Problem 23 in Chapter 10 presented data showing that mature soccer players, who have a history of hitting soccer balls with their heads, had significantly lower cognitive scores than mature swimmers, who do not suffer repeated blows to the head. The independent-measures t test produced t = 2.11 with df = 11 and a value of r2 = 0.288 (28.8%).
a. Convert the data from this problem into a form suitable for the point-biserial correlation (use 1 for the swimmers and 0 for the soccer players), and then compute the correlation.
b. Square the value of the point-biserial correlation to verify that you obtain the same r2 value that was computed in Chapter 10.