if the values of X and Y have been ranked and we compute correlation b/w ranks of X and Y will this correlation be equal to value of rk

In this case, the value of Pearson correlation coefficient will be equal to the value of Spearman rank correlation coefficient, provided ranks are not repeated. This is to say that when all the ranks are different, then the value of Karl Pearson correlation coefficient will be equal to that of Spearman rank correlation coefficient.

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