Spearman’s rank correlation, also known as Spearman’s rho correlation, is a non-parametric measure of the strength and direction of the association between two variables. It measures the degree of correspondence between the rankings or orders of the two variables.
Spearman’s rank correlation coefficient, denoted by the symbol ‘ρ’, ranges between -1 and +1. A Spearman’s rho correlation coefficient of +1 indicates a perfect positive correlation, which means that both variables move in the same direction with a similar magnitude. A Spearman’s rho correlation coefficient of -1 indicates a perfect negative correlation, which means that both variables move in opposite directions with a similar magnitude. A Spearman’s rho correlation coefficient of 0 indicates no correlation between the variables.
The formula to calculate Spearman’s rank correlation is:
ρ = 1 – ((6Σd^2) / (n(n^2-1)))
where:
- d is the difference between the ranks of the ith observation for the two variables being compared
- Σ is the summation symbol, which means “add up all the values”
- n is the number of observations
Spearman’s rank correlation is often used when the data being analyzed does not meet the assumptions of parametric correlation measures such as Pearson’s correlation. It is widely used in fields such as psychology, sociology, and marketing to analyze the relationship between two variables that are measured on an ordinal or continuous scale.
Spearman’s rank correlation assumes the following:
- Independence: The data points being analyzed should be independent of each other.
- Random sampling: The data should be collected using a random sampling technique.
- Ordinal measurement: The variables being correlated should be measured on an ordinal or continuous scale.
- Monotonicity: The relationship between the two variables being correlated should be monotonic, which means that the variables should move in the same direction, either increasing or decreasing, but not necessarily at a constant rate.
- No significant outliers: There should not be any significant outliers in the data that could influence the correlation coefficient.