The formula for Spearman's rank correlation coefficient is:
$$ r_s = 1 - \frac{6\sum d_i^2}{n(n^2-1)} \quad \text{(when there are no tied ranks)} $$
Where:
In practice, students are expected to use technology to calculate $r_s$ rather than performing manual calculations.
When two or more data points have the same value, they are assigned the average of the ranks they would have received if they had been distinct.
If we have the data set: 7, 9, 9, 10, 10, 11. The ranks would be: 1, 2.5, 2.5, 4.5, 4.5, 6.
This method ensures that the sum of the ranks remains the same as it would be for untied data.
While both Spearman's and Pearson's correlation coefficients measure the strength and direction of a relationship between two variables, they have distinct characteristics:
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