Assuming you have a set of data containing two groups, for example height of people, knowing that there are men and women, you can show that the groups differ in average height without knowing which height corresponds to which gender.
For example, having the data of n heights like (175cm, 178cm, 180cm, 182cm) instead of (female 175cm, male 178cm, female 180cm, male 182cm).
Is there a difference in the statistical confidence you can have in that the two groups differ in average height if you have the info on which height belongs to a female / male and if you don't?
EDIT: It's presumably necessary to have some assumption on how the heights within a group are distributed. A gaussian distribution is probably sufficient here.
