Mann-Whitney and Wilcoxon tests table
  • The U statistic is simple (but tedious) to calculate. For each case in group 1, the number of cases in group 2 with higher ranks is counted. Tied ranks count as 1/2. This process is repeated for group 2. The Mann-Whitney U statistic displayed in the table is the smaller of these two values.
  • The Wilcoxon W statistic is simply the smaller of the two rank sums displayed for each group in the rank table. The values displayed here are the rank sums for the treatment group.
  • A nice feature of the Mann-Whitney and Wilcoxon tests is that the Z statistic and normal distribution provide an excellent approximation as the sample size grows beyond 10 in either group. The negative Z statistics indicate that the rank sums are lower than their expected values.
  • Each two-tailed significance value estimates the probability of obtaining a Z statistic as or more extreme (in absolute value) as the one displayed, if there truly is no effect of the treatment.

The significantly lower rank sums of the treatment group indicate to the physicians that the additional emotional therapy had some beneficial effect on such activities of daily life as cooking and cleaning.