What significance test can I run on this data?

[Cinderblocks]

Hello,

i have 4 groups with a calculated weighted mean each. Groups were made from measured frequency of syndrome. One participant with said syndrome can be in more than one group. I want to compare if there is any significant difference between groups. What test can I run?
Thanks!

 

[fed2]

break off intersection into its own group. ie those in multiple groups are own group.

draw inference about original groups in terms of these new mutually exclusive groups via standard anova methods.

ie by writing a contrast:
a*Group a mean + b * intersection group + c*Group b mean == 0