Example on the Wilcoxon Rank Sum Test

Researchers sampled private and public sector organizations in Australia to study the planning undertaken by their information systems departments. As part of that process they asked each sample organization how much it had spent on information systems and technology in the previous fiscal year as a percentage of the organization's total revenues. The results are reported below.

  Private Sector (%)                      Public Sector (%)
  ------------------                      -----------------

    2.58                                        5.40

    5.05                                        2.55

    0.05                                        9.00 

    6.10                                       10.55

    4.30                                        1.02 

    2.25                                        5.11 

    2.50                                       12.42 

    1.94                                        1.67 

    2.33                                        3.33

Do the two sampled populations have identical probability distributions or is the distribution for public sector organizations in Australia located to the right of Australia's private sector firms? Test at $\alpha = 0.05$.

NOTE: To confuse us, Minitab calls this a Mann-Whitney test.

Mann-Whitney Test and CI: Private, Public

Private    N =   9     Median =       2.500
Public     N =   9     Median =       5.110
Point estimate for ETA1-ETA2 is      -2.500
95.8 Percent CI for ETA1-ETA2 is (-6.670,0.921)
W = 70.0
Test of ETA1 = ETA2  vs  ETA1 < ETA2 is significant at 0.0927

Cannot reject at alpha = 0.05