Mann-Whitney U test

1. Mixing and sorting.
2. Ranking;
   1. Each element names es a rank corresponding to its position in the list. Element whihc have the same value receive the same rank:
3. Compute rank sums Ra, Rb
   1. Like this.
   2. For these sums, the following always holds:
4. Compute Sample statistics UA, UB
   1. Like this.
   2. Where the following always holds: UA + UB = nanb ------> 7 + 41 = 6*8 = 48
5. Set u = min {UA, UB}
   1. U = min {UA, UB }= min {7, 41} = 7
6. Compute critical U α Values
   1. For the significant level α the critical U α value s can be computed for the two-sided test:
   2. Where Z is the "probity" function, the inverse cumulative distribution function of the standard normal distribution.
   3. The value of Z can be looked up in the standard normal distribution table appendix.
7. U <u α => different between UA and UB significant
   1. The different between UA and UB is significant at an error level A only if u is smaller than UA.
   2. If u <UA, and UA <UB: A is from a distribution with a smaller median than B (this is wrong with a probability of no more than)
   4. For this example:

 

Mann-Whitney U test