Question

Perform rank correlation analysis on the following data set:

x	y
-4	3.7
-3	2.8
-2.3	3.3
-1.55	1.7
-0.6	0.6
0.4	1.2
1.25	1.8
2	1.2
2.95	2.7
3.9	4.4
4.85	5.7

What is the rank correlation coefficient?  (Round to three decimal places.)

What is the critical rho value at a 0.01 significance?

Do we have correlation?

• Yes, the rank correlation coefficient is larger (in absolute value) than the critical rho value.
• No, the rank correlation coefficient is smaller (in absolute value) than the critical rho value.
• Yes, the rank correlation coefficient is smaller (in absolute value) than the critical rho value.
• No, the rank correlation coefficient is larger (in absolute value) than the critical rho value.

Answer 1

 > x = c(-4,-3,-2.3,-1.55,-0.6,0.4,1.25,2,2.95,3.9,4.85) > y = c(3.7,2.8,3.3,1.7,0.6,1.2,1.8,1.2,2.7,4.4,5.7) > #correlation test > cor.test(x,y, method = "spearman",conf.level = 0.99)     Spearman's rank correlation rho data: x and y S = 185.92, p-value = 0.6493 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.1548979 

The rank correlation coefficient is 0.155

the critical value at 0.01 significance is 0.765

since p-value is 0.6493 >0.01 so, we have correlation in data

Yes, the rank correlation coefficient is smaller (in absolute value) than the critical rho value