Using your completed table you can calculate the Spearman co

Using your completed table, you can calculate the Spearman correlation in two different ways. One way is to use the Pearson correlation formula on the ranks of the data. When you do this, you get r_s = -0.62. The second way to calculate the Spearman correlation is to use the following formula: r_s = 1 - 6 sigmaD^2/n(n^2 - 1) In this formula, D represents the difference between ranks for each individual. Using this formula, you get r_s = -0.51. These two estimates of the Spearman correlation are different for the following reason: The Pearson correlation formula applied to the ranks loses accuracy when there are many ties. The formula that uses the differences (D) is always only a rough estimate of r_s. The formula that uses the differences (D) loses accuracy when there are many ties. You do not use the Pearson correlation formula when calculating the Spearman correlation.

Solution

There are two methods to calculate Spearman\'s correlation depending on whether: (1) your data does not have tied ranks or (2) your data has tied ranks.The formula applied to the ranks loses accuracy when there are many ties.