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

Sure! In order to determine whether there is a significant difference between the two groups (Group A and Group B), you need to compare the calculated rank sum values with the critical values.

First, let's understand what a rank sum is. The rank sum is a statistic used in the Mann-Whitney U test. It represents the sum of the ranks assigned to the observations in each group. In your case, Group A has a rank sum of 97.5, and Group B has a rank sum of 92.5.

To interpret the results:

1. Look at the critical values: For a given significance level (in this case, p=0.05), you have two critical values available: 65 and 115.

2. Compare the calculated rank sums with the critical values:
- If the calculated rank sum value is less than the smaller critical value, it means the difference between the two groups is considered significant at the given significance level (p=0.05).
- If the calculated rank sum value is greater than the larger critical value, it means the difference between the two groups is not considered significant.

In your case:
- Group A rank sum = 97.5, Group B rank sum = 92.5
- Critical values: 65 and 115

Since the calculated rank sums (97.5 and 92.5) are both greater than the smaller critical value (65), it means that there is no significant difference between the two groups at a significance level of 0.05. In other words, the difference in rank sums falls within the range of values expected under the null hypothesis, indicating that the two groups are not significantly different from each other.

Remember that these conclusions are based on a p-value threshold of 0.05, which is commonly used in statistical analysis. If you had chosen a different significance level (e.g., p=0.01 or p=0.10), you would have different critical values to compare with your rank sums.