Question

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA. Extracurricular Activity College Freshman GPA Yes 3.49 Yes 3.35 Yes 3.91 Yes 3.68 No 2.93 No 3.86 No 3.39 No 2.76 No 3.86 No 2.83

(a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)

Answer 1

First converting yes to 1 and no to 0 we get,

	x	y	(x-xbar)^2	(y-y bar)^2	(x-xbar)(y-y bar)
	1	3.49	0.36	0.007056	0.0504
	1	3.35	0.36	0.003136	-0.0336
	1	3.91	0.36	0.254016	0.3024
	1	3.68	0.36	0.075076	0.1644
	0	2.93	0.16	0.226576	0.1904
	0	3.86	0.16	0.206116	-0.1816
	0	3.39	0.16	0.000256	0.0064
	0	2.76	0.16	0.417316	0.2584
	0	3.86	0.16	0.206116	-0.1816
	0	2.83	0.16	0.331776	0.2304
Total	4	34.06	2.4	1.72744	0.806
Mean	0.4	3.406	ssx	ssy	sxy
			0.395848

The point biserial correlation coefficient =0.396

Please do the comment for any doubt or clarrification.