The two-tailed probability is therefore: 8/70 = 0.114.

Notice that this probability value is slightly higher than the 0.0857 obtained with the randomization test for these same data. This rank randomization test for differences between two groups has several names. It is most often called the Mann-Whitney U test or the Wilcoxon Rank Sum test. In practice, tables are available to look up the probability value based on the sum of the ranks of the group with the lower mean rank. For these data, the sum of the ranks is: 2+6+1+3 =12. A table would show that for a one-tailed test to be significant at the 0.05 level, the sum of the ranks must be ≤ 11. Since 12>11, the test is not significant at this level. This agrees with the calculated probability value of 0.057. The purpose of this section is to present the concepts rather than the details of the computations. Therefore, if you wish to actually perform this test, you should find a textbook with appropriate tables. An online table and further discussion can be found here.