Spearman correlation - admission															
															
"During the admission procedure, the evaluation was performed by commissions and by a special program. "															
"Based on the ranking of the ten students, decide whether both assessments are dependent."															
															
	Student	A	B	C	D	E	F	G	H	I	J				
	commission grade	4	6	1	5	10	2	7	3	9	8				
	program grade	1	3	5	7	8	4	6	2	10	9				
	difference														
	difference squared														
															
															
H0….correlation between the two grading =0															
H1….correlation between the two grading <>0															
##### Sheet/List 2 #####
														
Test1	Test2 		You are given test results (points) from two subjects of 8 randomly selected students.											
80	65		Determine the correlation of a linear dependence of these results by the Spearman and Pearson coefficients.											
50	60													
36	35													
58	39													
72	48													
60	44													
56	48													
68	61													
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
##### Sheet/List 3 #####
Data displays the association between the IQ of 10 adolescent in a sample with the number of hours they listen to rock music per month.														
Determine the strength of the correlation between IQ and rock music using both the Pearson’s correlation coefficient and Spearman’s rank correlation. Compare the results.														
														
														
IQ	Rock m.		rank IQ	rank rock	d									
99	2													
120	0													
98	25													
102	45													
123	14													
105	20													
85	15													
110	19													
117	22													
90	4													
														
														
														
##### Sheet/List 4 #####
Example: Ice Cream Sales								
								
The local ice cream shop keeps track of how much ice cream they sell versus the temperature of that day for the last 12 days:								
Formulate a null hypothesis and verify it by Pearsons and Spearman coefficients								
								H0= There is no correlation between the amount of icecream sold and the temperature outside.
								H0= There is a correlation.
								
								
	Temperature (°C)	Ice Cream Sales ($)		rank t	rank sales	d		
	14.2	215		11	11	0		
	16.4	325		9	10	-1		
	11.9	185		12	12	0		
	15.2	332		10	9	1		
	18.5	406		6	8	-2		
	22.1	522		4	3	1		
	19.4	412		5	6	-1		
	25.1	614		1	1	0		
	23.4	544		2	2	0		
	18.1	421		7	5	2		
	22.6	445		3	4	-1		
	17.2	408		8	7	1		
						14	sum squared	
						0.951048951	.=rs	
								
						"crit(0,05)="	0.587	
						The calculated value is larger than critical value.		
						"The null hypothesis is rejected. Therefore, there is a colleration."		
								
	average							
	18.7	402.4						
								
	differences		dx*dy					
	-4.5	-187.4	838.69					
	-2.3	-77.4	176.12					
	-6.8	-217.4	1473.00					
	-3.5	-70.4	244.70					
	-0.2	3.6	-0.63					
	3.4	119.6	409.57					
	0.7	9.6	6.95					
	6.4	211.6	1359.42					
	4.7	141.6	668.98					
	-0.6	18.6	-10.69					
	3.9	42.6	167.14					
	-1.5	5.6	-8.24					
								
	177.0	174754.9	5325.03		r=	0.957506623		
					d.o.f.=	10		
					alpha=	0.05		
					critical=	0.576		
								
					The calculated value is above the critical one.			
					"Therefore, the null hypothesis is rejected. There is a correlation."