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A common measure of association for random variables X and Y is the rank correlation, or Spearman`s correlation. The X values are ranked, and the observations are replaced by their ranks; similarly the Y observations are replaced by their ranks. For example, for a sample of size 5 the observations
are replaced by
Let r(Xt) denote the rank of XI and r( Yt) the rank of Yt. Using these paired ranks, the ordinary sample correlation is computed:
(b) Compute the ordinary correlation and Spearman`s correlation for the above data.