How to prove that a ranked list have more items from category A than B?

#1
Hi

I have a ranked list of 50 items, that consists of items that either belong to category A or B. Is there a way/test to prove with some significance that:
1- The list have more items of category A
2- Category A items got higher rank than category B

Many thanks
 

hlsmith

Omega Contributor
#2
So for every item (50), the response could be either A or B. Given this you have a list of 50 responses of either As and/or Bs, now you want to prove there are more As.

Unclear where the ranking comes into play, is it just a ranking of A or B, or do these values get ranked as well. May help to present an example item.
 
#3
For example , group of 100 student from school A and B compete in different sports. From 100 we will select the top 50 students.
1- We want to see which school ( A or B) achieved more medals
2- Which school was ranked higher in terms of the medals

Example
Student - Medal - School
1 - 20 - A
2- 18 - B
3- 17 - A
4- 12 - B
...
 
#5
The Wilcoxon rank sum test talks about 2 groups that I can't figure out

In case of 6 rankings
1- A
2- B
3- A
4- A
5- B
6- B

A is in more top rankings than B, how Wilcoxon rank sum test or other test prove that?