Question

Consider the two groups below that do not seem to come from a normal distribution.
Perform a Wilcoxon Rank Sum test to see if group 1 has greater values than (is shifted to the right of) group 2. Use α=0.05.

Group 1: 31, 37, 40, 42, 43, 43, 48

Group 2: 30, 35, 37, 38, 41, 42, 42

Answer 1

Group 1	Group 2	rank for sample 1	rank for sample 2
31	30	2	1
37	35	4.5	3
40	37	7	4.5
42	38	10	6
43	41	12.5	8
43	42	12.5	10
48	42	14	10

Group 1   
sample size ,    n1 =    7      
sum of ranks ,    R1 =    62.5      
              
Group 2
sample size ,    n2 =    7      
sum of ranks ,   R2 =    42.5      
              
W=sum of ranks for smaller sample size =       62.5      
              
mean ,µ =    n1(n1+n2+1)/2 =    52.5      
              
std dev,σ =    √(n1*n2*(n1+n2+1)/12) =   7.8262      
              
Z-stat =    (W - µ)/σ =    1.2778      
              
Z*, Z critical value =        -2.326      
              
P-value =        0.1007      
Conclusion:         P-value>α , Do not reject null hypothesis      

Hence group 1 has not greater values than group 2

Please let me know in case of any doubt.

Thanks in advance!

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