Spearman's Coefficient

Also known as Spearmans Rank Correction Coefficient


The simplest method is the Spearman's rho coefficient
In calculating the Rho coefficient you must rank the scores


The spearman is the non parametric version of the Pearsons
The spearman coefficient measures the strength of association between two ranked variables
The spearman coefficient can be any number between +1 and -1


Assumptions:
1- The two groups contain values that represent ordinal, interval or ratio values
2- That the relationship between them is monotonic



Two Type of Calculation
There are two methods for calculating the coefficient depending on whether there are any tied ranks
1- If your data has no tied ranks then you use:

2- If your data does contain tied ranks then you use:

https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide.php


Let's consider two groups of numbers
A - (2,4,5,9,12,13)
B - (2,4,5,9,12,13)
Let us put these two groups into a table (in different columns)
In the next two columns, add the Rank for each of the items in each of the groups Ra and Rb
If you have two identical values (or ties) then you need to take the average of the ranks they would have occupied.


In the next column add the difference between the paired ranks





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