Definition and Calculation
The Spearman correlation coefficient is defined as the Pearson correlation coefficient between the ranked variables. For a sample of size n, the n raw scores are converted to ranks, and ρ is computed from these:
Identical values (rank ties or value duplicates) are assigned a rank equal to the average of their positions in the ascending order of the values. In the table below, notice how the rank of values that are the same is the mean of what their ranks would otherwise be:
| Variable | Position in the ascending order | Rank |
|---|---|---|
| 0.8 | 1 | 1 |
| 1.2 | 2 | |
| 1.2 | 3 | |
| 2.3 | 4 | 4 |
| 18 | 5 | 5 |
In applications where duplicate values (ties) are known to be absent, a simpler procedure can be used to calculate ρ. Differences between the ranks of each observation on the two variables are calculated, and ρ is given by:
Read more about this topic: Spearman's Rank Correlation Coefficient
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