A correlation between variables indicates that as one variable changes in value, the other variable tends to change in a specific direction. A correlation coefficient measures both the direction and the strength of this tendency to vary together.
- A positive correlation indicates that as one variable increases the other variable tends to increase.
- A correlation near zero indicates that as one variable increases, there is no tendency in the other variable to either increase or decrease.
- A negative correlation indicates that as one variable increases the other variable tends to decrease.
The correlation coefficient can range from -1 to 1. The extreme values of -1 and 1 indicate a perfectly linear relationship where a change in one variable is accompanied by a perfectly consistent change in the other. In practice, you won’t see either type of perfect relationship.
The two most common types of correlation coefficients are Pearson’s product moment correlation and the Spearman rank-order correlation.
Pearson product moment correlation
The Pearson correlation evaluates the linear relationship between two continuous variables. A relationship is linear when a change in one variable is associated with a proportional change in the other variable.
Spearman rank-order correlation
Also called Spearman’s rho, the Spearman correlation evaluates the monotonic relationship between two continuous or ordinal variables. In a monotonic relationship, the variables tend to change together, but not necessarily at a constant rate. The Spearman correlation coefficient is based on the ranked values for each variable rather than the raw data.