Q-test TEST FOR OUTLIERS (non-parametric)											
											
	ug/l	sorted	Q								
1	14.27										
2	13.43										
3	14.25										
4	14.83										
5	14.64										
6	14.09										
7	15.19										
8	12.93										
9	13.94										
10	11.20										
	alpha=										
	range=										
	Qcrit=										
											
	H0…..										
##### Sheet/List 2 #####
Confidence interval				https://www.youtube.com/watch?v=cxUWQCwxQgk
for MEDIAN				
(non-parametric distributions)				
				
Find 95%-confidence interval of medians for both samples A and B:				
				
	species A	species B		
	16	34		
	32	36		
	37	38		
	39	45		
	40	50		
	41	54		
	42	56		
	50	59		
	82	69		
		91		
				
				
				
##### Sheet/List 3 #####
Wilcoxon signed-rank test										
FOR PAIRS (DEPENDENT SAMPLES)										
										
A new drug for blood pressure correction was tested on 9 patients.										
The pressure was measured before and after application.										
"Decide, if there is an effect of the drug!"										
										
										
										
	after	84	75	88	91	85	65	71	90	75
	before	97	72	93	110	95	78	69	115	75
										
	differences									
										
	abs									
										
	rank									
##### Sheet/List 4 #####
Mann-Whitney U-test													
"There were selected 11 fields of similar quality. On 5 randomly selected fields a new fertilizer was tested, the rest was kept without the fertilizer."													
"Yields of wheat obtained in August were: 5.1, 6.7, 5.6, 6.3, 5.9 t/ha and 4.5, 5.4, 4.8, 4.4, 5.3, 5.0 t/ha, resp. "													
"Find, if the fertilizer has an effect."													
													
													
fertilizer	no fertil.												
5.1	4.5												
6.7	5.4												
5.6	4.8												
6.3	4.4												
5.9	5.3												
	5.0												
													
													
													
													
													
													
													
													
													
													
													
													
													
													
													
													
##### Sheet/List 5 #####
Kruskal-Wallis test								
"In 3 samples of crude oils, Ni was determined by AAS. Decide (applying Kruskal-Wallis test), "								
if there is a significant difference among the samples.								
								
Sample								
1	14.2	16.8	19.1	15.5	16	15.9		
2	14.5	20	18	15.4	16.1	17.7		
3	18.3	20.1	17.7	17.9	19.3	16.9		
								
								alpha=0.05
##### Sheet/List 6 #####
NON-PARAMETRIC										PARAMETRIC				
	data	sorted	Q								data	sorted	G	
1	32.56	30.10	0.35	"< 0,526"						1	32.56	30.10	1.8745	"< 2,1266"
2	35.14	32.56								2	35.14	32.56		
3	34.10	33.33								3	34.10	33.33		
4	33.33	34.10								4	33.33	34.10		
5	37.10	34.45								5	37.10	34.45		
6	34.45	35.12								6	34.45	35.12		
7	35.12	35.14								7	35.12	35.14		
8	30.10	37.10	0.28	"< 0,526"						8	30.10	37.10	1.5008	"< 2,1266"
														
														
Q-test										Grubbs test				
	alpha:	0.05								mean:	33.9875			
	range:	7.00								stand. dev. (sample): 	2.0739			
	Qcritical:	0.526	OK							Gcritical: 	2.1266	OK		
														
	H0:	Accepted. There is no outlier present								H0:	Accepted. There is no outlier present			
														
														
														
Confidence interval estimation										 Student's confident interval				
	data	sorted									data	sorted		
1	32.56	30.10								1	32.56	30.10		
2	35.14	32.56								2	35.14	32.56		
3	34.10	33.33								3	34.10	33.33		
4	33.33	34.10								4	33.33	34.10		
5	37.10	34.45								5	37.10	34.45		
6	34.45	35.12								6	34.45	35.12		
7	35.12	35.14								7	35.12	35.14		
8	30.10	37.10								8	30.10	37.10		
														
										count = 	8			https://www.youtube.com/watch?v=MUD390jtgQs
count:	8									mean = 	33.99			
95% CI = 	"<30,10;35,14>"									stand. dev. (sample) = 	2.0739			
										v = 	n - 1 			
										v = 	 8 - 1			
										v = 	7			
										alpha/2 = 	0.025			
										tv;alpha/2 = 	2.3646			
														
										95% CI = 	mean +/- tv;alpha/2 * (stand. dev. (sample) / SQUARE(count))			
										95% CI = 	"33,99 +/-"	1.7338		
											32.254			
											35.721			
										95% CI = 	"<32,254;35,721>"			
														
														
														
Conclusion: 	In my opinion in this case is better Student's CI because it is more acuracy than CI estimation. Non-parametric is much more suitable when we don't know distribution data.