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 number of ice cream sell and the temperature
						
				Spearman	we accept	H1 there is a correlation between the number of ice cream sell and the temperature
	Temperature (°C)	Ice Cream Sales ($)		Rank T°	Rank ice cream	differnce 
	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
	N	12			rs	0.951048951
	N^3	1728			Critical value	0.587
	Pearsons 					
averarge	18.7	402.4166667				
			dx*dy			
	-4.5	-187.4166667	838.6895833			
	-2.3	-77.41666667	176.1229167			
	-6.8	-217.4166667	1472.997917			
	-3.5	-70.41666667	244.6979167			
	-0.2	3.583333333	-0.627083333			
	3.4	119.5833333	409.5729167			
	0.7	9.583333333	6.947916667			
	6.4	211.5833333	1359.422917			
	4.7	141.5833333	668.98125			
	-0.6	18.58333333	-10.68541667			
	3.9	42.58333333	167.1395833			
	-1.5	5.583333333	-8.235416667			
	-18.7	-402.4166667	7515.13125			
						
	525.7	336694.0903	12840.15625			
						
r	0.965090023					
d.f	0.576