Calculating Correlation

Understanding Correlation

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.
A positive correlation means that as one variable increases, the other also increases; and as one decreases the other also decreases.
A negative correlation represents the opposite; when one variable increases, the other decreases.
Correlation coefficients range from -1 to 1. A value of +/- 1 indicates a perfect degree of linear association between two variables.

Calculating the Correlation Coefficient

The correlation coefficient, often denoted by r, is a measure that determines the degree to which two variables’ movements are associated.
It is calculated using the Pearson Product-Moment Correlation formula.
A correlation coefficient near to +1 or -1 shows a strong correlation, while a correlation coefficient near to 0 shows a weak correlation.
To calculate the correlation coefficient, first calculate the covariance of the two variables, then divide by the product of their standard deviations.

Interpreting Correlation Coefficients

A correlation coefficient between 0 and 0.3 (or 0 and -0.3) shows a weak correlation.
A correlation coefficient between 0.3 and 0.7 (-0.3 and -0.7) shows a moderate correlation.
A correlation coefficient between 0.7 and 1.0 (-0.7 and -1.0) shows a strong correlation.

Properties of the Correlation Coefficient

The correlation coefficient is symmetric, meaning correlation from X to Y is the same as correlation from Y to X.
The correlation coefficient has the unitless property, which allows you to compare correlation coefficients across different pairs of variables.
The sign (+/-) of the correlation coefficient represents the direction of the relationship between two variables.
Correlation does not imply causation. A high correlation between two variables X and Y does not mean that changes in X cause changes in Y (and vice versa).

Spearman’s Rank Correlation Coefficient

When the normal Pearson Product-Moment Correlation might not reflect the true relationship between two variables, we can use the Spearman’s rank correlation coefficient.
It is used when the relationship between the variables is nonlinear or when the variables are both ranked.
This rank version of correlation coefficient is calculated the same way as the standard correlation coefficient, but with ranked values.