Question

An anthropologist records the heights (in inches) of ten fathers and their sons. Use the Spearman rank correlation test to analyze the results.

Heights

Son's Height	Father's Height
64	64
57	66
52	79
50	78
41	77
40	90
66	81
78	80
58	61
56	82

Step 1 of 2:

Find the value of the correlation coefficient to test for an association between the heights of the fathers and the heights of their sons. Round your answer to four decimal places, if necessary.

Answer 1

( X)	( Y)	X^2	Y^2	X*Y
64	64	4096	4096	4096
57	66	3249	4356	3762
52	79	2704	6241	4108
50	78	2500	6084	3900
41	77	1681	5929	3157
40	90	1600	8100	3600
66	81	4356	6561	5346
78	80	6084	6400	6240
58	61	3364	3721	3538
56	82	3136	6724	4592

calculation procedure for correlation

sum of (x) = 562

sum of (y) = 758

sum of (x^2) = 32770

sum of (y^2) = 58212

sum of (x*y) = 42339

to calculate value of r( x,y) = co variance ( x,y ) / sd (x) * sd (y)

co variance ( x,y ) = [ sum (x*y - N *(sum (x/N) * (sum (y/N) ]/n-1

= 42339 - [ 10 * (562/10) * (758/10) ]/10- 1

= -26.06

and now to calculate r( x,y) = -26.06/ (SQRT(1/10*42339-(1/10*562)^2) ) * ( SQRT(1/10*42339-(1/10*758)^2)

=-26.06 / (10.8885*8.6925)

=-0.2753

value of correlation is =-0.2753

coefficient of determination = r^2 = 0.0758

properties of correlation

1. If r = 1 Correlation is called Perfect Positive Correlation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = -0.2753< 0, negative correlation