Question

Use the Spearman's rank correlation coefficient at the 0.05 CI to investigate the relation between two variables X and Y below.

X	Y
97	0
93	0
90	1
86	1
82	0
177	4
171	1
155	3
142	1
141	1
60	4
55	1
29	0
26	0
20	0
12	0
133	1
126	0
125	4
123	1
119	1
117	2

Answer 1

X	Rank(X)	Y	Rank(Y)
97	11	0	4.5
93	10	0	4.5
90	9	1	13
86	8	1	13
82	7	0	4.5
177	22	4	21
171	21	1	13
155	20	3	19
142	19	1	13
141	18	1	13
60	6	4	21
55	5	1	13
29	4	0	4.5
26	3	0	4.5
20	2	0	4.5
12	1	0	4.5
133	17	1	13
126	16	0	4.5
125	15	4	21
123	14	1	13
119	13	1	13
117	12	2	18

	Rank(X)	Rank(Y)	Rank(X)*Rank(Y)	Rank(X)2	Rank(Y)2
	11	4.5	49.5	121	20.25
	10	4.5	45	100	20.25
	9	13	117	81	169
	8	13	104	64	169
	7	4.5	31.5	49	20.25
	22	21	462	484	441
	21	13	273	441	169
	20	19	380	400	361
	19	13	247	361	169
	18	13	234	324	169
	6	21	126	36	441
	5	13	65	25	169
	4	4.5	18	16	20.25
	3	4.5	13.5	9	20.25
	2	4.5	9	4	20.25
	1	4.5	4.5	1	20.25
	17	13	221	289	169
	16	4.5	72	256	20.25
	15	21	315	225	441
	14	13	182	196	169
	13	13	169	169	169
	12	18	216	144	324
Sum =	253	253	3354	3795	3691

Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero.