Question

for some independent data using the mann whitney test

group a has rank sum of 97.5 with group size = 9
group b has a rank sum of 92.5 with a group size of 10
from the data table i have the two critical values for p=0.05 are 65 and 115

i know im supposed to compare them and decide whether there is a significant difference between them but im not sure which way round they go could you explain it please

thank you

Answer 1

The determination of the U-statistic in the Mann-Whitney U test is the smaller of the two values of group A and group B as calculated by the following:

U-statistic Group A = n1n2 + {[n1(n1 + 1)]/2} - R1
= (9)(10) + {[9(9 + 1)]/2} - 97.5
= 90 + 45 - 97.5
= 37.5

U-statistic Group A = n1n2 + {[n2(n2 + 1)]/2} - R2
= (9)(10) + {[10(10 + 1)]/2} - 92.5
= 90 + 55 - 92.5
= 52.5

Note: n1 = sample size of group A; n2 = sample size of group B; R1 = summed rank score of group A; R2 = summed rank score of Group B.

The smaller of the two values calculated is 37.5. The next step is to compare the observed value of U against the critical value of U. The observed value of U is statistically different if it is less than or equal to the critical U.

I'll let you take it from here to draw your final conclusion.

Answer 2

One correction: the second calculation should read as U-statistic Group B.