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
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.
One correction: the second calculation should read as U-statistic Group B.
Certainly! In order to determine whether there is a significant difference between two groups using the Mann-Whitney test, we compare the rank sums of the two groups with critical values.
In your case, group A has a rank sum of 97.5 and group B has a rank sum of 92.5. The critical values for p=0.05 are given as 65 and 115.
To interpret these values, we need to compare the rank sums with the critical values. If the rank sum of a group is lower than the lower critical value, it means that the group's ranks significantly differ from the ranks of the other group. On the other hand, if the rank sum is higher than the upper critical value, there is no significant difference between the groups.
In your example, let's compare the rank sums of both groups with the given critical values:
- Group A has a rank sum of 97.5. Comparing it with the critical values: 97.5 > 65 and 97.5 < 115. Since the rank sum of Group A is higher than the lower critical value of 65, and lower than the upper critical value of 115, there is no significant difference between Group A and Group B.
- Group B has a rank sum of 92.5. Comparing it with the critical values: 92.5 > 65 and 92.5 < 115. Since the rank sum of Group B is also higher than the lower critical value of 65, and lower than the upper critical value of 115, there is no significant difference between Group B and Group A.
Therefore, based on the comparison of rank sums with the critical values, we can conclude that there is no significant difference between Group A and Group B in your data.