How to tell if the “clusters” I see in my pair plots are statistically significant or occurring by random chance? I have a data set with one row per subject. Some variables include laboratory parameters for blood chemistry, hematology, etc. I also have some flag variables: any = 1 if the subject experienced an adverse event, 0 if not; and ser_flag = 1 if the subject experienced a serious adverse event, 0 if not.

There doesn't seem to be any difference in the distribution of laboratory parameters between subjects who experienced an adverse event (any=1) and subjects who did not (any = 0). When I do a pair plot of all the lab parameters against each other and color by the any flag, there doesn't seem to be any clustering or separation of subjects.

However, when I do the same pair plot and color by ser_flag - I notice that the 20 subjects who experienced a serious adverse events seem to be clustered together in many of the plots.

What test (if any) can I use to determine if these clusters I think I am seeing are occurring randomly, by chance...or if they statistically significant?
The easiest test is equality of means of two distributions. Student's t-test