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Spearman’s Correlation Coefficient calculates the direction and strength of the relationship between two variables that are ranked in a specific order. Charles Spearman founded Spearman Correlation. He also proposed a general factor of intelligence that occurs in different degrees in human beings. Charles Spearman is known for his exceptional contribution to the field of statistics.
Denoted by ρ, i.e., rho, Spearman’s Rank Correlation is said to be Pearson product-moment correlation’s non-parametric version. Karl Pearson invented Pearson’s Correlation Coefficient, and it calculates the direction and strength of the linear relationship between two variables. Spearman’s Correlation Coefficient identifies the direction and strength of the monotonic relationship between two variables. In the monotonic relationship, the rate of change between two variables is constant. In contrast, no such thing is required in a linear relationship as long as one variable influences the other.
The formula for calculating Spearman’s Correlation Coefficient is given below:
where
di is the difference in ith observation’s rank
n is the number of observations that 2 variables have
The value of p can vary between –1 to 1.
If the value of ρ is –1, it suggests that there is a perfect negative link between the variables. If the value of ρ is 1, it suggests that there is a perfect positive link between the variables. However, if the value of ρ is 0, it means that there is no link between the 2 variables.
When the value of ρ is closer to 0, it means that the link between 2 variables is weaker irrespective of whether it is a positive or negative link.
Monotonic relationship
When two variables are such that the change in one’s value affects the other, they are said to be in a monotonic relationship. The increase in one variable’s value might decrease or increase the other variable’s value. The change in the value of one variable is usually related to the other variable’s change in direction. When the variables don’t reflect changes in the same direction, they are said to be in a non-monotonic relationship.
Difference between Spearman’s Rank Correlation & Pearson’s Correlation Coefficient
The key differences between Spearman’s Rank Correlation and Pearson’s Correlation Coefficient are mentioned in the below table:
Importance of Ranking in Spearman’s Rank Correlation
The ranking is done to find the relationship between two values or numbers. The values can be either equal, greater, or less than each other, and a lesser value is given the highest or lowest ranking depending upon the purpose of ranking.
For example, when it comes to marks, the highest mark has to get the highest ranking, which is one. On the contrary, when it comes to determining which items have better chances of floating on water, the higher weight will get the lowest ranks.
When two values have equal values, the arithmetic mean of the two ranks is assigned to each value. Spearman’s Rank Correlation compares two data sets based on their ranking of the individual observations. Therefore, ranking plays a huge role in determining the relationship between the data sets.
Types of Ranking
SCR: SCR or Standard Competition Ranking is a ranking method in which equal values get equal rank, and the next lower value is assigned with the next highest rank.
Ordinal Ranking: Every value gets a position in the sequence numbers in the Ordinal Ranking. No two positions are the same or equal in this type of ranking.
Fractional Ranking: In Fractional Ranking, the numbers are ordered from low to high or from high to low. Equal values get the arithmetic mean of the rank.
