strength of relationship - or rather the strength of linear relationship between the variables. Closer the coefficients are to +1.0 or -1.0, greater is the strength of the linear relationship.
As a rule of thumb, the following guidelines are often useful (though many experts could somewhat disagree on the choice of boundaries).