Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman's rank correlation coefficient.
Question 1 Report
Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman's rank correlation coefficient.
Answer Details
Spearman's rank correlation coefficient is a measure of the strength of a relationship between two variables and is used when the variables are measured on an ordinal scale. The formula for calculating Spearman's rank correlation coefficient is:
$$r_{s} = 1 - \frac{6\sum d^{2}}{n(n^{2} - 1)}$$
where \(d\) is the difference between the ranks of each observation in the two variables, and \(n\) is the sample size.
In this case, we are given that \(n = 10\) and \(\sum d^{2} = 20\). Substituting these values into the formula, we get:
$$r_{s} = 1 - \frac{6(20)}{10(10^{2} - 1)} = 1 - \frac{120}{990} = 1 - 0.121 = 0.879$$
Therefore, the Spearman's rank correlation coefficient is 0.879.
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